\r\n\tNotably, the book encourages academic scholars and researchers to contribute to the modern concepts of CSR. Fundamentally, it speaks for well-developed literature for entrepreneurs and managers, thus assisting them in the decision-making process. \r\n\tFurthermore, this book is of great value to policymakers, practitioners, and corporations, thus contributing to various disciplines (e.g., social science and management). \r\n\tThese proposed themes encourage future researchers and professionals to share their ideas, concepts and work concerning these subject domains. All these suggested topics had recommended under the rubrics of CSR. Perhaps, all the professionals, researchers, and scholars are welcome to submit their piece of work, in particular to the suggested topics. \r\n\tIndeed, the recommended topics include the following but are not limited to these only. \r\n\t• Corporate Governance and Sustainability \r\n\t• Green Innovation and CSR \r\n\t• Social Entrepreneurship \r\n\t• Green Economy and Social and Environmental Sustainability \r\n\t• Sustainable Development and Industrialization
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1. Introduction
Gliomas are primary tumors of the central nervous system. They are derived from glial cells. They are the most common cause of solid tumors in the intracranial space in children [1]. Nearly 70,000 new cases of malignant primary and benign brain tumors of the central nervous system (CNS) are diagnosed in the United States each year. Of these, approximately 28% are gliomas, and 36% are meningiomas. Gliomas represent 80% of the primary malignant brain tumors. The incidence rates of brain tumors have increased in the last three decades. For all CNS tumors, of which brain tumors account for approximately 88%, the average annual incidence rate adjusted for age (2006 to 2010) for women (22.8 per 100,000) is higher than for men (19.1 per 100,000) [1, 2].
According to the World Health Organization (WHO) classification of brain tumors, they are divided into gliomas of the low and high degree of malignancy. Low-grade gliomas - I and II, are represented by pilocytic astrocytoma, diffuse glioma, and gemistocytic astrocytoma. They have a benign clinical course with a long survival time. High-grade gliomas, anaplastic astrocytoma (grade III) and glioblastoma multiforme (grade IV), are characterized by a rapid growth rate, extensive white matter infiltration, and poor short-term prognosis [3, 4]. Therefore, the histopathological diagnosis and its proper classification are crucial for treating patients. Diffuse astrocytoma (WHO grade II) is characterized by slow growth and infiltration of neighboring brain structures Figure 1 [5, 6, 7].
Figure 1.
Intraoperative cerebral edema during emergency surgery in a patient with neurological deterioration secondary to a brain tumor bleeding.
In pediatric patients, the central nervous system’s tumors represent the second cause of cancer mortality after leukemia. The magnetic resonance imaging technique renders the integration of different structural images (FLAIR, diffusion, perfusion, SPGR, TRUFFI), functional aspects (DTI, BOLD), and metabolic profile (spectroscopy). They evaluated peritumoral edema by diffusion and perfusion sequences [8, 9]. The use of sequences that provide functional information allows the early identification of the risks associated with neurosurgical treatment and each case’s functional prognosis [10]. Some reports show a characteristic uptake pattern for the degree of malignancy of different neoplasms. In the case of primary tumors of the CNS, significant alterations can be observed in the uptake of glucose, methionine, and tyrosine. One of the technological resources that have changed the treatment of patients with CNS neoplasms is neuronavigation.
2. Characteristics of Magnetic Resonance Imaging Studies for Neuronavigation
The radiological evaluation of brain tumors makes it possible to identify the structural, functional, and metabolic characteristics of neoplastic lesions and, for prognostic purposes, their relationship with healthy brain tissue by combining diverse image acquisition techniques.
The MRI imaging modalities currently used in presurgical planning for brain tumor resection are functional magnetic resonance imaging (fMRI), diffusion tensioner (DTI) imaging, diffusion tension tractography, and BOLD [2].
2.1 Diffusion Tensor Images (DTI)
The diffusion tensor images allow the visualization and characterization of white matter tracts [11, 12, 13]. DTI images have been used to study the architecture of white matter and the integrity of normal and diseased brains. This magnetic resonance technique is based on the general principle that the anatomical microstructure directs water diffusion, being an echo-planar technique that maps the diffusion speed [14]. In brain tissue, diffusion rates are slower due to the typical parenchyma components that impede water movement. In specific pathological processes, water diffusion is restricted, which reduces the apparent diffusion coefficient (ADC), as in acute infarcts secondary to cytotoxic edema, abscess, lymphoma [12, 15]. Fiber tracking is the only non-invasive method to visualize the course, displacement, or interruption of white matter’s main tracts according to the DTI technique. Multiple studies have shown that fiber tracking can reconstruct white matter’s major fiber structures in the brain. Identifying the tracts is done by defining a rectangular interest volume (VOI) in the registered standard T1 anatomical datasets. A fast acquisition gradient echo sequence prepared with 3D magnetization weighted in T1 is used to acquire the images. T2-weighted images are acquired, inversion recovery images attenuated by T2 fluid, and 3D images weighted in T1 postcontrast are scanned. Intraoperative examinations are performed immediately when the operator considers that the lesion has been resected or intraoperative exploration was necessary to correct the cerebral displacement. For DTI, applies a sequence of echo-planar images weighted by spin-echo diffusion of a single shot (echo time, 147 milliseconds, repetition time, 9400 milliseconds, matrix size, 128 × 128, the field of view, 251 × 251 mm, the thickness of cut, 3 mm, bandwidth, 1502 Hz per pixel, diffusion encoding gradients in 12 directions with b values of 0 and 1000 s/mm2, and voxel size, 1.9 × 1.9 × 3 mm) [12, 13, 16]. The 3D segmental reconstruction of the tumor is performed based on the high-resolution 3D postcontrast anatomical data set.
In the case of tumors with high uptake of contrast medium - glioblastoma multiforme, metastasis, the edge of the outermost lesion that enhances post-contrast, for example, glioblastoma, and the edge of hyperintensity or mixed hypointensity in the lesion, such as the non-malignant entity, cavernoma, represented the limit of segmentation. In non-enhancing lesions such as low-grade glioma, the T2-weighted image is used to determine the tumor’s edge. For this reason, most tumors that do not have post-contrast enhancement have optimal visibility in this sequence. The existence of significant edema, which cannot be clearly distinguished from the low-grade glioma, was ruled out based on the findings of inversion recovery images with T2 fluid. The segmentation of the tumor is performed by cutting in a mode of 3D anatomical data. After profiling all the sections that contained the lesion, the three-dimensional reconstruction of the lesion was performed [13].
The techniques of DTI and tractography have overcome this obstacle and are now widely used to study the white matter in vivo. Diffusion images calculate the local direction of white matter from water diffusion measurements. Tractography takes this a step further to evaluate the functional connection between several different areas inside the same or contralateral hemisphere. The identification of water molecule’s movement in all directions is known as isotropic diffusion. In the central nervous system, anisotropic diffusion is used to define water’s movement in a parallel sense in the withe matter tracts defined by axons’ groups. Thus, creating maps of movement of water that define the structure and orientation of with matter tracts [2, 3].
Three-dimensional visualization of white substance fibers, such as the corticospinal (pyramidal) tract, corpus callosum, cerebellar peduncles, optical radiation, and arcuate fascicle, is of great value at the preoperative evaluation and intraoperative navigation Figure 2 [4].
Figure 2.
3D reconstructions for white matter tracts with DTI-MRI technique. (A) Thalamic high-grade glioma and his relationship with the pyramidal tract. (B) Parasagittal meningioma and its relationship with corpus callosum and pyramidal tract. (C) Supratentorial Ependymoma and its relations with Corpus callosum. (D) Fourth ventricle tumor and middle cerebellar peduncle displacement.
2.2 Perfusion
There are three main techniques for perfusion imaging: T2 * enhanced dynamic magnetic susceptibility enhanced perfusion in T1-enhanced dynamic contrast, and arterial spin marking techniques, involving repetitive serial images through the tumor during blood passage been marked with contrast material. Theoretically, the degree of a signal drop is proportional to the concentration of gadolinium in the tissue, obtaining relative curves of concentration - time. Dynamic contrast images weighted in T1, where the main focus is estimating tumor permeability, allow the contrast to filter into the extravascular space and reach equilibrium during multiple contrast bolus passes through the tumor bed. An arterial spin is a form of perfusion without the use of intravenous contrast; a powerful magnetic gradient is applied to the blood inlet to reverse the magnetization, effectively labeling the blood that flows upward, have impeded its application for long periods of imaging and decrease in spatial resolution compared to gadolinium [16]. Different types of tumors and grades differ in their perfusion characteristics. For example, there is a strong correlation between the degree of astrocytoma and the relative measurements of cerebral blood volume (CBV) [17]. However, low-grade astrocytomas tend to have a high cerebral blood volume, associated with the process of angiogenesis and dense capillary networks that characterize these tumors.
2.3 Magnetic resonance spectroscopy
It provides an analysis of the different metabolites in a delimited area within the brain and may be useful in the initial diagnosis of brain tumors. It can be done with a single voxel technique, in which a single spectrum is produced for a tissue volume, or a multivoxel technique, in which a greater volume of tissue is evaluated [18]. The primary metabolites evaluated include N-acetyl aspartate (NAA) (typical neuronal marker), choline (cell membrane marker), creatine (energy marker), lactate (metabolic acidosis), and lipids (tissue breakdown and cell death). The spectral patterns of intracranial neoplasms vary significantly due to differences in tumor types and grades. However, most CNS tumors manifest with elevated choline-creatine and co-NAA ratios caused by increases in cellularity (choline elevation) and a relative decrease in normal neurons (reduction of NAA).
2.4 Functional MRI Images
Functional MRI (fMRI) mapping of eloquent language cortex in patients with brain tumors after surgery is feasible and may serve as a useful reference assessment for preoperative neurosurgical planning [19].
Functional magnetic resonance imaging (MR) is an advanced tool for studying brain functions in healthy subjects and neuropsychiatric patients, identifying and locating specific metabolism and neural activity phenomena [20].
BOLD is a measure of changes in oxygenated and deoxygenated blood proportion during a particular paradigm’s execution. The most commonly mapped functions during functional MRI studies include motor, auditory, somatosensory, visual perception, and language production and comprehension. When evaluating motor centers, typical tasks include tapping with fingers, pouting with lips, and flexing and extending toes [21]. Patients with mild to severe motor paresis of the hand may clench their fists instead of tapping with their fingers.
Several reports mention that a silent area around a brain tumor could recover his eloquence after the surgical resection of malignant tissue [22]. There is a latency of several seconds in the signal change observed in BOLD images, making the temporal resolution of functional MRI poor compared to other techniques such as DES or electroencephalography [23]. Because of the “delay of hemodynamic response” given the time required for the production and diffusion of vascular signal substances to dilate the vascular bed and cause a deoxygenated hemoglobin wash. Another consideration is that BOLD fMRI does not directly measure neural activity but changes in the region’s hemodynamic properties. So, the variability between functional localization among subjects may result from physiological differences in the BOLD signal without differences in neuronal activity per se. It has been found that several pharmacological agents may influence the BOLD signal [24].
2.5 The utility of fMRI and DTI in presurgical planning
The use of fMRI in conjunction with DTI for presurgical planning is currently the most established clinical application of these neuroimaging techniques. The aim is to provide the surgeon with functional information about the tumor’s area and its connections to adjacent areas. The regions of interest can be defined anatomically. However, the advance of functional imaging techniques allows us to define white matter tracts more precisely. Some reports mention that it is reliable in healthy ones but maybe inaccurate in those who harbor brain injuries Figure 3 [21].
Figure 3.
The utility of fMRI and tractography for surgical planning. An 8-years-old boy presents at the emergency unit with a history of intermittent language disturbances and right-hemiparesis. fMRI (language paradigm) and DTI (Pyramidal tract, Corpus callous, Arcuate fascicle) images were performed. A 3D reconstruction at the Brainlab neuronavigation station was performed. (A) Pyramidal tract reconstruction and his relationship with a neoplastic lesion (Yellow) and language areas visualized with fMRI (Red). (B) Arcuate fascicle reconstruction and language areas and their relation to the neoplastic lesion. (C) 3D reconstruction of arcuate fascicle (Yellow), language areas (Red), and neoplastic lesion (Cyan).
3. Nuclear medicine for imaging brain tumors
In Mexico, PET positron emission tomography equipment began with opening the PET-Cyclotron Unit of the National Autonomous University of Mexico in 2002. We use nuclear medicine to determine the degree of malignancy of the lesions, evaluate the response to treatment, identify early recurrence, and radiotherapy planning.
