Comparison between the ant algorithms.
\r\n\tIn the book the theory and practice of microwave heating are discussed. The intended scope covers the results of recent research related to the generation, transmission and reception of microwave energy, its application in the field of organic and inorganic chemistry, physics of plasma processes, industrial microwave drying and sintering, as well as in medicine for therapeutic effects on internal organs and tissues of the human body and microbiology. Both theoretical and experimental studies are anticipated.
\r\n\r\n\tThe book aims to be of interest not only for specialists in the field of theory and practice of microwave heating but also for readers of non-specialists in the field of microwave technology and those who want to study in general terms the problem of interaction of the electromagnetic field with objects of living and nonliving nature.
",isbn:"978-1-83968-227-8",printIsbn:"978-1-83968-226-1",pdfIsbn:"978-1-83968-228-5",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"8f6a41e4f5ce0e9c48628516d7c92050",bookSignature:"Prof. Gennadiy Churyumov",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10089.jpg",keywords:"Electromagnetic Wave, Microwave Energy Application, Electromagnetic Energy Generation, Intelligent Microwave Heating, Microwave Organic Chemistry, Microwave Reactor, Microwave Discharge, Microwave Plasma, Microwave Drying System, Tissue Microwave Heating, Measurement Automation, Industrial Microwave Process",numberOfDownloads:224,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"July 3rd 2020",dateEndSecondStepPublish:"July 24th 2020",dateEndThirdStepPublish:"September 22nd 2020",dateEndFourthStepPublish:"December 11th 2020",dateEndFifthStepPublish:"February 9th 2021",remainingDaysToSecondStep:"7 months",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:"Prof. Gennadiy I. Churyumov is a professor at two universities: Kharkiv National University of Radio Electronics, and Harbin Institute of Technology and a senior IEEE member.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"216155",title:"Prof.",name:"Gennadiy",middleName:null,surname:"Churyumov",slug:"gennadiy-churyumov",fullName:"Gennadiy Churyumov",profilePictureURL:"https://mts.intechopen.com/storage/users/216155/images/system/216155.jfif",biography:"Gennadiy I. Churyumov (M’96–SM’00) received the Dipl.-Ing. degree in Electronics Engineering and his Ph.D. degree from the Kharkiv Institute of Radio Electronics, Kharkiv, Ukraine, in 1974 and 1981, respectively, as well as the D.Sc. degree from the Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine, in 1997. \n\nHe is a professor at two universities: Kharkiv National University of Radio Electronics, and Harbin Institute of Technology. \n\nHe is currently the Head of a Microwave & Optoelectronics Lab at the Department of Electronics Engineering at the Kharkiv National University of Radio Electronics. \n\nHis general research interests lie in the area of 2-D and 3-D computer modeling of electron-wave processes in vacuum tubes (magnetrons and TWTs), simulation techniques of electromagnetic problems and nonlinear phenomena, as well as high-power microwaves, including electromagnetic compatibility and survivability. \n\nHis current activity concentrates on the practical aspects of the application of microwave technologies.",institutionString:"Kharkiv National University of Radio Electronics (NURE)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"24",title:"Technology",slug:"technology"}],chapters:[{id:"74623",title:"Influence of the Microwaves on the Sol-Gel Syntheses and on the Properties of the Resulting Oxide Nanostructures",slug:"influence-of-the-microwaves-on-the-sol-gel-syntheses-and-on-the-properties-of-the-resulting-oxide-na",totalDownloads:94,totalCrossrefCites:0,authors:[null]},{id:"75284",title:"Microwave-Assisted Extraction of Bioactive Compounds (Review)",slug:"microwave-assisted-extraction-of-bioactive-compounds-review",totalDownloads:12,totalCrossrefCites:0,authors:[null]},{id:"75087",title:"Experimental Investigation on the Effect of Microwave Heating on Rock Cracking and Their Mechanical Properties",slug:"experimental-investigation-on-the-effect-of-microwave-heating-on-rock-cracking-and-their-mechanical-",totalDownloads:28,totalCrossrefCites:0,authors:[null]},{id:"74338",title:"Microwave Synthesized Functional Dyes",slug:"microwave-synthesized-functional-dyes",totalDownloads:21,totalCrossrefCites:0,authors:[null]},{id:"74744",title:"Doping of Semiconductors at Nanoscale with Microwave Heating (Overview)",slug:"doping-of-semiconductors-at-nanoscale-with-microwave-heating-overview",totalDownloads:45,totalCrossrefCites:0,authors:[null]},{id:"74664",title:"Microwave-Assisted Solid Extraction from Natural Matrices",slug:"microwave-assisted-solid-extraction-from-natural-matrices",totalDownloads:25,totalCrossrefCites:0,authors:[null]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"252211",firstName:"Sara",lastName:"Debeuc",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/252211/images/7239_n.png",email:"sara.d@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"63701",title:"Wetland Monitoring and Mapping Using Synthetic Aperture Radar",doi:"10.5772/intechopen.80224",slug:"wetland-monitoring-and-mapping-using-synthetic-aperture-radar",body:'\nWetlands are defined based on the Canadian Wetland Classification System as land that is saturated with water long enough to promote wetland or aquatic processes as indicated by poorly drained soils, hydrophytic vegetation and various kinds of biological activity which are adapted to a wet environment [1]. Wetlands are important ecological systems which play a critical role in hydrology and act as water reservoirs, affecting water quality and controlling runoff rate [2]. Also, they are amongst the most productive ecosystems, providing food, construction materials, transport, and coastline protection. They provide many important environmental functions and habitat for a diversity of plant and animal species [2]. Furthermore, wetlands bring economic value with social benefits for people, providing significant tourism opportunities and recreation that can be a key source of income. For these reasons, the continuous and accurate monitoring of wetlands is necessary, especially for better urban planning and improved natural resources management [3]. The formation of wetlands requires the presence of the appropriate hydrological, geomorphological and biological conditions [2].