By obtaining functional information of cellular and biological processes like glucose metabolism, protein synthesis, the PET with 18 fluoro-deoxy-glucose (FDG) PET was initially used to detect and distinguish tumors of a low and high degree of malignancy. 18 Fluoro-ethyl-tyrosine (18 F FET) evaluates the metabolism of amino acids. It provides well-contrasted images in both high and low-grade tumors. It is beneficial to take biopsies guided by image to establish a primary brain tumor diagnosis in the planning of radiotherapy treatments and distinguish between tumor recurrence or radionecrosis after initial therapy Figure 4 [4].
Figure 4.
MRI and PET/CT 18F -FET fusion for brain tumor recurrence resection.
It has a sensitivity of 94% and specificity of 88% for the diagnosis of brain tumors. Although the 18-FDG and 18-FET quantitative parameters allow the distinction between low and high-grade tumors, only the 18-F FET values can distinguish between tumor and non-tumor lesions, confirming the superiority of 18-F FET over 18 FDG for the characterization of brain lesions. Since 18-FDG is unreliable for predicting the neoplastic nature due to absorption by inflammatory lesions, amino acid tracers such as FET have been developed in recent decades to increase specificity. However, to date, only a few studies limited to small population of patients compared the diagnostic value of 18-FDG and 18-FET. Goldman and Pirotte thoroughly reviewed the clinical management, images, and PET role [25].
On average, glioblastoma multiforme and medulloblastoma had a uniform and intense uptake throughout the tumor, while brainstem gliomas had a low uptake in less than 50% of the tumor and ependymoma had a low uptake throughout the tumor. When more than 50% of the tumor had uptake, the apparent diffusion coefficient was lower, which agrees with the increase in cellularity. In refractory/recurrent brain gliomas, the low correlation between uptake and enhancement is associated with decreased patient survival. It may reflect concurrent tissue degradation in the disease sites that received treatment and the development of new malignancy sites characterized by increased uptake of 18-F-FDG [26, 27].
The PET/MRI fusion tool in evaluating postoperative and radiooncological treatments provides information for tumor response, progression, and necrosis by radiation, affording the patients’ oncological and functional prognosis Figure 5.
Figure 5.
The utility of Multimodal Neuronavigation for brain tumor resection. A 15-years-old girl was received with a history of left hemiparesis and tonic–clonic seizures. MRI was performed, and a low-grade glioma was suspected. DTI sequences were obtained. A PET-CT 18F-FET was obtained, and fusion with structural and DTI images was performed at the Brainlab workstation. (A) Structural MRI, 18F-FET PET-CT, and DTI for pyramidal tract were fused during neuronavigation planning. (B) Right, Transoperative 3D ultrasonographic images were obtained and fused with the previous neuronavigational plan. Left, Histopathological analysis reveals a diffuse glioma. (C) At 48 months of follow-up, a new 18F-FET PET-CT was performed, no metabolic activity was detected.
4. Neuronavigation principles
Neuronavigation systems provide intraoperative guidance to the surgeon. Nevertheless, its real advantage is also to help them plan a proper surgical approach to avoid injury and incorporates functional data provided by preoperative images of magnetic resonance imaging, nuclear medicine, intraoperative sonographic studies, and in some places, magnetoencephalography (MEG) to prevent damage to eloquent areas during brain surgery [1].
Image-guided neuronavigation uses the principle of stereotaxy. The brain is considered a geometric entity divided into three imaginary spatial planes that intersect, orthogonal to each other (axial, coronal, and sagittal). Theoretically, any point within the brain is designated by a specific series of coordinates in each plane.
Neuronavigation platforms provide the unique opportunity to translate the two-dimensional information obtained from several imaging techniques – CT scan, MRI, fMRI, PET-CT, into 3D information in the patient’s brain of a computational interface at the operating room [16]. The predefined targets on the navigational plan increase the chance to perform a safe and functional gross total resection of malignant primary brain tumors.
Its main objective is to facilitate the extensive resection of the lesion, minimize the risk of neurological sequelae, and favor the prognosis of survival. After registering the patient, the system’s accuracy is checked by identifying constant anatomical references or craniometric points. The contour of the lesion and the functional data are fused on the reference structures. In some cases, it is possible to transfer the images to the surgical microscope’s eyepieces during surgery.
The intraoperative accuracy of neuronavigation can be affected by changes in intracranial volume caused by tumor resection, brain inflammation, and cerebrospinal fluid flow Figure 1. Nevertheless, transoperative images can be combined with ultrasound, tomography, or magnetic resonance images. The intraoperative images offer the possibility of evaluating the residual tumor volume as the surgery progresses Figure 6.
Figure 6.
3D intraoperative ultrasonographic reconstruction increases the usefulness of multimodal neuronavigation for brain tumor resection. A 17-years-old boy with a history of neurofibromatosis type 1 arrives at the emergency department with a headache and left hemiparesis. On an MRI study, a glioblastoma multiforme was suspected. (A) MRI T1-enhanced Gd images acquired for surgery planning at (B) Brainlab workstation. (C) 3D ultrasonographic acquisition to fusion with predefined neuronavigation’s plan to achieve a gross total resection. (D) Immediate postoperative CT Scan.
4.1 DTI and fMRI in functional neuronavigation
Neuronavigation is currently applied in brain surgery, and it is a regular technological resource to increase safety in most neurosurgical procedures (27).
The functional navigation was described as a technological tool for brain tumor resection. It results from the merging of structural, DTI, and BOLD information concerning a malignant tumor’s localization. It allows us to know the precise location of functional areas in the human brain [28].
Clinical articles have suggested that the brain shift observed after the opening of the dura and cerebrospinal fluid depletion is the main disadvantage for neuronavigation precision. Nevertheless, several reports suggest that intraoperative MRI use can solve this consequence of brain displacement satisfactorily [29]. In our country, these facilities are not available. To solve it, we correct the brain shit with three-dimensional ultrasound (3D-US) scans before the dural opening, after the dural opening, and at the end of the resective surgery. Taking advantage of merging this new 3D-US information with previously developed navigation plans with information on the different modalities of structural, functional, and metabolic information tumor and the neighboring tissue. In order to preserve and restore the functional status of each patient. Some limitations to consider for applying these techniques are the biological variability among individuals, the displacement of deep brain structures, and the previously mentioned brain-shift.
5. Neuronavigation and intraoperative electrical stimulation
Prof. Hugues Duffau considers the brain as an entirely eloquent organ; every millimeter of the cerebral cortex represents, sometimes a well-recognized function, and others the association area for several complex functions as language and his diverse characteristics that sometimes define a person, visuospatial perception, auditive integration, and so forth.
In the pediatric patient, the patient’s age determines a more complex scenario because the stage of neurodevelopment at the time of brain tumor surgery determines the functions’ profile to evaluate. Some functions depend on the correct integration of cortical and subcortical areas in the developing brain. Thus, the extensive evaluation and integration in neuronavigation devices of structural, functional, and metabolic imaging techniques are essential to reduce the chance to produce functional sequels.
Undoubtedly, DTI has contributed substantially to the intraoperative identification of withe matter tracts. Perhaps the most studied are those related to motor function. It has been widely described that subcortical continuous monopolar stimulation can help identify the pyramidal pathway with a comprehensive concordance with its counterpart visualized by DTI.
Transoperative electrical stimulation is one more of the resources available to promote extensive glioma resection. The purpose is to preserve the patient’s functionality while attempting to dry out as much of the injury as possible [30].
In our experience, the integration of neuronavigation with intraoperative electrical stimulation and brain mapping considerably reduces the risk of lesions secondary to brain tumor resection.
Monopolar continuous stimulation seems to be the most useful and reproducible procedure for the pyramidal tract’s subcortical characterization. With the aid of DTI, it is possible to identify the modifications preoperatively in the trajectory, density, and resultant distortion secondary to a CNS malignancy. The neuronavigation plan defines precisely the location of the pyramidal tract. In the operative field, the neuronavigation tools and the intraoperative monopolar stimulation can effectively identify its location at subcortical, thalamic, and peduncular regions.
Recently advances suggest that intraoperative acquisition of DTI images can reduce the risk of sequelae.
6. Conclusions
The current neuronavigational technologies allow us to reach deep regions inside the human brain without an increased risk of disability.
The interrelation of different radiological information modalities – structural, functional, and metabolic, in the planning phase of the case and during the surgical procedure permit us to increase the gross-total resection rate for brain tumor resection.
The integration of neurophysiological information into the neuronavigational platform during the neurosurgical procedure reduces complications by monitoring and stimulating withe matter tracts related to language and motor functions.
All multidisciplinary effort is directed to increase surgical techniques’ safety to benefit the quality of life of children who suffer from brain tumor disease.
Acknowledgments
Many people have changed my life, mom, sister, wife, son, and teachers. We acknowledge the incredible patient’s confidence; thank you for touching my life, by improving yours.
This work is dedicated to respect and honor relatives and all medical staff members who fell during the COVID-19 pandemic.
Conflict of interest
“The authors declare no conflict of interest.”
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However, its real usefulness remains in integrating multimodal information from advanced magnetic resonance imaging, as tractography (DTI), functional studies that evaluate motor and sensitive language, motor function (BOLD techniques with different paradigms), and nuclear medicine. At the operating room, the fusion of sonographic information acquired in real-time with the predefined plan increase the chance to achieve gross-total resection of primary brain tumors. Combining these different image modalities with brain mapping and motor stimulation information in selected cases is possible, increasing surgery safety. 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Introduction",level:"1"},{id:"sec_2",title:"2. Characteristics of Magnetic Resonance Imaging Studies for Neuronavigation",level:"1"},{id:"sec_2_2",title:"2.1 Diffusion Tensor Images (DTI)",level:"2"},{id:"sec_3_2",title:"2.2 Perfusion",level:"2"},{id:"sec_4_2",title:"2.3 Magnetic resonance spectroscopy",level:"2"},{id:"sec_5_2",title:"2.4 Functional MRI Images",level:"2"},{id:"sec_6_2",title:"2.5 The utility of fMRI and DTI in presurgical planning",level:"2"},{id:"sec_8",title:"3. Nuclear medicine for imaging brain tumors",level:"1"},{id:"sec_9",title:"4. Neuronavigation principles",level:"1"},{id:"sec_9_2",title:"4.1 DTI and fMRI in functional neuronavigation",level:"2"},{id:"sec_11",title:"5. Neuronavigation and intraoperative electrical stimulation",level:"1"},{id:"sec_12",title:"6. Conclusions",level:"1"},{id:"sec_13",title:"Acknowledgments",level:"1"},{id:"sec_16",title:"Conflict of interest",level:"1"}],chapterReferences:[{id:"B1",body:'Ganslandt O, Behari S, Gralla J, Fahlbusch R, Nimsky C. Neuronavigation: concept, techniques and applications. Neurol India. 2002 Sep;50(3):244-255. PMID: 12391447'},{id:"B2",body:'Kyle M. Walsh, Epidemiology of Brain Tumors. Neurological Surgery. 2017; 118: p. 856-863'},{id:"B3",body:'Floeth, F.W., Pauleit, D., Wittsack, H.J., et al. 2005. Multimodal metabolic imaging of cerebral gliomas: positron emission tomography with [18F] fluoroethyl-L- tyrosine and magnetic resonance spectroscopy. Journal Neurosurgery., 102 p. 318-327'},{id:"B4",body:'Dunet, V., Rossier, C., Buck, A., et al. 2012. Performance of 18F-fluoro-ethyl-tyrosine (18F-FET) PET for the differential diagnosis of primary brain tumor: a systematic review and metaanalysis. 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J Magn Reson Im 23: 887-905'},{id:"B28",body:'Rasmussen IA Jr, Lindeth F, Rygh O, Berntsen E, Selbekk T, Xu J, Hernes TN, Harg E, Haberg A, Unsgaard G (2007) Functional neuronavigation combined with intraoperative 3D ultrasound: initial experiences during surgical resections close to brain areas eloquent and future directions in automatic compensation for cerebral displacement of preoperative data. Acta Neurochir (Vienna) 149: 365-378'},{id:"B29",body:'Kleiser R, Staempfli P, Valvanis A, Boesiger P, Kollias S (2010) Impact of advanced fMRI-guided DTI fiber tracking techniques on their clinical applications in patients with brain tumors. Neuroradiology 52: 37-46'},{id:"B30",body:'Nossek, E., Korn, A., Shahar, T., Kanner, A. A., Yaffe, H., Marcovici, D., Ben-Harosh, C., Ben Ami, H., Weinstein, M., Shapira-Lichter, I., Constantini, S., Hendler, T., & Ram, Z. (2011). Intraoperative mapping and monitoring of the corticospinal tracts with neurophysiological assessment and 3-dimensional ultrasonography-based navigation, Journal of Neurosurgery JNS, 114(3), 738-746'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Roberto Garcia-Navarrete",address:"roberto.gns@gmail.com",affiliation:'
Neurosurgery Department, Centro Medico Naval, Secretaria de Marina, Mexico
Neurosurgery Department, Instituto Nacional de Pediatria, Mexico
Neurosurgery Department, Centro Medico ABC, Mexico
Neurosurgery Department, Instituto Nacional de Pediatria, Mexico
'},{corresp:null,contributorFullName:"Juan Alberto Díaz Ponce Medrano",address:null,affiliation:'
Centro Medico Naval, Secretaria de Marina, Mexico
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1. Introduction
The TSP is one of the most intensively investigated optimization problems and often treated as the prototypical combinatorial optimization problem that has provided much motivation for design of new search algorithms, development of complexity theory, and analysis of solution space and search space [1, 2]. The TSP is defined as a complete graph Q=VEC, where V=vi:i=12…n is a set of n nodes, E=eij:ij=12…ni≠jn×n is an edge matrix containing the set of edges that connects the n nodes, and C=cij:ij=12…ni≠jn×n is a cost matrix holding a set of traveling costs associated with the set of edges. The solution space S contains a finite set of all feasible tours that a salesman may traverse. A tour s∈S is a closed route that visits every node exactly once and returns to the starting node at the end. Like many real-world optimization problems, the TSP is inherently multimodal; that is, it may contain multiple optimal tours in its solution space. We assume that a TSP instance Q contains h≥1 optimal tours in S. We denote f(s) as the objective function, s∗=mins∈Sfs as an optimal tour and S∗ as the set of h optimal tours. The objective of the TSP is to find all h optimal tours in the solution space, that is, S∗⊂S. Therefore, the argument is
argmins∈Sfs=S∗=s1∗s2∗…sh∗E1
Under this definition, the salesman wants to know what all best alternative tours are available. Finding all optimal solutions is the essential requirement for an optimization search algorithm. In practice, knowledge of multiple optimal solutions is extremely helpful, providing the decision-maker with multiple options, especially when the sensitivity of the objective function to small changes in its variables may be different at the alternative optimal points. Obviously, this TSP definition is elegantly simple but full of challenge to the optimization researchers and practitioners.
Optimization has been a fundamental tool in all scientific and engineering areas. The goal of optimization is to find the best set of the admissible conditions to achieve our objective in our decision-making process. Therefore, the fundamental requirement for an optimization search algorithm is to find all optimal solutions within a reasonable amount of computing time. The focus of computational complexity theory is to analyze the intrinsic difficulty of an optimization problem and the asymptotic property of a search algorithm to solve it. The complexity theory attempts to address this question: “How efficient is a search algorithm for a particular optimization problem, as the number of variables gets large?”
The TSP is known to be NP-hard [2, 3]. The problems in NP-hard class are said to be intractable because these problems have no asymptotically efficient algorithm, even the seemingly “limitless” increase of computational power will not resolve their genuine intractability. The intrinsic difficulty of the TSP is that the solution space increases exponentially as the problem size increases, which makes the exhaustive search infeasible. When a TSP instance is large, the number of possible tours in the solution space is so large to forbid an exhaustive search for the optimal tours. A feasible search algorithm for the TSP is one that comes with a guarantee to find all best tours in time at most proportional to nk for some power k.
Do we need to explore all the possibilities in the solution space to find the optimal solutions? Imagine that searching for the optimal solution in the solution space is like treasure hunting. We are trying to hunt for a hidden treasure in the whole world. If we are “blindfolded” without any guidance, it is a silly idea to search every single square inch of the extremely large space. We may have to perform a random search process, which is usually not effective. However, if we are able to use various clues to locate the small village where the treasure was placed, we will then directly go to that village and search every corner of the village to find the hidden treasure. The philosophy behind this treasure-hunting case for optimization is that: if we do not know where the optimal point is in the solution space, we can try to identify the small region that contains the optimal point and then search that small region thoroughly to find that optimal point.
Optimization researchers have developed many optimization algorithms to solve the TSP. Deterministic approaches such as exhaustive enumeration and branch-and-bound can find exact optimal solutions, but they are very expensive from the computational point of view. Stochastic optimization algorithms, such as simple heuristic local search, Evolutionary Algorithms, Particle Swarm Optimization and many other metaheuristics, can find hopefully a good solution to the TSP [1, 4, 5, 6, 7]. The stochastic search algorithms trade in guaranteed correctness of the optimal solution for a shorter computing time. In practice, most stochastic search algorithms are based on the heuristic local search technique [8]. Heuristics are functions that help us decide which one of a set of possible solutions is to be selected next [9]. A local search algorithm iteratively explores the neighborhoods of solutions trying to improve the current solution by a local change. However, the scope of local search is limited by the neighborhood definition. Therefore, heuristic local search algorithms are locally convergent. The final solution may deviate from the optimal solution. Such a final solution is called a locally optimal solution, denoted as s′ in this chapter. To distinguish from locally optimal solutions, the optimal solution s∗ in the solution space is usually called the globally optimal solution.
This chapter studies the TSP from a novel perspective and presents a new search algorithm for the TSP. This chapter is organized in the following sections. Section 2 presents the ABSS algorithm for the TSP. Section 3 describes the important data structure that is a critical player in solving the TSP. Section 4 discusses the nature of heuristic local search algorithm and introduces the concept of solution attractor. Section 5 describes the global optimization features of the ABSS. Section 6 discusses the computational complexity of the ABSS. Section 7 concludes this chapter.
2. The attractor-based search system for the TSP
Figure 1 presents the Attractor-Based Search System (ABSS) for the TSP. In this algorithm, Q is a TSP instance with the edge matrix E and cost matrix C. At beginning of search, the matrix E is initialized by assigning zeros to all elements of E. The function InitialTour() constructs an initial tour si using any tour-construction technique. The function LocalSearch() takes si as an input, performs local search using any type of local search technique, and returns a locally optimal tour sj. The function UpdateE() updates the matrix E by recording the edge configuration of tour sj into the matrix. K is the number of search trajectories. After the edge configurations of K locally optimal tours are stored in the matrix E, the function ExhaustedSearch() searches E completely using the depth-first tree search technique, which is a simple recursive search method that traverses a directed graph starting from a node and then searches adjacent nodes recursively. Finally, the ABSS outputs a set of all best tours S∗ found in the edge configuration of E. The search strategy in the ABSS is straightforward: generating K locally optimal tours, storing their edge configurations in the matrix E, and then identifying the best tours by evaluating all tours represented by the edge configuration of E. The ABSS is a simple and efficient computer program that can solve the TSP effectively. This search algorithm shows strong features of effectiveness, flexibility, adaptability, scalability and efficiency. The computational model of the ABSS is inherently parallel, facilitating implementation on concurrent processors. It can be implemented in many different ways: series, parallel, distributed, or hybrid.
Figure 1.
The ABSS algorithm for the TSP.
Figure 2 uses a 10-node instance as an example to illustrate how the ABSS works. We randomly generate K=6n=60 initial tours, which edge configurations hit all elements of the matrix E (marked as black color), as shown in Figure 2(a). It means that these 60 random tours hit all 45 edges that represent all 181440 tours in the solution space. We let each of the search trajectories run 5000 iterations and obtain 60 locally optimal tours. However, due to the small size of the instance, most locally optimal tours have identical edge configurations. Among the 60 locally optimal tours, we find only four distinct locally optimal tours as shown in Figure 2(b). Figure 2(c) shows the union of the edge configurations of the 60 locally optimal tours, in which 18 edges are hit. Then we use the depth-first tree search, as illustrated in Figure 2(d), to identify all five tours in the edge configuration of E, which are listed in Figure 2(e). In fact, one of the five tours is the globally optimal tour. This simple example indicates that (1) local search trajectories converge to small set of edges, and (2) the union of the edge configurations of K locally optimal tours is not just a countable union of the edge configurations of the these tours, but also include the edge configurations of other locally optimal tours. The ABSS consists of two search phases: local search phase and exhaustive search phase. The task of the local search phase is to identify the region that globally optimal tour is located (i.e. the village hiding the treasure), and the task of the exhaustive search phase is to find the globally optimal tour (i.e. find the hidden treasure). The remaining sections will briefly explain the features of the ABSS.
Figure 2.
A simple example of the ABSS algorithm. (a) Union of the edge configurations of 60 random initial tours, (b) four distinct locally optimal tours, (c) union of the edge configurations of the 60 locally optimal tours, (d) the depth-first tree search on the edge configuration of E, and (e) five tours found in E.
In all experiments mentioned in the chapter, we generate symmetric TSP instances with n nodes. The element cij of the cost matrix C is assigned a random integer independently drawn from a uniform distribution of the range [1, 1000]. The triangle inequality cij+cjk≥cik is not assumed in the instances. Although this type of problem instances is application-free, it is mathematically significant. A TSP instance without triangle inequality cannot be approximated within any constant factor. A heuristic local search algorithm usually performs much worse for this type of TSP instances, which offers a strikingly challenge to solving them [2, 3, 6, 10, 11]. We use the 2-opt local search technique in the local search phase. The 2-opt neighborhood can be characterized as the neighborhood that induces the greatest correlation between function values of neighboring tours, because neighboring tours differ in the minimum possible four edges. Along the same reasoning line, the 2-opt may have the smallest expected number of locally optimal points [12]. The local search process randomly selects a solution in the neighborhood of the current solution. A move that gives the first improvement is chosen. The great advantage of the first-improvement pivoting rule is to produce randomized locally optimal points. The software program written for the experiments use several different programming languages and are run in PCs with different versions of Window operating system.
3. The edge matrix E
Usually the edge matrix E is not necessary to be included in the TSP definition because the TSP is a complete graph. However, the edge matrix E is an effective data structure that can help us understand the search behavior of a local search system. General local search algorithm may not require much problem-specific knowledge in order to generate good solutions. However, it may be unreasonable to expect a search algorithm to be able to solve any problem without taking into account the data structure and properties of the problem at hand.
To solve a problem, the first step is to create a manipulatable description of the problem itself. For many problems, the choice of data structure for representing a solution plays a critical role in the analysis of search behavior and design of new search algorithm. For the TSP, a tour can be represented by an ordered list of nodes or an edge configuration of a tour in the edge matrix E, as illustrated in Figure 3. The improvement of the current tour represents the change in the order of the nodes or the edge configuration of a tour.
Figure 3.
Two representations of a tour: an ordered list of nodes and an edge configuration of a tour.
Observing the behavior of search trajectories in a local search system can be quite challenging. The edge matrix E is a natural data structure that can help us trace the search trajectories and understand the dynamics of a local search system. An edge eij is the most basic element of a tour, but contains a piece of information about each of n−2! tours that go through it. Essentially, the nature of local search for the TSP is an edge-selection process: preservation of good edges and rejection of bad edges according to the objective function fs. Each edge has an implicit probability to be selected by a locally optimal tour. A better edge has higher probability to be included in a locally optimal tour. Therefore, the edges in E can be divided into three groups: globally superior edges, G-edges, and bad edges. A globally superior edge is the edge that occurs in many or all locally optimal tours. Although each of these locally optimal tours selects this edge based on its own search trajectory, the edge is globally superior since the edge is selected by these individual tours from different search trajectories going through different search regions. The globally superior edges have higher probability to be selected by a locally optimal tour. A G-edge is the edge that is included in a globally optimal tour. All G-edges are globally superior edges and can be treated as a special subset of the globally superior edges. The edges that are discarded by all search trajectories or selected by only few locally optimal tours are bad edges. A bad edge is impossible to be included in a globally optimal tour. A locally optimal tour usually consists of some G-edges, some globally superior edges and a few bad edges.