\nThe Canadian Wetland Classification System divides wetlands into five classes based on their developmental characteristics and the environment in which they exist [1]. As shown in Figure 1, these classes are: bogs, fens, marches, swamps, and shallow water. Bogs (Figure 2a) are peatlands with a peat layer of at least 40 cm thickness, consisting partially decomposed plants. Bogs surface is usually higher relatively to the surrounding landscape and characterized by evergreen trees and shrubs and covered by sphagnum moss. The only source of water and nutrients in this type of wetlands is the rainfall [4]. Bogs are extremely low in mineral nutrients and tend to be strongly acidic [1].
\nWetland classes hierarchy.
Wetland classes as defined by the Canadian Wetland Classification System: (a) bog, (b) fen, (c) marsh, (d) swamp and (e) shallow open water.
Like bogs, fens (Figure 2b) are also peatlands that accumulate peats. Fens occurs in regions where the ground water discharges to the surface [1]. This type of wetlands is usually covered by grasses, sedges, reeds, and wildflowers. Typically, fens have more nutrients than bogs, and the water is less acidic [4]. Marshes (Figure 2c) are wetlands that are periodically or permanently flooded with standing or slowly moving water and hence are rich in nutrients [4]. Some marshes accumulate peats, though many do not. Marshes are characterized by non-woody vegetation, such as cattails, rushes, reeds, grasses and sedges [1]. Similar to marshes, swamps (Figure 2d) are wetlands that are subject to relatively large seasonal water level fluctuations [4]. Swamps are characterized by woody vegetation, such as dense coniferous or deciduous forest and tall shrubs. Some marshes accumulate peats, though many do not [1]. Shallow open water wetlands (Figure 2e) are ponds of standing water bodies, which represent a transition stage between lakes and marshes. This type of wetlands is free of vegetation with a depth of less than 2 m [1].
\nSpaceborne remote sensing technology is necessary for effective monitoring and mapping of wetlands. The use of this technology provides a practical monitoring and mapping approach of wetlands, especially for those located in remote areas [5].
\nWetlands are usually located in remote areas with limited accessibility. Thus, remote sensing technology is attractive for mapping and monitoring wetlands. Synthetic Aperture Radar (SAR) systems are active remote sensing systems independent of weather and sun illumination. SAR systems transmit electromagnetic microwave from their radar antenna and record the backscattered signal from the radar target [6]. The sensitivity of SAR sensors is a function of the: (1) band, polarization, and incidence angle of the transmitted electromagnetic signal and (2) geometric and dielectric properties of the radar target [7]. Radar targets can be discriminated in a SAR image if their backscattering components are different and the radar spatial resolution is sufficient to distinguish between targets [6]. Conventional SAR systems are linearly polarized radar systems which transmit horizontally and/or vertically polarized radar signal and receive the horizontal and/or vertical polarized components of the backscattered signal (Figure 3). In SAR systems, polarization is referred to the orientation of the electrical field of the electromagnetic wave.
\nHorizontally and vertically polarized radar signal.
A single polarized SAR system is a SAR system which transmits one horizontally or vertically polarized signal and receives the horizontal or vertical polarized component of the returned signal. A dual polarized SAR system is a SAR system which transmits one horizontally or vertically polarized signal and receives both the horizontal and vertical polarized components of the returned signal. A single or dual polarized SAR system acquires partial information with respect to the full polarimetric state of the radar target. A fully polarimetric SAR system transmits alternatively horizontally and vertically polarized signal and receives returns in both orthogonal polarizations, allowing for complete information of the radar target [6, 8]. While full polarimetric SAR systems provide complete information about the radar target, the coverage of these systems is half of the coverage of single or dual polarized SAR systems. Also, the energy required by the satellite for the acquisition of full polarimetric SAR imagery and the pulse repetition frequency of the SAR sensor are twice the single or dual polarized SAR systems.