The changes of the edge configuration of the matrix E represent the transformations of the search trajectories in a local search system. When all search trajectories reach their end points, the final edge configuration of E represents the final state of the local search system. For a tour sk, we define an element eij of E as
eij=1if the elementeijis in the toursk0otherwiseE2
Then the hit-frequency value eij in the element eij is defined as the number of occurrence of the element in K tours, that is
eij=∑k=1KeijkE3
When K search trajectories reach their end points, the value eij+eji/K can represent the probability of the edge eij being hit by a locally optimal tour. We can use graphical technique to observe the convergent behavior of the search trajectories through the matrix E. The hit-frequency value eij can be easily converted into a unit of half-tone information in a computer, a value that we interpret as a number Hij somewhere between 0 and 1. The value 1 corresponds to black color, 0 to white color, and any value in between to a gray level. Let K be the number of search trajectories, the half-tone information Hij on a computer screen can be represented by the hit-frequency eij in the element eij of E:
Hij=eijKE4
Figure 4 illustrates a simple example of visualization showing the convergent behavior of 100 search trajectories for a 50-node instance. Figure 4(a) shows the image of the edge configurations of 100 random initial tours. Since each element of E has equal chance to be hit by these initial tours, almost all elements are hit by these initial tours, and all elements have very low Hij values, ranging from 0.00 to 0.02. When the local search system starts searching, the search trajectories constantly change their edge configurations, and therefore the colors in the elements of E are changed accordingly. As the search continues, more and more elements become white (i.e. they are discarded by all search trajectories) and other elements become darker (i.e. they are selected by more search trajectories). When all search trajectories reach their end points, the colored elements represent the final edge configuration of the search system. Figure 4(b) and (c) show the images of edge configuration of E when all search trajectories completed 2000 iterations and 5000 iterations, respectively. At 5000th iteration, the range of Hij values in the elements of E is from 0.00 to 0.42. The value 0.42 means that 42% of the search trajectories select this element. Majority of the elements of E become white color.
Figure 4.
Visualization of the convergent dynamics of local search system. (a) the image of the edge configurations of 100 initial tours, (b) and (c) the images of edge configurations when the search trajectories are at 2000th and 5000th iteration, respectively.
This simple example has great explanatory power about the global dynamics of the local search system for the TSP. As search trajectories continue searching, the number of edges hit by them becomes smaller and smaller, and better edges are hit by more and more search trajectories. This edge-convergence phenomenon means that all search trajectories are moving closer and closer to each other, and their edge configurations become increasingly similar. This phenomenon describes the globally asymptotic behavior of the local search system.
It is easily verified that under certain conditons, a local search system is able to find the set of the globally optimal tours S∗ when the number of search trajectories is unlimited, i.e.
limK→∞PS∗⊂S=1E5
However, the required search effort may be very huge – equivalent to enumerating all tours in the solution space. Now one question for the ABSS is “How many search trajectories in the search system do we need to find all globally optimal tours?” The matrix E consists of nn−1 elements (excluding the diagonal elements). When we randomly construct a tour and record its edge configuration in E, n elements of E will be hit by this tour. If we construct more random tours and record their edge configurations in E, more elements will be hit. We define K as the number of randomly-constructed initial tours, whose edge configurations together will hit all elements of E. We know that all elements of E represent all combinatorial possibilities in the solution space. Therefore, K is the number of search trajectories such that the union of edge configurations of ther initial tours covers the entire solution space. In our experiments, we found that the edge configurations of at most 6n randomly-constructed tours can guarantee to hit all elements of E. From the tour perspective, K=6n random tours represent only a small set of the tours in the solution space. However, from the view of edge-configuration, the union of the edge configurations of 6n random tours represents the edge configurations of all tours in the solution space. It reveals an amazing fact: the union of the edge configurations of only 6n random tours contains the edge configurations of all nn−1!/2 tours in the solution space. It reflects the combinatorial nature of the TSP: the tours in the solution space are formed by different combinations of the edges. The union of the edge configurations of a set of tours contains information about many other tours because one tour shares its edges with many other tours. One fundamental theory that can help us explain this phenomenon is the information theory [13]. According to the information theory, each solution point contains some information about its neighboring solutions that can be modeled as a function, called information function or influence function. The influence function of the ith solution point in the solution space S is defined as a function Ωi:S→R, such that Ωi is a decreasing function of the distance from a solution point to the ith solution point. The notion of influence function has been extensively used in datamining, data clustering, and pattern recognition.
4. The nature of heuristic local search
Heuristic local search is based on the concept of neighborhood search. A neighborhood of a solution si, denoted as Nsi, is a set of solutions that are in some sense close to si. For the TSP, a neighborhood of a tour si is defined as a set of tours that can be reached from si in one single transition. From edge-configuration perspective, all tours in Nsi are very similar because they share significant number of edges with si. The basic operation of local search is iterative improvement, which starts with an initial tour and searches the neighborhood of the current tour for a better tour. If such a tour is found, it replaces the current tour and the search continues until no improvement can be made. The local search algorithm returns a locally optimal tour.
The behavior of a local search trajectory can be understood as a process of iterating a search function gs. We denote s0 as an initial point of search and gts as the tth iteration of the search function gs. A search trajectory s0,gs0,g2s0,…,gts0,… converges to a locally optimal point s′ as its limit, that is,
glimt→∞gts0=limt→∞gt+1s0=s′E6
Therefore, a search trajectory will reach an end point (a locally optimal point) and will stays at this point forever.
In a heuristic local search algorithm, there is a great variety of ways to construct initial tour, choose candidate moves, and define criteria for accepting candidate moves. Most heuristic local search algorithms are based on randomization. In this sense, a heuristic local search algoorithm is a randomized system. There are no two search trajectories that are exactly alike in such a search system. Different search trajectories explore different regions of the solution space and stop at different final points. Therefore, local optimality depends on the initial points, the neighborhood function, randomness in the search process, and time spent on search process. On the other hand, however, a local search algorithm essentially is deterministic and not random in nature. If we observe the motion of all search trajectories, we will see that the search trajectories go towards the same direction, move closer to each other, and eventually converge into a small region in the solution space.
Heuristic local search algorithms are essentially in the domain of dynamical systems. A heuristic local search algorithm is a discrete dynamical system, which has a solution space S (the state space), a set of times T (search iterations), and a search function g:S×T→S that gives the consequents to a solution s∈S in the form of st+1=gst. A search trajectory is the sequence of states of a single search process at successive time-steps, which represents the part of the solution space searched by this search trajectory. The questions about the behavior of a local search system over time are actually the questions about its search trajectories. The most basic question about the search trajectories is “Where do they go in the solution space and what do they do when they get there?”
The attractor theory of dynamical systems is a natural paradigm that can be used to describe the search behavior of a heuristic local search system. The theory of dynamical systems is an extremely broad area of study. A dynamical system is a model of describing the temporal evolution of a system in its state space. The goal of dynamical system analysis is to capture the distinctive properties of certain points or regions in the state space of a given dynamical system. The theory of dynamical systems has discovered that many dynamical systems exhibt attracting behavior in the state space [14, 15, 16, 17, 18, 19, 20, 21, 22]. In such a system, all initial states tend to evolve towards a single final point or a set of points. The term attractor is used to describe this single point or the set of points in the state space. The attractor theory of dynamical systems describes the asymptotic behavior of typical trajectories in the dynamical system. Therefore, the attractor theory provides the theoretical foundation to study the search behavior of a heuristic lcoal search system.
In a local search system for the TSP, no matter where we start a search trajectory in the solution space, all search trajectories will converge to a small region in the solution space for a unimodal TSP instance or h small regions for a h-model TSP. We call this small region a solution attractor of the local search system for a given TSP instance, denoted as A. Therefore, the solution attractor of a local search system for the TSP can be defined as an invariant set A⊂S consisting of all locally optimal tours and the globally optimal tours. A single search trajectory typically converges to either one of the points in the solution attractor. A search trajectory that is in the solution attractor will remain within the solution attractor forward in time. Because a globally optimal tour s∗ is a special case of locally optimal tours, it is undoubtedly embodied in the solutioin attractor, that is, s∗∈A. For a h-modal TSP instance, a local search system will generate h solution attractors A1A2…Ah that attract all search trajectories. Each of the solution attractors has its own set of locally optimal tours, surrounding a globally optimal tour si∗i=12…h. A particular search trajectory will converge into one of the h solution attractors. All locally optimal tours will be distributed to these solution attractors. According to dynamical systems theory [20], the closure of an arbitrary union of attractors is still an attractor. Therefore, the solution attractor A of a local search system for a h-modal TSP is a complete collection of h solution attractors A=A1∪A2∪…∪Ah.
The concept of solution attractor of local search system describes where the search trajectories actually go and where their final points actually stay in the solution space. Figure 5 visually summarizes the concepts of search trajectories and solution attractors in a local search system for a multimodal optimization problem, describing how search trajectories converge and how solution attractors are formed. In summary, let gs be a search function in a local search system for the TSP, the solution attractor of the search system has the following properties [23, 24, 25]:
Convexity, i.e. ∀si∈S,gtsi∈A for sufficient long t;
Centrality, i.e. the globally optimal tour si∗ is located centrally with respect to the other locally optimal tours in Aii=12…h;
Invariance, i.e. ∀s′∈A,gts′=s′ and gtA=A for all time t;
Inreducibility, i.e. the solution attractor A contains a limit number of invariant locally optimal tours.
Figure 5.
Illustration of the concepts of serch trajectories and solution attractors in a local search system for a multimodal optimization problem.
A search trajectory in a local search system changes its edge configuration during the search according to the objective function fs and its neighborhood structure. The matrix E can follow the “footprints” of search trajectories to capture the dynamics of the local search system. When all search trajectories reach their end points – the locally optimal tours, the edge configuration of the matrix E will become fixed, which is the edge configuration of the solution attractor A. This fixed edge configuration contains two groups of edges: the edges that are not hit by any of locally optimal tours (non-hit edges) and the edges that are hit by at least one of the locally optimal tours (hit edges). Figure 6 shows the edge grouping in the edge configuration of E when all search trajectories stop at their final points.
Figure 6.
The grouping of the edges in E when all search trajectories reach their end points.
In the ABSS, we use K search trajectories in the local search phase. Different sets of K search trajectories will generate different final edge configuration of E. Suppose that, we start the local search from a set of K initial points and obtain a edge configuration Ma in E when the local search phase is terminated. Then we start the local search process again from a different set of K initial points and obtains a little different edge configuration Mb in E. Which edge configuration truly describes the edge configuration of the real solution attractor? Actually, Ma and Mb are structurally equivalent because they are different only in the set of bad edges, thus Ma precisely replicates the dynamical properties of Mb. The final edge configuration of the constructed solution attractor generated from K search trajectories is not sensitive to the selection of K search trajectories. This property indicates that a heuristic local search system actually is a deterministic system: although a single search trajectory appears stochastic, all search trajectories from differeitn initial points will be always trapped into the same small region in the solution space and the final edge configuration of E will always converge to the same set of the globally optimal edges.
The convergence of the search trajectories can be measured by the change in the edge configuration of the matrix E. In the local search process, search trajectories collect all available topology information about the quality of the edges from their search experience and record such information in the matrix E. The changes in the edge configuration of E fully reflects the real search evolution of the search system. A state of convergence is achieved once no any more local search trajectory can change the edge configuration of E. For a set of search trajectories to be converging, they must be getting closer and closer to each other, that is, their edge configurations become increasingly similar. As a result, the edge configurations of the search trajectories converge to a small set of edges that contains all globally superior edges and some bad edges. Let W denote total number of edges in E, αt the number of the edges that are hit by all search trajectories at time t, βt the number of the edges that are hit by one or some of the search trajectories, and γt the number of edges that have no hit at all, then at any time t, we have
W=αt+βt+γtE7
For a given TSP instance, W is a constant value W=nn−1/2 for a symmetric instance or W=nn−1 for an asymmetric instance. During the local search process, the values for αt and γt will increase and the value for βt will decrease. However, these values cannot increase or decrease foreover. At certain point of time, they will become constant values, that is,
W=limt→∞αt+limt→∞βt+limt→∞γt=Α+B+ΓE8
Our experiments confirmed this inference about αt, βt and γt. Figure 7 illustrates the patterns of αt, βt and γt curves generated in our experiments. Our experiments also found that, for unimodal TSP instances, the ratio γt/W could approach to 0.70 quickly for different sizes of TSP instances. For multimodal TSP instances, this ratio depends on the number of the globally optimal points. However, the set of hit edges is still very small.
Figure 7.
The αt, βt and γt curves with search iterations.
In summary, we assume a TSP instance Q has a solution space with h≥1 globally optimal tours (s1∗,s2∗,…,sh∗), and correspondingly there exist h set of G-edges G1G2…Gh. A local search system for the Q will generate h solution attractors A1A2…Ah that attract all search trajectories. The edge configuration of the solution attractor A is the union of the edge configurations of the h solution attractors. The final edge configuration of E represents the edge configuration of A with three properties:
It contains all locally optimal tours;
It contains a complete collection of solution attractors, i.e. A=A1∪A2∪…∪Ah;
It contains a complete collection of G-edges, i.e. G=G1∪G2∪…∪Gh.
From this analysis, we can see that the edge matrix E is an extremely useful data structure that not only collcets the information about search trajectories, but also convert local search behavor of individual search trajectories into global search behavor of the search system. The global convergence and deterministic property of the search trajectories make the local search system always converge to the same solution attractors and the edge configurations of the search trajectories always converge to the same set of globally superior edges. The matrix E shows us clearly where the search trajectories go and where all locally optimal points are located. We found the village! However, it is still difficult to identify all G-edges among the globally superior edges. The ABSS uses the exhaustive search phase to find all tours in the solution attractor. Since the local search phase has significantly reduced the size of the search space for the exhaustive search phase, the complete search in the solution attractor becomes feasible.
5. Global optimization feature of the ABSS
The task of a global optimization system is to find all absolutely best solutions in the solution space. There are two major tasks performed by a global optimization system: (1) finding all globally optimal points in the solution space and (2) making sure that they are globally optimal. So far we do not have any effective and efficient global search algorithm to solve NP-hard combinatorial problems. We do not even have well-developed theory or analysis tool to help us design efficient algorithms to perform these two tasks. One critical question in global optimization is how to recognize the globally optimal solutions. Modern search algorithms lack practical criteria that decides when a locally optimal solution is a globally optimal one. What is the necessary and sufficient condition for a feasible point si to be globally optimal point? The mathematical condition for the TSP is ∀s∈S,fs∗≤fs. To meet this condition, an efficient global search system should have the following properties:
The search system should be globally convergent.
The search system should be deterministic and have a rigorous guarantee for finding all globally optimal solutions without excessive computational burden.
The optimality criterion in the system must be based on information on the global behavior of the search system.
The ABSS combines beautifully two crucial aspects in search: exploration and exploitation. In the local search phase, K search trajectories explore the full solution space to identify the globally superior edges, which form the edge configuration of the solution attractor. These K search trajectories are independently and invidually executed, and therefore they create and maintain diversity from beginning to the end. The local search phase is a randomized process due to randomization in the local search function gs. In this sense, the K search trajectories actually perform the Monte Carlo simulation to sample locally optimal tours. The essential idea of Monte Carlo method is using randomness to solve problems that might be deterministic in principle [26]. In the ABSS, K search trajectories start a sample of initial points from a uniform distribution over the solution space S, and, through the randomized local search process, generate a sample of locally optimal points uniformly distributed in the solution attractor A. The edge configuration of E is actually constructed through this Monte Carlo sampling process.
Each of the K search trajectories passes through many neighborhoods on its way to the final point. For any tour si, the size of Nsi is greater than n2! [12]. Let Nsi′ denote the neighborhood of the final point si′ of the ith search trajectory and ΩNstrani as the union of the neighborhoods of all transition points of the search trajectory, then we can believe that the search space covered by K search trajectories is
Ns1′∪ΩNstran1∪Ns2′∪ΩNstran2…∪NsK′∪ΩNstranK=SE9
That is, the solution attractor A is formed through the entire solution space S. The solution attractor A contains h unique minimal “convex” sets Aii=12…h. Each Ai has a unique best tour si∗ surrounded by a set of locally optimal tours. The tour si∗ in Ai satisfies fsi∗<fs for all s∈Ai and fs1∗=fs2∗=…=fsh∗.
We see that the matrix E plays a critical role to transform local search process of the individual search trajectories into a collective global search process of the system. Each time when a local search trajectory finds a better tour and updates the edge configuraton of E, the conditional distribution on the edges are updated. More values are attached to the globally superior edges, and bad edges are discarded. Let W be the complete set of the edges in E and WA the set of edges in the edge configuration of the solution attractor A such that gW is contained in the interior of W. Then the intersection WA of the nested sequence of sets is
W⊃gW⊃g2W⊃…⊃gtW⊃…⊃WAE10
and limt→∞gtWA=WA. As a result, the edge configurations of K search trajectories converge to a small set of edges.
The “convexity” property of the solution attractor A allows the propagation of the minimum property of si∗ in the solution attractor Ai to the whole solution space S through the following conditions:
∀s∈Ai,fsi∗<fs
fs1∗=fs2∗=…=fsh∗
mins∈Afs=mins∈Sfs
Therefore the global convergence and deterministic property of the search trajectories in the local search phase make the ABSS always find the same set of globally optimal tours. We conducted several experiments to confirm this argument empirically. In our experiments, for a given TSP instance, the ABSS performed the same search process on the instance several times, each time using a different set of K search trajectories. The ABSS outputed the same set of the best tours in all trials.
Table 1 shows the results of two experiments. One experiment generated n=1000 instance Q1000, the other generated n=10000 instance Q10000. We conducted 10 trials on each of the instances respectively. In each trial, the ABSS used K=6n search trajectories. Each search trajectory stopped when no improvement was made during 10n iterations. The matrix E stored the edge configurations of the K final tours and then was searched completely using the depth-first tree search process. Table 1 lists the number of tours found in the constructed solution attractor A, the cost range of these tours, and the number of the best tours found in the constructed solution attractor. For instance, in trial 1 for Q1000, the ABSS found 6475824 tours with the cost range [3241, 4136] in the constructed solution attractor. There was a single best tour in the solution attractor. The ABSS found the same best tour in all 10 trials. For the instance Q10000, the ABSS found the same set of four best tours in all 10 trials. These four best tours have the same cost value, but with different edge configurations. If any trial had generated a different set of the best tours, we could immediately make a conclusion that the best tours in the constructed solution attractor may not be the globally optimal tours. From practical perspective, the fact that the same set of the best tours was detected in all trials provides an empirical evidence of the global optimality of these tours. The fact also indicates that the ABSS converges in solution. Convergence in solution means that the search system can identify all optimal solutions repeatedly. Always finding the same set of optimal solutions actually is the fundamental requirement for global optimization systems.
Trial number
Number of tours in A
Range of tour cost
Number of best tours in A
Q1000 (6000 search trajectories)
1
6475824
[3241, 4236]
1
2
6509386
[3241, 3986]
1
3
6395678
[3241, 4027]
1
4
6477859
[3241, 4123]
1
5
6456239
[3241, 3980]
1
6
6457298
[3241, 3892]
1
7
6399867
[3241, 4025]
1
8
6423189
[3241, 3924]
1
9
6500086
[3241, 3948]
1
10
6423181
[3241, 3867]
1
Q10000 (60000 search trajectories)
1
8645248
[69718, 87623]
4
2
8657129
[69718, 86453]
4
3
8603242
[69718, 86875]
4
4
8625449
[69718, 87053]
4
5
8621594
[69718, 87129]
4
6
8650429
[69718, 86978]
4
7
8624950
[69718, 86933]
4
8
8679949
[69718, 86984]
4
9
8679824
[69718, 87044]
4
10
8677249
[69718, 87127]
4
Table 1.
Tours in constructed solution attractor A for Q1000 and Q10000.
6. Computing complexity of the ABSS
With current search technology, the TSP is an infeasible problem because it is not solvable in a reasonable amount of time. Faster computers will not help. A feasible search algorithm for the TSP is one that comes with a guarantee to find all best tours in time at most proportional to nk for some power k. The ABSS can guarantee to find all globally optimal tours for the TSP. Now the question is how efficient it is?
The core idea of the ABSS is that, if we have to use exhaustive search to confirm the globally optimal points, we should first find a way to quickly reduce the effective search space for the exhaustive search. When a local search trajectory finds a better tour, we can say that the local search trajectory finds some better edges. It is an inclusive view. We also can say that the local search trajectory discards some bad edges. It is an exclusive view. The ABSS uses the exclusive strategy to conquer the TSP. The local search phase in the ABSS quickly prunes out large number of edges that cannot possibly be included in any of the globally optimal tours. Thus, a large useless area of the solution space is excluded. When the first edge is discarded by all K search trajectories, n−2! tours that go through that edge are removed from the search space for the exhaustive search phase. Each time when an edge is removed, large number of tours are removed from the search space. Although the complexity of finding a true locally optimal tour is still open, and we even do not know any nontrivial upper bounds on the number of iterations that may be needed to reach local optimality [27, 28], decades of empirical evidence and practical research have found that heuristic local search converges quickly, within low order polynomial time [1, 8, 27, 29]. In practice, we are rarely able to find perfect locally optimal tour because we simply do not allow the local search process to run enough long time. Usually we let a local search process run a predefined number of iterations, accept whatever tour it generates, and treat it as a locally optimal tour. Therefore, the size of the constructed solution attractor depends not only on the problem structure and the neighborhood function, but also on the amount of search time invested in the local search process. As we increase local search time, we will constructe a smaller and stronger solution attractor. The local search phase in the ABSS can significantly reduce the search space for the exhaustive search phase by excluding a large number of edges. Usually the local search phase can remove about 60% of edges of the matrix E in On2.
Now an essential question is naturally raised: What is the relationship between the size of the constructed solution attractor and the size of the problem instance? Unfortunately, there is no theoretical analysis tool available in the literature that can be used to answer this question. We have to depend on empirical results to lend some insights. We conducted several experiments to observe the relationship between the size of the constructed solution attractor and the TSP instance size. Figures 8–10 show the results of one of our experiments. All other similar experiments reveal the same pattern. In this experiment, we generated 10 unimodal TSP instances in the size from 1000 to 10000 nodes with 1000-node increment. For each instance, the ABSS generated K=6n search trajectories. We first let each search trajectory stop when no tour improvement was made during 10000 iterations regardless of the size of the instance (named “fixed search time”). Then we did the same search procedures on these instances again. This time we made each search trajectory stop when no improvement was made during 10n iterations (named “varied search time 1”) and 100n iterations (named “varied search time 2”) respectively. Figure 8 shows the number of the edges that were discarded at the end of local search phase. Figure 9 shows the number of tours in the constructed solution attractor for each instance, and Figure 10 shows the effective branching factors in the exhaustive search phase.
Figure 8.
The number of discarded edges at the end of local search phase.
Figure 9.
Relationship between the size of the constructed solution attractor and instance size.
Figure 10.
The b∗ values for different instance size n in our experiment.
In Figure 8, we can see that the search trajectories can quickly converge to a small set of edges. In the fixed-search-time case, about 60% of the edges were discarded by search trajectories for the 1000-node instance, but this percentage decreases as instance size increases. For the 10000-node instance, only about 46% of the edges are discarded. However, if we increase the local search time linearly when the instance size increases, we can keep the same percentage of discarded-edge for all instance sizes. In the varied-search-time-1 case, about 60% of the edges are abandoned for all different instance sizes. In the varied-search-time-2 case, this percentage increases to 68% for all instances. Higher percentage of abandoned edges means that majority of the branches are removed from the search tree.
Figure 9 shows the number of tours exist in the constructed solution attractor for these instances. All curves in the chart appear to be linear relationship between the size of constructed solution attractor and the size of the problem instance, and the varied-search-time curves have much flatter slope because longer local search time makes a smaller constructed solution attractor. Figures 8 and 9 indicate that the search trajectories in the local search phase can effectively and efficiently reduce the search space for the exhaustive search, and the size of the solution attractor increases linearly as the size of the problem instance increases. Therefore, the local search phase in the ABSS is an efficiently asymptotical search process that produces an extremely small search space for further exhaustive search.
The completely searching of the constructed solution attractor is delegated to the exhaustive search phase. This phase may still need to examine tens or hundreds of millions of tours but nothing a computer processor cannot handle, as opposed to the huge number of total possibilities in the solution space. The exhaustive search phase can find the exact globally optimal tours for the problem instance after a limited number of search steps.