\nA new SAR configuration named compact polarimetric SAR is currently being implemented in SAR systems, where a circular polarized signal (Figure 4) is transmitted and two orthogonal polarizations (horizontal and vertical) are coherently received [9]. Thus, the relative phase between the two receiving channels is preserved and calibrated, but the swath coverage is not reduced.
\nCircular polarized radar signal.
In comparison to the full polarimetric SAR systems, compact polarimetric SAR operates with half pulse repetition frequency, reducing the average transmit power and increasing the swath width. Consequently, this SAR configuration is associated with low-cost and low-mass constraints of the spaceborne polarimetric SAR systems. The wider coverage of the compact SAR system reduces the revisit time of the satellite, making this system operationally viable [10]. These advantages come with an associated cost in the loss of full polarimetric information. Hence, generally, a compact polarimetric SAR system cannot be “as good as” a full polarimetric system [11]. Such SAR architecture is already included in the current Indian Radar Imaging Satellite-1 (RISAT-1) and the Japanese Advanced Land Observing Satellite-2 (ALOS-2) carrying the Phased Array type L-band Synthetic Aperture Radar-2 (PALSAR-2). Also, compact polarimetric SAR will be included in the future Canadian RADARSAT Constellation Mission (RCM).
\nFully polarimetric SAR systems measure the complete polarimetric information of a radar target in the form of a scattering matrix [S]. The scattering matrix [S] is an array of four complex elements that describes the transformation of the polarization of a wave pulse incident upon a reflective medium to the polarization of the backscattered wave and has the form [6]:
\nwhere H and V refer to horizontal and vertical polarized signals, respectively. The elements of the scattering matrix [S] are complex scattering amplitudes. For most natural targets including wetlands, the reciprocity assumption holds where HV = VH. The diagonal elements HH and VV are called co-polarized elements, while the off-diagonal elements HV and VH are called cross-polarized elements. Two polarimetric scattering vectors can be extracted from the target scattering matrix, which are the lexicographical scattering vector and the Pauli scattering vector [12]. Assuming the reciprocity condition, the lexicological scattering vector has the form:
\nwhere the superscript T denotes the vector transpose. The multiplication of the cross-polarization with 2 is to preserve the total backscattered power of the returned signal. The Pauli scattering vector can be obtained from the complex Pauli spin matrices [6] and, assuming the reciprocity condition, has the form:
\nDeterministic scatterers can be described completely by a single scattering matrix or vector. However, for remote sensing SAR applications, the assumption of pure deterministic scatterers is not valid. Thus, scatterers are non-deterministic and cannot be described with a single polarimetric scattering matrix or vector. This is because the resolution cell is bigger than the wavelength of the incident wave. Non-deterministic scatterers are spatially distributed. Therefore, each resolution cell is assumed to contain many deterministic scatterers, where each of these scatterers can be described by a single scattering matrix [Si]. Therefore, the measured scattering matrix [S] for one resolution cell consists of the coherent superposition of the individual scattering matrices [Si] of all the deterministic scatterers located within the resolution cell [6, 12].
\nAn ensemble average of the complex product between the lexicological scattering vector \n
where \n
The relationship between the covariance matrix [C] and the coherency matrix [T] is linear. Both matrices are full rank, hermitian positive semidefinite and have the same real non-negative eigenvalues, but different eigenvectors. Moreover, both matrices contain the complete information about variance and correlation for all the complex elements of the scattering matrix [S] [12].
\nA compact polarimetric SAR system transmits a right- or left-circular polarized signal, providing a scattering vector of two elements:
\nwhere R refers to a transmitted right-circular polarized signal. A four-element vector called Stokes vector [g] can be calculated from the measured compact polarimetric scattering vector, as follow [11]:
\nwhere Re and Im are the real and imaginary parts of a complex number. The first Stokes element g0 is associated with the total power of the backscattered signal while the fourth Stokes vector is associated with the power in the right-hand and left-hand circularly polarized component [13]. The elements of the Stokes vector can be used to derive an average coherency matrix, which takes the form [14]:
\nRadar backscattering is a function of the radar target properties (dielectric properties, roughness, target geometry) and the radar system characteristics (polarization, band, incidence angle). Three major backscattering mechanisms can take place during the backscattering process. These are the surface, double bounce and volume scattering mechanism (Figure 5).
\nThe three major scattering mechanisms: surface, double bounce and volume.