The exhaustive search phase can use any enumerative technique. However, the edge configuration of E can be easily searched by the depth-first tree search algorithm. One of the advantages of depth-first tree search is less memory requirement since only the nodes on the current path are stored. When using tree-search algorithm, we usually use branching factor, average branching factor, or effective branching factor to measure the computing complexity of the algorithm [30, 31, 32, 33]. In the data structure of search tree, the branching factor is the number of successors generated by a given node. If this value is not uniform, an average branching factor can be calculated. An effective branching factor b∗ is the number of sucessors generated by a typical node for a given tree-search problem. We use the following definition to calculate effective brancing factor b∗ for the exhaustive search phase:
N=b∗+b∗2+…+b∗nE11
where n is the size of the TSP instance, representing the depth of the tree, and N is total number of nodes generated in the tree from the origin node. In our experiments, the tree-search process always starts from node 1 (the first row of E). N is total number of nodes that are processed to construct all valid tours and incomplete (therefore abandoned) tours in E. N does not count the node 1 (the origin node), but includes the node 1 as the end node of a valid tour. We use Figure 2(d) as an example. The depth-first search process searches the edge configuration of E and will generate N=58 nodes. Therefore, b∗≈1.3080, that is, 58≈1.3080+1.30802+…+1.308010. Figure 10 shows the effective branching factor b∗ in our experiment. The low values of b∗ indicates that the edge configuration of the solution attractor represents a tree with extremely sparse branches, and the degree of sparseness does not changes as the problem size increase if we linearly increase local search time in the local search phase for a large instance. The search time in the exhaustive search phase is probably in On2 since the size of the constructed solution attractor might be linearly increased with the problem size n and the number of edges in E is polynomially increased with the problem size. Our experiments shows that the ABSS can significantly reduce the computational complexity for the TSP and solve the TSP efficiently with global optimality guarantee.
Therefore, the ABSS is a simple algorithm that increases in computational difficulty polynomially with the size of the TSP. In the ABSS, the objective pursued by the local search phase is “quickly eliminating unnecessary search space as much as possible.” It can provide an answer to the question “In which small region of the solution space is the optimal solution located?” in time of On2. The objective of the exhaustive search phase is “identifying the best tour in the remaining search space.” It can provide an anwer to the question “Which is the best tour in this small region?” in time of On2. All together, the ABSS can answer the question “Is this tour the best tour in the solution space?” in time of On2. Therefore, the ABSS is probably with computing complexity of On2 and memory space requirement of On2. This suggests that the TSP might not be as complex as we might have expected.
7. Conclusion
Advances in computational techniques on the determination of the global optimum for an optimization problem can have great impact on many scientific and engineering fields. Although both the TSP and heuristic local search algorithms have huge literature, there is still a variety of open problems. Numerous experts have made huge advance on the TSP research, but two fundamental questions of the TSP remain essentially open: “How can we find the optimal tours in the solution space, and how do we know they are optimal?”
The P-vs-NP problem is about how fast we can search through a huge number of solutions in the solution space [34]. Do we ever need to explore all the possibilities of the problem to find the optimal one? Actually, the P-vs-NP problem asks whether, in general, we can find a method that completely searches only the region where the optimal points are located [34, 35, 36]. Most people believe P≠NP because we have made little fundamental progress in the area of exhaustive search. Modern computers can greatly speed up the search, but the extremely large solution space would still require geologic search time to find the exact optimal solution on the fastest machines imaginable. A new point of view is needed to improve our capacity to tackle these difficulty problems. This paper describe a new idea: using efficient local search process to effectively reduce the search space for exhaustive search. The concept of solution attractor in heuristic local search systems may change the way we think about both local search and exhaustive search. Heuristic local search is an efficient search system, while exhaustive search is an effective search system. The key is how we combines these two systems into one system beautifully to conquer the fundamental issues of the hard optimization problems. In the TSP case, the edge matrix E, a problem-specific data structure, plays a critical role of reducing the search space and transforming local search to global search.
The ABSS is designed for the TSP. However, the concepts and formulation behind the search algorithm can be used for any combinatorial optimization problem requiring the search of a node permutation in a graph.
\n',keywords:"combinatorial optimization, global optimization, heuristic local search, computational complexity, traveling salesman problem, multimodal optimization, dynamical systems, attractor",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/75156.pdf",chapterXML:"https://mts.intechopen.com/source/xml/75156.xml",downloadPdfUrl:"/chapter/pdf-download/75156",previewPdfUrl:"/chapter/pdf-preview/75156",totalDownloads:437,totalViews:0,totalCrossrefCites:0,dateSubmitted:"September 23rd 2020",dateReviewed:"January 20th 2021",datePrePublished:"February 9th 2021",datePublished:"June 30th 2021",dateFinished:"February 9th 2021",readingETA:"0",abstract:"The Traveling Salesman Problem (TSP) is believed to be an intractable problem and have no practically efficient algorithm to solve it. The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. When a TSP instance is large, the number of possible solutions in the solution space is so large as to forbid an exhaustive search for the optimal solutions. The seemingly “limitless” increase of computational power will not resolve its genuine intractability. Do we need to explore all the possibilities in the solution space to find the optimal solutions? This chapter offers a novel perspective trying to overcome the combinatorial complexity of the TSP. When we design an algorithm to solve an optimization problem, we usually ask the critical question: “How can we find all exact optimal solutions and how do we know that they are optimal in the solution space?” This chapter introduces the Attractor-Based Search System (ABSS) that is specifically designed for the TSP. This chapter explains how the ABSS answer this critical question. The computing complexity of the ABSS is also discussed.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/75156",risUrl:"/chapter/ris/75156",signatures:"Weiqi Li",book:{id:"9237",type:"book",title:"Theory of Complexity",subtitle:"Definitions, Models, and Applications",fullTitle:"Theory of Complexity - Definitions, Models, and Applications",slug:"theory-of-complexity-definitions-models-and-applications",publishedDate:"June 30th 2021",bookSignature:"Ricardo López-Ruiz",coverURL:"https://cdn.intechopen.com/books/images_new/9237.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-78985-214-1",printIsbn:"978-1-78985-213-4",pdfIsbn:"978-1-83962-855-9",isAvailableForWebshopOrdering:!0,editors:[{id:"9849",title:"Prof.",name:"Ricardo",middleName:null,surname:"López-Ruiz",slug:"ricardo-lopez-ruiz",fullName:"Ricardo López-Ruiz"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"312758",title:"Dr.",name:"Weiqi",middleName:null,surname:"Li",fullName:"Weiqi Li",slug:"weiqi-li",email:"weli@umich.edu",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. The attractor-based search system for the TSP",level:"1"},{id:"sec_3",title:"3. The edge matrix E",level:"1"},{id:"sec_4",title:"4. The nature of heuristic local search",level:"1"},{id:"sec_5",title:"5. Global optimization feature of the ABSS",level:"1"},{id:"sec_6",title:"6. Computing complexity of the ABSS",level:"1"},{id:"sec_7",title:"7. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Applegate DL, Bixby RE, Chaátal V, Cook WJ. The Traveling Salesman Problem: A Computational Study. Princeton: Princeton University Press; 2006'},{id:"B2",body:'Papadimitriou CH, Steiglitz K. Combinatorial Optimization: Algorithms and Complexity. New York: Dover Publications; 1998'},{id:"B3",body:'Papadimitriou CH, Steiglitz K. On the complexity of local search for the traveling salesman problem. SIAM Journal on Computing. 1977:6:76–83'},{id:"B4",body:'Gomey J. Stochastic global optimization algorithms: a systematic formal approach. Information Science. 2019:472:53–76'},{id:"B5",body:'Korte B, Vygen J. Combinatorial Optimization: Theory and Algorithms. New York: Springer; 2007'},{id:"B6",body:'Rego C, Gamboa D, Glover F, Osterman C. Traveling salesman problem heuristics: leading methods, implementations and latest advances. European Journal of Operational Research. 2011:211:427–411'},{id:"B7",body:'Zhigliavsky A, Zillinakas A. Stochastic Global Optimization. New York: Springer; 2008'},{id:"B8",body:'Aart E, Lenstra JK. Local Search in Combinatorial Optimization. Princeton: Princeton University Press; 2003'},{id:"B9",body:'Michalewicz Z, Fogel DB. How to Solve It: Modern Heuristics. Berlin: Springer; 2002'},{id:"B10",body:'Sahni S, Gonzales T. P-complete approximation problem. Journal of the ACM. 1976:23:555–565'},{id:"B11",body:'Sourlas N. Statistical mechanics and the traveling salesman problem. Europhysics Letters. 1986:2:919–923'},{id:"B12",body:'Savage SL. Some theoretical implications of local optimality. Mathematical Programming. 1976:10:354–366'},{id:"B13",body:'Shammon CE. A mathematical theory of communication. Bell System Technical Journal. 1948:27:379–423&623–656'},{id:"B14",body:'Alligood KT, Sauer TD, York JA. Chaos: Introduction to Dynamical System. New York: Springer; 1997'},{id:"B15",body:'Auslander J, Bhatia NP, Seibert P. Attractors in dynamical systems. NASA Technical Report NASA-CR-59858; 1964'},{id:"B16",body:'Brin M, Stuck G. Introduction to Dynamical Systems. Cambridge: Cambridge University Press'},{id:"B17",body:'Brown R. A Modern Introduction to Dynamical Systems. New York: Oxford University Press'},{id:"B18",body:'Denes A, Makey G. Attractors and basis of dynamical systems. Electronic Journal of Qualitative Theory of Differential Equations. 2011:20(20):1–11'},{id:"B19",body:'Fogedby H. On the phase space approach to complexity. Journal of Statistical Physics. 1992:69:411–425'},{id:"B20",body:'Milnor J. On the concept of attractor. Communications in Mathematical Physics. 1985:99(2):177–195'},{id:"B21",body:'Milnor J. Collected Papers of John Milnor VI: Dynamical Systems (1953–2000). American Mathematical Society; 2010'},{id:"B22",body:'Ruelle D. Small random perturbations of dynamical systems and the definition of attractor. Communications in Mathematical Physics. 1981:82:137–151'},{id:"B23",body:'Li W. Dynamics of local search trajectory in traveling salesman problem. Journal of Heuristics. 2005:11:507–524'},{id:"B24",body:'Li W, Feng M. Solution attractor of local search in traveling salesman problem: concepts, construction and application. International Journal of Metaheuristics. 2013:2(3):201–233'},{id:"B25",body:'Li W, Li X. Solution attractor of local search in traveling salesman problem: computational study. International Journal of Metaheuristics. 2019:7(2):93–126'},{id:"B26",body:'Kroese DP, Taimre T, Botev ZI. Handbook of Monte Carlo Methods. New York: John Wiley & Sons; 2011'},{id:"B27",body:'Fischer ST. A note on the complexity of local search problems. Information Processing Letters. 1995:53(2):69–75'},{id:"B28",body:'Chandra B, Karloff HJ, Tovey CA. New results on the old-opt algorithm for the traveling salesman problem. SIAM Journal on Computing. 1999:28(6):1998–2029'},{id:"B29",body:'Grover, LK. Local search and the local structure of NP-complete problems. Operations Research Letters. 1992:12(4):235–243'},{id:"B30",body:'Baudet GM. On the branching factor of the alpha-beta pruning algorithm. Artificial Intelligence. 1978:10(23):173–199'},{id:"B31",body:'Edelkamp S, Korf RE. The branching factor of regular search space. Proceedings of the 15th National Conference on Artificial Intelligence. 1998:292–304'},{id:"B32",body:'Korf RE. Depth-first iterative deepening: an optimal admissible tree search. Artificial Intelligence. 1985:27:97–109'},{id:"B33",body:'Pearl J. The solution for the branching factor of the alpha-beta pruning algorithm and its optimality. Communication of the ACM. 1982:25(8):559–564'},{id:"B34",body:'Fortnow L. The Golden Ticket – P, NP, and the Search for the Impossible. Princeton: Princeton University Press; 2013'},{id:"B35",body:'Fortnow L. The status of the P versus NP problem. Communication of the ACM. 2009:52(9):78–86'},{id:"B36",body:'Sipser M. The history of status of the P verses NP question. Proceedings of 24th Annual ACM Symposium on Theory of Computing. 1992:603–618'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Weiqi Li",address:"weli@umich.edu",affiliation:'
School of Management, University of Michigan-Flint, Flint, USA
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The company was founded in Vienna in 2004 by Alex Lazinica and Vedran Kordic, two PhD students researching robotics. While completing our PhDs, we found it difficult to access the research we needed. So, we decided to create a new Open Access publisher. A better one, where researchers like us could find the information they needed easily. The result is IntechOpen, an Open Access publisher that puts the academic needs of the researchers before the business interests of publishers.
",metaTitle:"Our story",metaDescription:"The company was founded in Vienna in 2004 by Alex Lazinica and Vedran Kordic, two PhD students researching robotics. While completing our PhDs, we found it difficult to access the research we needed. So, we decided to create a new Open Access publisher. A better one, where researchers like us could find the information they needed easily. The result is IntechOpen, an Open Access publisher that puts the academic needs of the researchers before the business interests of publishers.",metaKeywords:null,canonicalURL:"/page/our-story",contentRaw:'[{"type":"htmlEditorComponent","content":"
We started by publishing journals and books from the fields of science we were most familiar with - AI, robotics, manufacturing and operations research. Through our growing network of institutions and authors, we soon expanded into related fields like environmental engineering, nanotechnology, computer science, renewable energy and electrical engineering, Today, we are the world’s largest Open Access publisher of scientific research, with over 4,200 books and 54,000 scientific works including peer-reviewed content from more than 116,000 scientists spanning 161 countries. Our authors range from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery.
\\n\\n
In the same year that IntechOpen was founded, we launched what was at the time the first ever Open Access, peer-reviewed journal in its field: the International Journal of Advanced Robotic Systems (IJARS).
\\n\\n
The IntechOpen timeline
\\n\\n
2004
\\n\\n
\\n\\t
Intech Open is founded in Vienna, Austria, by Alex Lazinica and Vedran Kordic, two PhD students, and their first Open Access journals and books are published.
\\n\\t
Alex and Vedran launch the first Open Access, peer-reviewed robotics journal and IntechOpen’s flagship publication, the International Journal of Advanced Robotic Systems (IJARS).
\\n
\\n\\n
2005
\\n\\n
\\n\\t
IntechOpen publishes its first Open Access book: Cutting Edge Robotics.
\\n
\\n\\n
2006
\\n\\n
\\n\\t
IntechOpen publishes a special issue of IJARS, featuring contributions from NASA scientists regarding the Mars Exploration Rover missions.
\\n
\\n\\n
2008
\\n\\n
\\n\\t
Downloads milestone: 200,000 downloads reached
\\n
\\n\\n
2009
\\n\\n
\\n\\t
Publishing milestone: the first 100 Open Access STM books are published
\\n
\\n\\n
2010
\\n\\n
\\n\\t
Downloads milestone: one million downloads reached
\\n\\t
IntechOpen expands its book publishing into a new field: medicine.
\\n
\\n\\n
2011
\\n\\n
\\n\\t
Publishing milestone: More than five million downloads reached
\\n\\t
IntechOpen publishes 1996 Nobel Prize in Chemistry winner Harold W. Kroto’s “Strategies to Successfully Cross-Link Carbon Nanotubes”. Find it here.
\\n\\t
IntechOpen and TBI collaborate on a project to explore the changing needs of researchers and the evolving ways that they discover, publish and exchange information. The result is the survey “Author Attitudes Towards Open Access Publishing: A Market Research Program”.
\\n\\t
IntechOpen hosts SHOW - Share Open Access Worldwide; a series of lectures, debates, round-tables and events to bring people together in discussion of open source principles, intellectual property, content licensing innovations, remixed and shared culture and free knowledge.
\\n
\\n\\n
2012
\\n\\n
\\n\\t
Publishing milestone: 10 million downloads reached
\\n\\t
IntechOpen holds Interact2012, a free series of workshops held by figureheads of the scientific community including Professor Hiroshi Ishiguro, director of the Intelligent Robotics Laboratory, who took the audience through some of the most impressive human-robot interactions observed in his lab.
\\n
\\n\\n
2013
\\n\\n
\\n\\t
IntechOpen joins the Committee on Publication Ethics (COPE) as part of a commitment to guaranteeing the highest standards of publishing.
\\n
\\n\\n
2014
\\n\\n
\\n\\t
IntechOpen turns 10, with more than 30 million downloads to date.
\\n\\t
IntechOpen appoints its first Regional Representatives - members of the team situated around the world dedicated to increasing the visibility of our authors’ published work within their local scientific communities.
\\n
\\n\\n
2015
\\n\\n
\\n\\t
Downloads milestone: More than 70 million downloads reached, more than doubling since the previous year.
\\n\\t
Publishing milestone: IntechOpen publishes its 2,500th book and 40,000th Open Access chapter, reaching 20,000 citations in Thomson Reuters ISI Web of Science.
\\n\\t
40 IntechOpen authors are included in the top one per cent of the world’s most-cited researchers.
\\n\\t
Thomson Reuters’ ISI Web of Science Book Citation Index begins indexing IntechOpen’s books in its database.
\\n
\\n\\n
2016
\\n\\n
\\n\\t
IntechOpen is identified as a world leader in Simba Information’s Open Access Book Publishing 2016-2020 report and forecast. IntechOpen came in as the world’s largest Open Access book publisher by title count.
\\n
\\n\\n
2017
\\n\\n
\\n\\t
Downloads milestone: IntechOpen reaches more than 100 million downloads
\\n\\t
Publishing milestone: IntechOpen publishes its 3,000th Open Access book, making it the largest Open Access book collection in the world
We started by publishing journals and books from the fields of science we were most familiar with - AI, robotics, manufacturing and operations research. Through our growing network of institutions and authors, we soon expanded into related fields like environmental engineering, nanotechnology, computer science, renewable energy and electrical engineering, Today, we are the world’s largest Open Access publisher of scientific research, with over 4,200 books and 54,000 scientific works including peer-reviewed content from more than 116,000 scientists spanning 161 countries. Our authors range from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery.
\n\n
In the same year that IntechOpen was founded, we launched what was at the time the first ever Open Access, peer-reviewed journal in its field: the International Journal of Advanced Robotic Systems (IJARS).
\n\n
The IntechOpen timeline
\n\n
2004
\n\n
\n\t
Intech Open is founded in Vienna, Austria, by Alex Lazinica and Vedran Kordic, two PhD students, and their first Open Access journals and books are published.
\n\t
Alex and Vedran launch the first Open Access, peer-reviewed robotics journal and IntechOpen’s flagship publication, the International Journal of Advanced Robotic Systems (IJARS).
\n
\n\n
2005
\n\n
\n\t
IntechOpen publishes its first Open Access book: Cutting Edge Robotics.
\n
\n\n
2006
\n\n
\n\t
IntechOpen publishes a special issue of IJARS, featuring contributions from NASA scientists regarding the Mars Exploration Rover missions.
\n
\n\n
2008
\n\n
\n\t
Downloads milestone: 200,000 downloads reached
\n
\n\n
2009
\n\n
\n\t
Publishing milestone: the first 100 Open Access STM books are published
\n
\n\n
2010
\n\n
\n\t
Downloads milestone: one million downloads reached
\n\t
IntechOpen expands its book publishing into a new field: medicine.
\n
\n\n
2011
\n\n
\n\t
Publishing milestone: More than five million downloads reached
\n\t
IntechOpen publishes 1996 Nobel Prize in Chemistry winner Harold W. Kroto’s “Strategies to Successfully Cross-Link Carbon Nanotubes”. Find it here.
\n\t
IntechOpen and TBI collaborate on a project to explore the changing needs of researchers and the evolving ways that they discover, publish and exchange information. The result is the survey “Author Attitudes Towards Open Access Publishing: A Market Research Program”.
\n\t
IntechOpen hosts SHOW - Share Open Access Worldwide; a series of lectures, debates, round-tables and events to bring people together in discussion of open source principles, intellectual property, content licensing innovations, remixed and shared culture and free knowledge.
\n
\n\n
2012
\n\n
\n\t
Publishing milestone: 10 million downloads reached
\n\t
IntechOpen holds Interact2012, a free series of workshops held by figureheads of the scientific community including Professor Hiroshi Ishiguro, director of the Intelligent Robotics Laboratory, who took the audience through some of the most impressive human-robot interactions observed in his lab.
\n
\n\n
2013
\n\n
\n\t
IntechOpen joins the Committee on Publication Ethics (COPE) as part of a commitment to guaranteeing the highest standards of publishing.
\n
\n\n
2014
\n\n
\n\t
IntechOpen turns 10, with more than 30 million downloads to date.
\n\t
IntechOpen appoints its first Regional Representatives - members of the team situated around the world dedicated to increasing the visibility of our authors’ published work within their local scientific communities.
\n
\n\n
2015
\n\n
\n\t
Downloads milestone: More than 70 million downloads reached, more than doubling since the previous year.
\n\t
Publishing milestone: IntechOpen publishes its 2,500th book and 40,000th Open Access chapter, reaching 20,000 citations in Thomson Reuters ISI Web of Science.
\n\t
40 IntechOpen authors are included in the top one per cent of the world’s most-cited researchers.
\n\t
Thomson Reuters’ ISI Web of Science Book Citation Index begins indexing IntechOpen’s books in its database.
\n
\n\n
2016
\n\n
\n\t
IntechOpen is identified as a world leader in Simba Information’s Open Access Book Publishing 2016-2020 report and forecast. IntechOpen came in as the world’s largest Open Access book publisher by title count.
\n
\n\n
2017
\n\n
\n\t
Downloads milestone: IntechOpen reaches more than 100 million downloads
\n\t
Publishing milestone: IntechOpen publishes its 3,000th Open Access book, making it the largest Open Access book collection in the world
\n
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It has become a massive part of our daily lives, making predictions based on experience, making this a fascinating area that solves problems that otherwise would not be possible or easy to solve. This topic aims to encompass algorithms that learn from experience (supervised and unsupervised), improve their performance over time and enable machines to make data-driven decisions. It is not limited to any particular applications, but contributions are encouraged from all disciplines.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/26.jpg",keywords:"Intelligent Systems, Machine Learning, Data Science, Data Mining, Artificial Intelligence"},{id:"27",title:"Multi-Agent Systems",scope:"Multi-agent systems are recognised as a state of the art field in Artificial Intelligence studies, which is popular due to the usefulness in facilitation capabilities to handle real-world problem-solving in a distributed fashion. The area covers many techniques that offer solutions to emerging problems in robotics and enterprise-level software systems. Collaborative intelligence is highly and effectively achieved with multi-agent systems. Areas of application include swarms of robots, flocks of UAVs, collaborative software management. Given the level of technological enhancements, the popularity of machine learning in use has opened a new chapter in multi-agent studies alongside the practical challenges and long-lasting collaboration issues in the field. It has increased the urgency and the need for further studies in this field. We welcome chapters presenting research on the many applications of multi-agent studies including, but not limited to, the following key areas: machine learning for multi-agent systems; modeling swarms robots and flocks of UAVs with multi-agent systems; decision science and multi-agent systems; software engineering for and with multi-agent systems; tools and technologies of multi-agent systems.",coverUrl:"https://cdn.intechopen.com/series_topics/covers/27.jpg",keywords:"Collaborative Intelligence, Learning, Distributed Control System, Swarm Robotics, Decision Science, Software Engineering"}],annualVolumeBook:{},thematicCollection:[],selectedSeries:{title:"Artificial Intelligence",id:"14"},selectedSubseries:null},seriesLanding:{item:{id:"25",title:"Environmental Sciences",doi:"10.5772/intechopen.100362",issn:"2754-6713",scope:"
\r\n\tScientists have long researched to understand the environment and man’s place in it. The search for this knowledge grows in importance as rapid increases in population and economic development intensify humans’ stresses on ecosystems. Fortunately, rapid increases in multiple scientific areas are advancing our understanding of environmental sciences. Breakthroughs in computing, molecular biology, ecology, and sustainability science are enhancing our ability to utilize environmental sciences to address real-world problems. \r\n\tThe four topics of this book series - Pollution; Environmental Resilience and Management; Ecosystems and Biodiversity; and Water Science - will address important areas of advancement in the environmental sciences. They will represent an excellent initial grouping of published works on these critical topics.