In the case of surface scattering mechanism (Figure 5), the incident radar signal features one or an odd number of bounces before returns back to the SAR antenna. In this case, a phase shift of 180o occurs between the transmitted and the received signal [6]. However, a very smooth surface could cause the radar incident signal to be reflected away from the radar antenna, causing the radar target to appear dark in the SAR image. In this case, scattering is called specular scattering. An example of such surfaces is the open water in wetlands [12]. In the case of double bounce scattering mechanism (Figure 5), the incident radar signal hits two surfaces, horizontal and adjacent vertical forming a dihedral angle, and almost all of incident waves return back to the radar antenna. Thus, the scattering from radar targets with double bounce scattering is very high. The phase difference between the transmitted and the received signal is equal to zero. Double bounce scattering mechanism is frequently observed in open wetlands, such as bog and marsh, as the results of the interaction of the radar signal between the standing water and vegetation [15]. In the case of volume scattering mechanism (Figure 5), the radar signal features multiple random scattering within the natural medium. Usually, a large portion of the transmitted signal is returned back to the SAR sensor, causing rise to cross polarizations (HV and VH). Thus, illuminated radar targets with volume scattering appear bright in a SAR image. Volume scattering is commonly observed in flooded vegetation wetlands due to multiple scattering in the vegetation canopy.
\nIn general, the penetration capabilities and the attenuation depth of radar signal in a medium, such as flooded vegetation, increases with the increasing of the wavelength [6, 12]. Figure 6 presents the penetration of radar signals for different bands. As shown in Figure 6, X-band SAR has a short wavelength signal with limited penetration capability, while L-band SAR has long wavelength signal with higher penetration capability. C-band SAR is assumed as a good compromise between X- and L-band SAR systems. As shown in Figure 6, the scattering mechanism of a radar target could be affected by the penetration depth of the radar signal. Thus, dense flooded vegetation could present volume scattering mechanism in X- or C-band SAR (return from canopy), but double bounce scattering mechanism in L-band due to scattering process from trunk-water interaction (Figure 6) [12].
\nThe radar signal penetration for different bands.
Different decomposition methods have been proposed to derive the target scattering mechanisms for both full polarimetric [6, 16, 17, 18, 19, 20, 21, 22, 23, 24] and compact polarimetric [11, 25] SAR data. One of the earliest and widely used decomposition methods is the Cloude-Pottier decomposition [17]. This method is incoherent decomposition method based on the eigenvector and eigenvalue analysis of the coherency matrix [T]. Given that [T] is hermitian positive semidefinite matrix, it can always be diagonalized using unitary similarity transformations. That is, the coherency matrix can be given as
\nwhere [Λ] is the diagonal eigenvalue matrix of [T], λ1 ≥ λ2 ≥ λ3 ≥ 0 are the real eigenvalues and [U] is a unitary matrix whose columns correspond to the orthogonal eigenvectors of [T]. Based on the Cloude-Pottier decomposition, three parameters can be derived [17]. The polarimetric entropy H (0 ≤ H ≤ 1) is defined by the logarithmic sum of the eigenvalues
\nwhere \n
The anisotropy A provides additional information only for medium values of H because in this case secondary scattering mechanisms, in addition to the dominant scattering mechanism, play an important role in the scattering process [6]. The alpha angle α (0 ≤ α ≤ 90o) provides information about the type of scattering mechanism
\nwhere cos(αi) in the magnitude of the first component of the coherency matrix eigenvector ei (i = 1, 2, 3).
\nAnother widely used polarimetric decomposition method is the Freeman-Durden method [18]. Contrary to the Cloude-Pottier decomposition, which is a purely mathematical construct, the Freeman-Durden decomposition method is a physically model-based incoherent decomposition based on the polarimetric covariance matrix. It relies on the conversion of a covariance matrix to a three-component model. The results of this decomposition are three coefficients corresponding to the weights of different model components. A polarimetric covariance matrix [C] can be decomposed to a sum of three components, corresponding to volume, surface, and double bounce scattering mechanisms [18]:
\nwhere fv, fs, and fd are the three coefficients corresponding to volume, surface, and double bounce scattering, respectively. The Freeman-Durden decomposition is particularly well adapted to the study of vegetated areas [18]. Thus, it is widely used for multitemporal wetland monitoring to track changes of shallow open water to flooded vegetation [26].
\nScattering mechanism information can also be obtained using compact polarimetric SAR data. Two decomposition methods are commonly used. The first is the m-δ decomposition method [11], which is based on the degree of polarization of the backscattered signal \n
where Vd, Vv, and Vs refer to double bounce, volume, and surface scattering mechanisms, respectively. The second decomposition method is the m-χ decomposition [25], which is based on the degree of polarization m and the ellipticity \n
where Pd, Pv, and Ps refer to even bounce, volume, and odd bounce scattering mechanisms, respectively.
\nThe accurate, effective, and continuous identification and tracking of changes in wetlands is necessary for monitoring human, climatic and other effects on these ecosystems and better understanding of their response. Wetlands are expected to be even more dynamic in the future with rapid and frequent changes due to the human stresses on environment and the global warming [27]. Different methodologies can be adopted to detect and track changes in wetlands using SAR imagery, depending on the type of the change and the available polarization option. For example, a change in the surface water level of a wetland area due to e.g. heavy rainfall could extend the wetland water surface, causing flooding in the surrounding areas. Such a change can be easily detected using SAR amplitude images before and after the event acquired with similar acquisition geometry. The specular scattering of the radar signal can highlight the open water areas (dark areas due to low returned signal). Spatiotemporal changes in wetlands as dynamic ecosystems could be interpreted using SAR amplitude imagery only. This is because changes within wetlands could change the surface type illuminated by the radar. Sometimes, the change could be more complex with alternations in surface water, flooded vegetation and upland boundaries. In this case, the additional polarimetric information from full or compact polarimetric SAR is necessary for the detection and interpretation of changes within wetlands.
\nAs shown in Figure 7, a change within a wetland from wet soil with a high dielectric constant to open water is usually accompanied with a change in the radar backscattering from surface scattering with a strong returned signal (Figure 7a) to specular reflection with a weak returned signal (Figure 7b). The change in wetland could also be due to its seasonal development over time. Hence, intermediate marsh with large vegetation stems properly oriented could allow for double bounce scattering mechanism (Figure 7c). As the marsh develops, the strong observed double bounce scattering mechanism gradually decreases in favor of the volume scattering (Figure 7d) from the dense canopy of the fully developed marsh [28]. Thus, polarimetric decomposition methods enable the identification of wetland classes (e.g. flooded vegetation) and monitoring changes within these classes by means of the temporal change in the backscattering mechanisms. The role of decomposition methods for identification and monitoring of wetlands was highlighted in a number of recent studies [26, 29, 30, 31]. Another way of monitoring changes within wetlands could be through polarimetric change detection methodologies using full [10], compact [10, 32], or even coherent dual [33] polarized SAR imagery. These methodologies are based on polarimetric coherency/covariance matrices. Herein, changes are flagged without information about the scattering mechanisms, which occurred during the scattering process. Test statistics, such as those proposed in [34, 35], were proven effective for polarimetric change detection over wetlands.
\n(a) Surface scattering mechanism from wet soil, (b) radar signal reflection from shallow open water, (c) double bounce scattering mechanism from signal interaction with vegetation stems and water surface and (d) volume scattering due to random scattering within the dense flooded vegetation canopy.
Ever since the launch of the Earth Resources Technology Satellite (ERTS) in 1972 there has been interest in using satellite remote sensing as a tool for wetland mapping and classification because the traditional air photo and field visit approaches are too costly and time consuming [36]. Wetlands are difficult to map and classify due to a large degree of spatial and temporal variability as well as structural and spectral similarities between wetland classes. Over the last decade or so a state-of-the-art approach for wetland classification has emerged. This is an object based classification approach using multi-source input data (optical and SAR) with a machine learning classification algorithm and a quality Digital Elevation Model (DEM) for identifying terrain suitability for wetlands or surface water [37, 38, 39, 40]. Using this approach, greater than 90% accuracy is often achieved for a wide variety of wetland classification systems [41].
\nThe early satellite SAR systems produced single channel intensity only output data, which limited its value for land cover and wetland classification. This type of data when used synergistically with optical data improved the wetland classification compared to using optical data alone but only to a minor degree [37, 42, 43, 44, 45]. This is largely due to the ability of the SAR wavelengths to penetrate wetland vegetation and “see” the underlying water, thereby improving the flooded vegetation class discrimination. The flooded vegetation tends to produce a double bounce scattering mechanism, as explained earlier, which increases the intensity of the backscatter. HH polarization is best for this due to the enhanced penetration in vegetation.
\nAs one goes up the polarization hierarchy from single channel intensity only data to dual-channel, compact polarimetry, and full polarimetry data sets the information content increases and the wetland classification subsequently improves [11, 46, 47, 48, 49, 50]. In general, dual channel SAR’s and polarization ratios outperform single channel intensity only data systems and compact polarimetric data is better than dual channel data. Fully polarimetric data consistently shows the best information content for wetland classification by using polarimetric parameters derived from the data matrices, or polarimetric decompositions such as the Cloude and Pottier [17], Freeman-Durden [18], or Touzi [24] decompositions. You can use the decompositions or polarimetric parameters such as the polarization phase difference to identify flooded vegetation due to the double bounce effect increasing intensity and producing the phase shift. The Shannon Entropy has also proven useful for wetland mapping [51] and may have some benefit for finding the transition from flooded to saturated soil and between flooded vegetation and open water. This is a two-parameter model with one parameter relating to intensity and the other polarization diversity, and it may be simpler than using the decompositions.