",coverUrl:"https://cdn.intechopen.com/series/covers/25.jpg",latestPublicationDate:"April 13th, 2022",hasOnlineFirst:!1,numberOfOpenTopics:4,numberOfPublishedChapters:9,numberOfPublishedBooks:1,editor:{id:"197485",title:"Dr.",name:"J. Kevin",middleName:null,surname:"Summers",fullName:"J. Kevin Summers",profilePictureURL:"https://mts.intechopen.com/storage/users/197485/images/system/197485.jpg",biography:"J. Kevin Summers is a Senior Research Ecologist at the Environmental Protection Agency’s (EPA) Gulf Ecosystem Measurement and Modeling Division. He is currently working with colleagues in the Sustainable and Healthy Communities Program to develop an index of community resilience to natural hazards, an index of human well-being that can be linked to changes in the ecosystem, social and economic services, and a community sustainability tool for communities with populations under 40,000. He leads research efforts for indicator and indices development. Dr. Summers is a systems ecologist and began his career at the EPA in 1989 and has worked in various programs and capacities. This includes leading the National Coastal Assessment in collaboration with the Office of Water which culminated in the award-winning National Coastal Condition Report series (four volumes between 2001 and 2012), and which integrates water quality, sediment quality, habitat, and biological data to assess the ecosystem condition of the United States estuaries. He was acting National Program Director for Ecology for the EPA between 2004 and 2006. He has authored approximately 150 peer-reviewed journal articles, book chapters, and reports and has received many awards for technical accomplishments from the EPA and from outside of the agency. Dr. Summers holds a BA in Zoology and Psychology, an MA in Ecology, and Ph.D. in Systems Ecology/Biology.",institutionString:null,institution:{name:"Environmental Protection Agency",institutionURL:null,country:{name:"United States of America"}}},subseries:[{id:"38",title:"Pollution",keywords:"Human activity, Pollutants, Reduced risks, Population growth, Waste disposal, Remediation, Clean environment",scope:"
\r\n\tPollution is caused by a wide variety of human activities and occurs in diverse forms, for example biological, chemical, et cetera. In recent years, significant efforts have been made to ensure that the environment is clean, that rigorous rules are implemented, and old laws are updated to reduce the risks towards humans and ecosystems. However, rapid industrialization and the need for more cultivable sources or habitable lands, for an increasing population, as well as fewer alternatives for waste disposal, make the pollution control tasks more challenging. Therefore, this topic will focus on assessing and managing environmental pollution. It will cover various subjects, including risk assessment due to the pollution of ecosystems, transport and fate of pollutants, restoration or remediation of polluted matrices, and efforts towards sustainable solutions to minimize environmental pollution.
",annualVolume:11966,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/38.jpg",editor:{id:"110740",title:"Dr.",name:"Ismail M.M.",middleName:null,surname:"Rahman",fullName:"Ismail M.M. Rahman",profilePictureURL:"https://mts.intechopen.com/storage/users/110740/images/2319_n.jpg",institutionString:null,institution:{name:"Fukushima University",institutionURL:null,country:{name:"Japan"}}},editorTwo:{id:"201020",title:"Dr.",name:"Zinnat Ara",middleName:null,surname:"Begum",fullName:"Zinnat Ara Begum",profilePictureURL:"https://mts.intechopen.com/storage/users/201020/images/system/201020.jpeg",institutionString:null,institution:{name:"Fukushima University",institutionURL:null,country:{name:"Japan"}}},editorThree:null,editorialBoard:[{id:"252368",title:"Dr.",name:"Meng-Chuan",middleName:null,surname:"Ong",fullName:"Meng-Chuan Ong",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRVotQAG/Profile_Picture_2022-05-20T12:04:28.jpg",institutionString:null,institution:{name:"Universiti Malaysia Terengganu",institutionURL:null,country:{name:"Malaysia"}}},{id:"63465",title:"Prof.",name:"Mohamed Nageeb",middleName:null,surname:"Rashed",fullName:"Mohamed Nageeb Rashed",profilePictureURL:"https://mts.intechopen.com/storage/users/63465/images/system/63465.gif",institutionString:null,institution:{name:"Aswan University",institutionURL:null,country:{name:"Egypt"}}},{id:"187907",title:"Dr.",name:"Olga",middleName:null,surname:"Anne",fullName:"Olga Anne",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bSBE5QAO/Profile_Picture_2022-04-07T09:42:13.png",institutionString:null,institution:{name:"Klaipeda State University of Applied Sciences",institutionURL:null,country:{name:"Lithuania"}}}]},{id:"39",title:"Environmental Resilience and Management",keywords:"Anthropic effects, Overexploitation, Biodiversity loss, Degradation, Inadequate Management, SDGs adequate practices",scope:"
\r\n\tThe environment is subject to severe anthropic effects. Among them are those associated with pollution, resource extraction and overexploitation, loss of biodiversity, soil degradation, disorderly land occupation and planning, and many others. These anthropic effects could potentially be caused by any inadequate management of the environment. However, ecosystems have a resilience that makes them react to disturbances which mitigate the negative effects. It is critical to understand how ecosystems, natural and anthropized, including urban environments, respond to actions that have a negative influence and how they are managed. It is also important to establish when the limits marked by the resilience and the breaking point are achieved and when no return is possible. The main focus for the chapters is to cover the subjects such as understanding how the environment resilience works, the mechanisms involved, and how to manage them in order to improve our interactions with the environment and promote the use of adequate management practices such as those outlined in the United Nations’ Sustainable Development Goals.
",annualVolume:11967,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/39.jpg",editor:{id:"137040",title:"Prof.",name:"Jose",middleName:null,surname:"Navarro-Pedreño",fullName:"Jose Navarro-Pedreño",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRAXrQAO/Profile_Picture_2022-03-09T15:50:19.jpg",institutionString:"Miguel Hernández University of Elche, Spain",institution:null},editorTwo:null,editorThree:null,editorialBoard:[{id:"177015",title:"Prof.",name:"Elke Jurandy",middleName:null,surname:"Bran Nogueira Cardoso",fullName:"Elke Jurandy Bran Nogueira Cardoso",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRGxzQAG/Profile_Picture_2022-03-25T08:32:33.jpg",institutionString:"Universidade de São Paulo, Brazil",institution:null},{id:"211260",title:"Dr.",name:"Sandra",middleName:null,surname:"Ricart",fullName:"Sandra Ricart",profilePictureURL:"https://mts.intechopen.com/storage/users/211260/images/system/211260.jpeg",institutionString:null,institution:{name:"University of Alicante",institutionURL:null,country:{name:"Spain"}}}]},{id:"40",title:"Ecosystems and Biodiversity",keywords:"Ecosystems, Biodiversity, Fauna, Taxonomy, Invasive species, Destruction of habitats, Overexploitation of natural resources, Pollution, Global warming, Conservation of natural spaces, Bioremediation",scope:"
\r\n\tIn general, the harsher the environmental conditions in an ecosystem, the lower the biodiversity. Changes in the environment caused by human activity accelerate the impoverishment of biodiversity.
\r\n
\r\n\tBiodiversity refers to “the variability of living organisms from any source, including terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are part; it includes diversity within each species, between species, and that of ecosystems”.
\r\n
\r\n\tBiodiversity provides food security and constitutes a gene pool for biotechnology, especially in the field of agriculture and medicine, and promotes the development of ecotourism.
\r\n
\r\n\tCurrently, biologists admit that we are witnessing the first phases of the seventh mass extinction caused by human intervention. It is estimated that the current rate of extinction is between a hundred and a thousand times faster than it was when man first appeared. The disappearance of species is caused not only by an accelerated rate of extinction, but also by a decrease in the rate of emergence of new species as human activities degrade the natural environment. The conservation of biological diversity is "a common concern of humanity" and an integral part of the development process. Its objectives are “the conservation of biological diversity, the sustainable use of its components, and the fair and equitable sharing of the benefits resulting from the use of genetic resources”.
\r\n
\r\n\tThe following are the main causes of biodiversity loss:
\r\n
\r\n\t• The destruction of natural habitats to expand urban and agricultural areas and to obtain timber, minerals and other natural resources.
\r\n
\r\n\t• The introduction of alien species into a habitat, whether intentionally or unintentionally which has an impact on the fauna and flora of the area, and as a result, they are reduced or become extinct.
\r\n
\r\n\t• Pollution from industrial and agricultural products, which devastate the fauna and flora, especially those in fresh water.
\r\n
\r\n\t• Global warming, which is seen as a threat to biological diversity, and will become increasingly important in the future.
",annualVolume:11968,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/40.jpg",editor:{id:"209149",title:"Prof.",name:"Salustiano",middleName:null,surname:"Mato",fullName:"Salustiano Mato",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRLREQA4/Profile_Picture_2022-03-31T10:23:50.png",institutionString:null,institution:{name:"University of Vigo",institutionURL:null,country:{name:"Spain"}}},editorTwo:{id:"60498",title:"Prof.",name:"Josefina",middleName:null,surname:"Garrido",fullName:"Josefina Garrido",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRj1VQAS/Profile_Picture_2022-03-31T10:06:51.jpg",institutionString:null,institution:{name:"University of Vigo",institutionURL:null,country:{name:"Spain"}}},editorThree:{id:"464288",title:"Dr.",name:"Francisco",middleName:null,surname:"Ramil",fullName:"Francisco Ramil",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y00003RI7lHQAT/Profile_Picture_2022-03-31T10:15:35.png",institutionString:null,institution:{name:"University of Vigo",institutionURL:null,country:{name:"Spain"}}},editorialBoard:[{id:"220987",title:"Dr.",name:"António",middleName:"Onofre",surname:"Soares",fullName:"António Soares",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRNtzQAG/Profile_Picture_1644499672340",institutionString:null,institution:{name:"University of the Azores",institutionURL:null,country:{name:"Portugal"}}}]},{id:"41",title:"Water Science",keywords:"Water, Water resources, Freshwater, Hydrological processes, Utilization, Protection",scope:"
\r\n\tWater is not only a crucial substance needed for biological life on Earth, but it is also a basic requirement for the existence and development of the human society. Owing to the importance of water to life on Earth, early researchers conducted numerous studies and analyses on the liquid form of water from the perspectives of chemistry, physics, earth science, and biology, and concluded that Earth is a "water polo". Water covers approximately 71% of Earth's surface. However, 97.2% of this water is seawater, 21.5% is icebergs and glaciers, and only 0.65% is freshwater that can be used directly by humans. As a result, the amount of water reserves available for human consumption is limited. The development, utilization, and protection of freshwater resources has become the focus of water science research for the continued improvement of human livelihoods and society.
\r\n
\r\n\tWater exists as solid, liquid, and gas within Earth’s atmosphere, lithosphere, and biosphere. Liquid water is used for a variety of purposes besides drinking, including power generation, ecology, landscaping, and shipping. Because water is involved in various environmental hydrological processes as well as numerous aspects of the economy and human society, the study of various phenomena in the hydrosphere, the laws governing their occurrence and development, the relationship between the hydrosphere and other spheres of Earth, and the relationship between water and social development, are all part of water science. Knowledge systems for water science are improving continuously. Water science has become a specialized field concerned with the identification of its physical, chemical, and biological properties. In addition, it reveals the laws of water distribution, movement, and circulation, and proposes methods and tools for water development, utilization, planning, management, and protection. Currently, the field of water science covers research related to topics such as hydrology, water resources and water environment. It also includes research on water related issues such as safety, engineering, economy, law, culture, information, and education.
",annualVolume:11969,isOpenForSubmission:!0,coverUrl:"https://cdn.intechopen.com/series_topics/covers/41.jpg",editor:{id:"349630",title:"Dr.",name:"Yizi",middleName:null,surname:"Shang",fullName:"Yizi Shang",profilePictureURL:"https://mts.intechopen.com/storage/users/349630/images/system/349630.jpg",institutionString:"China Institute of Water Resources and Hydropower Research",institution:{name:"China Institute of Water Resources and Hydropower Research",institutionURL:null,country:{name:"China"}}},editorTwo:null,editorThree:null,editorialBoard:[{id:"216491",title:"Dr.",name:"Charalampos",middleName:null,surname:"Skoulikaris",fullName:"Charalampos Skoulikaris",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002bRMsbQAG/Profile_Picture_2022-04-21T09:31:55.jpg",institutionString:null,institution:{name:"Aristotle University of Thessaloniki",institutionURL:null,country:{name:"Greece"}}},{id:"300124",title:"Prof.",name:"Thomas",middleName:null,surname:"Shahady",fullName:"Thomas Shahady",profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0030O00002kuIgmQAE/Profile_Picture_2022-03-18T07:32:10.jpg",institutionString:null,institution:{name:"Lynchburg College",institutionURL:null,country:{name:"United States of America"}}}]}]}},libraryRecommendation:{success:null,errors:{},institutions:[]},route:{name:"chapter.detail",path:"/chapters/76107",hash:"",query:{},params:{id:"76107"},fullPath:"/chapters/76107",meta:{},from:{name:null,path:"/",hash:"",query:{},params:{},fullPath:"/",meta:{}}}},function(){var e;(e=document.currentScript||document.scripts[document.scripts.length-1]).parentNode.removeChild(e)}()