\nThere have been numerous frequency effect evaluations since the early observations of enhanced scattering from flooded vegetation on SEASAT imagery [52]. This effect for swamps and many vegetated wetlands with high biomass is quite evident in L-band data due to the increased canopy penetration and better interaction with the water/trunk/stem interface, resulting in the double bounce scattering mechanism [53, 54]. It is also evident at C-band and in some cases at X-band depending on the biomass and density of the canopy and the subsequent wavelength dependent penetration [41, 55, 56, 57, 58, 59, 60]. In general, X- and C-band are preferred for herbaceous wetlands and less dense canopies while L-band is preferred for woody wetlands such as swamps and other wetland classes with high biomass.
\nSAR data has also proven effective for mapping peatlands, which is becoming more important because of climate change and carbon emission issues [61, 62, 63, 64]. Due to the penetration of these longer wavelengths and the ability to penetrate beneath the plant canopy, there have been some indications that L-band polarimetric SAR can be used to differentiate between bog and fen peatlands due to the sensitivity of the water flow characteristics beneath the surface [65].
\nSAR does not penetrate water so provides little information on invasive aquatic submersive plants, but L-band and to a lesser degree C-band have shown some success at identifying invasive Phragmites [66]. This tall dense invasive provides significant SAR backscatter and can be separated from other land-cover due to this characteristic and its location in the landscape. It helps to use LiDAR as well as SAR due to the relative height and landscape position of the Phragmites [67].
\nIn general, one wants to use a steep incidence angle for woody wetlands or flooded vegetation mapping in order to enhance the penetration to reach the water surface and realize the enhanced scattering effect due to double bounce scattering between the vegetation and the water surface. A shallow angle may be preferred if the focus is on the open water mapping as this can enhance the contrast between the specular scattering of surface water and the flooded vegetation with volume and double bounce scattering. Recent reviews of wetland remote sensing and SAR are provided in [40, 41, 68, 69, 70].
\nThe specular backscatter from calm water surfaces allows for easy discrimination of open water from upland and flooded vegetation using SAR data. At the same time, the double bounce scattering from flooded vegetation allows discrimination from upland and open water as described earlier. This, combined with the all-weather data collection capabilities, makes SAR an ideal sensor for mapping flood as well as dynamic surface water and flooded vegetation [40].
\nFlood mapping is operational with SAR data in many countries using data from a variety of SAR systems from X- to L-band (see for example [71, 72, 73, 74]). Intensity thresholding techniques have traditionally been used for open water mapping [75]. Texture, cross-polarization data, and other techniques are being developed to solve the problem when the water is brighter due to wind or current induced roughness, as well as to automate the process [76, 77, 78, 79].
\nAs described in the section on wetland mapping the double bounce effect and enhanced scattering from flooded vegetation makes SAR a good sensor for mapping flooded vegetation from non-flooded vegetation [40, 59, 80]. This allows the delineation of wetland extent and with multi-temporal data can be very useful for monitoring seasonal and/or annual changes in the wetland size and extent. [81] showed that flooded vegetation tends to remain coherent using InSAR techniques and this can then be used to map wetland type and extent. Thus, SAR is an ideal sensor for monitoring the spatially and temporally dynamic flooded vegetation components of wetlands.
\nThe development of standard coverages, like that used for the Sentinel program, results in stacks of data with the same geometry and facilitates the use of temporal filters for speckle noise reduction. The use of a multi-temporal filter rather than the conventional spatial filtering approach can be an effective way to reduce the speckle while maintaining the spatial resolution and the ability to detect small objects and edges [82, 83]. This also allows the use of intensity metrics rather than thresholds to separate water from land, which can also help solving the wind roughness problem [84]. The multi-temporal coverage provided by SAR systems enables generating hydro-period and dynamic surface water as well as flooded vegetation masks [85, 86]. This enables better mapping of temporary, seasonal and ephemeral water bodies as well as the permanent water bodies, which are static and much easier to map. A recent review of SAR flood mapping and flood studies with SAR is provided in [87], while [88] provides a review of flooded vegetation mapping with SAR.
\nWetland interferometric synthetic aperture radar (InSAR) is a relatively new application of the InSAR technology that detects water level changes over wide areas with 5–100 m pixel resolution and several centimeters vertical accuracy [89, 90, 91]. The wetland InSAR technique works where vegetation emerges above the water surface due to the “double bounce” effect, in which the radar pulse is backscattered twice from the water surface and vegetation [53]. InSAR observations were successfully used to study wetland hydrology in the Everglades [90, 91, 92, 93], Louisiana [94, 95, 96] and the Sian Ka’an in Yucatan [97].
\nOne of the key issues in using the InSAR observations for assessing wetland hydrology is the calibration of the InSAR observations, which are relative in both space and time. In time, the measurements provide the change in water level (not the actual water level) that occurred between the two data acquisitions. In space, the measurements describe the relative change of water levels in the entire interferogram with respect to a zero change at an arbitrary reference point, because the actual range between the satellite and the surface cannot be determined accurately. However, the relative changes between pixels can be determined at the cm-level. In many other InSAR applications, such as earthquake or volcanic induced deformation, the reference zero change point is chosen to be in the far-field, where changes are known to be negligible [98]. However, in wetland InSAR, the assumption of zero surface change in the far-field does not hold, because flow and water levels can be discontinuous across the various water control structures or other flow obstacles.
\nThe calibration stage requires additional information on water level changes, which can be derived from various sources. In areas monitored by stage (water level) stations, as in the Everglades, the stage data can be used for the InSAR calibration, as conducted by [90]. Another calibration technique relies on spaceborne radar altimetry, which detects absolute water level changes over a few km wide footprints with accuracy of 5–10 cm [94]. However, the altimetry observations are limited in space and time, as the radar altimeter data can only be acquired along the satellite tracks, which are spaces roughly 100 km apart. Also, the altimetry data is not always synchronized with the InSAR observations, which are acquired by different satellites.
\nWetland biomass is of increasing interest due to methane emission contributions to climate change from degraded and thawing wetlands. Wetland change can also be used as an indicator of climate change impacts. Wetland vegetation biomass can therefore be an important indicator of carbon sequestration in wetlands and is essential for understanding the carbon cycle of these ecosystems. SAR data has the potential to estimate vegetation biomass in wetlands because radar is particularly sensitive to the vegetation canopy over an underlying water surface [99]. The biomass of totora reeds and bofedal in water-saturated Andean grasslands was mapped with ERS-1 data in [100]. The goal was to protect this ecosystem from overgrazing. They found that the backscatter signal of ERS-1 was sensitive to the humid and dry biomass of reeds and grasslands and their biomass maps were useful for the livestock management in the study region. [101] developed regression and analytical models for estimating mangrove wetland biomass in South China using RADARSAT images. [102, 103] also found that L-band ALOS PALSAR can be used to estimate the aboveground biomass because of the correlation between HH and HV backscatter signals. C-band backscatter characteristics from RADARSAT-2 data were used by [104] to estimate the biomass of the Poyang Lake wetlands in China. Also, [105] used ENVISAT ASAR data to estimate wetland vegetation biomass in Poyang Lake. These studies have shown that it is possible to estimate above water biomass in wetlands with SAR data.
\nAs shown in the previous section, spaceborne SAR remote sensing technology is recognized as essential tool for effective wetland observation. With the presence of global warming and its associated risks on Earth systems, there is an expressed interest in increased temporal and spatial resolution of satellite measurements. Thus, a trend toward increased temporal and spatial resolution of SAR imagery is noted in recent and future SAR missions. The Sentinel-1 SAR mission with its two identical SAR satellites (Sentinel-1A&B) is a good example of a recent SAR mission with a spatial resolution ranging from 5 m to 100 m and a revisit time of 6 days. This high temporal and spatial resolution is expected to be even higher in the near future with the launch of the RCM in late 2018. The RCM is expected to provide SAR imagery in a spatial resolution ranging from 1 m to 100 m, in a revisit time of only 4 days [32]. The increased temporal and spatial resolution would be required to adequately monitor wetlands and characterize the actual implications of climate change. Also, it is expected to further improve our understanding of climate change in wetlands and water quality, allowing ecosystem managers and decision makers to have sufficient information regarding wetland preservation.
\nWith the availability of different remote sensing data with various information contents, the application of multi-source data for advanced wetland applications is demonstrated in a number of studies; see for example [2, 44, 61, 67, 106]. In addition to SAR imagery, experiments on the integration of topographic and remote sensing data, such as optical imagery and LiDAR data, were conducted. The ultimate objective of these experiments was the improved mapping accuracy of wetlands. The integration of SAR imagery with optical and topographic data from multiple sensors was shown in [44, 106] to be necessary for improved wetland mapping and classification during the growing season. However, the integration of SAR imagery and LiDAR data did not improve significantly the classification accuracy of wetland in [61, 67]. The modern advances in remote sensing technology and the availability of multi-source information are shifting the manner in which Earth observation data are used for wetland monitoring, indicating the need for automated and efficient techniques. Different studies, such as [2, 44, 61, 106], have highlighted the effectiveness of machine learning algorithms for automated wetland classification. An example of these algorithms is the Random Forest (RF) classification algorithm proposed in [107]. This shift toward the automated machine learning algorithms comes to fulfill the requirement for operational wetland monitoring systems.
\nThe continuing advancements in computer processing power and software development as well as the trend toward free and open access to remote sensing imagery, such as those from the current Sentinel satellites and the future RCM, are enabling the ingestion of data into a centralized archive. This also supports the application of a standard rapid processing chain to generate analysis-ready wetland products. The provision of analysis-ready products to a wide range of users would revolutionize the role of remote sensing in Earth system science [108].
\nThis chapter highlighted the SAR remote sensing technology and its potential for wetland monitoring and mapping. It was shown that a wide range of wetland applications can be addressed using SAR remote sensing imagery. SAR data with enhanced target information provided by full or compact polarimetric SAR systems can provide information for advanced wetland applications. In many studies, the information about the polarimetric scattering mechanisms was found necessary for observing the temporal development of wetlands and detecting their changes. This chapter shows that the fusion of multi-source data improves wetland mapping, especially during the growing season. Furthermore, a relatively new application of the InSAR technology is currently implemented for water level monitoring. Given the problem of climate change, wetland biomass estimation using SAR imagery is becoming necessary for the evaluation of methane emission contributions to climate change from degraded and thawing wetlands. The current advanced computing capabilities along with the shift toward free and open access remote sensing data are enabling analysis-ready products for a wide range of users.
\nAuthors would like to thank Mr. Jean Granger and Dr. Bahram Salehi from the Memorial University of Newfoundland and Dr. Koreen Millard form Environment and Climate Change Canada for their help in providing pictures of different wetland classes.
\nAuthors declare no conflict of interest.
SAR | synthetic aperture radar |
HH | horizontal transmitted horizontal received signal |
VV | vertical transmitted vertical received signal |
HV | horizontal transmitted vertical received signal |
VH | vertical transmitted horizontal received signal |
RH | right circular transmitted horizontal received signal |
RV | right circular transmitted vertical received signal |
RISAT-1 | Radar Imaging Satellite-1 |
ALOS-2 | Advanced Land Observing Satellite-2 |
PALSAR-2 | Phased Array type L-band Synthetic Aperture Radar-2 |
RCM | RADARSAT Constellation Mission |
InSAR | interferometric synthetic aperture radar |
RF | random forest |
DEM | digital elevation model |
The lives of ordinary consumers have changed almost beyond recognition in the past 20 years. First, with the introduction of high-speed internet access; but, more recently, with the arrival of mobile computing devices such as smartphones and tablets. According to data from the 2017 Gallup World Survey [1], 93 of adults in high-income economies have their cell phones, while 79
In the transportation segment, a central theme is how the digital revolution has created opportunities to consider new models of delivering services under the paradigm of Mobility as a Service (MaaS) [2]. There is a growing interes
This study deals with a novel optimization model that can improve the services provided by on-demand mobility platforms, called Quota Traveling Salesman Problem with Passengers, Incomplete Ride, and Collection Time (QTSP-PIC). In this problem, the salesman is the vehicle driver and can reduce travel costs by sharing expenses with passengers. He must respect the budget limitations and the maximum travel time of every passenger. Each passenger can be transported directly to the desired destination or an alternate destination. Lira et al. [4] suggest pro-environmental or money-saving concerns can induce users of a ride-sharing service to agree to fulfill their needs at an alternate destination.
The QTSP-PIC can model a wide variety of real-world applications. Cases related to sales and tourism are the most pertinent ones. The salesman must choose which cities to visit to reach a minimum sales quota, and the order to visit them to fulfill travel requests. In the tourism case, the salesman is a tourist that chooses the best tourist attractions to visit during a vacation trip and can use a ride-sharing system to reduce travel expenses. In both cases, the driver negotiates discounts with passengers transported to a destination similar to the desired one.
The QTSP-PIC was introduced by Silva et al. [5]. They presented a mathematical formulation and heuristics based on Ant Colony Optimization (ACO) [6]. To support the ant algorithms, they proposed a Ride-Matching Heuristic (RMH) and a local search with multiple neighborhood operators, called Multi-neighborhood Local Search (MnLS). They tested the performances of the ant algorithms on 144 instances up to 500 vertices. One of these algorithms, the Multi-Strategy Ant Colony System (MS-ACS), provided the best results. They concluded that their most promising algorithm could improve with learning techniques to choose the source of information regarding the instance type and the search space.
In this study, a MAX-MIN Ant System (MMAS) adaptation to the QTSP-PIC, called Multi-Strategy MAX-MIN Ant System (MS-MMAS), is discussed. MMAS improves the design of Ant System [6], the first ACO algorithm, with three important aspects: only the best ants are allowed to add pheromone during the pheromone trail update; use of a mechanism for limiting the strengths of the pheromone trails; and, incorporation of local search algorithms to improve the best solutions. Plenty of recent studies proved good effectiveness of the MMAS in correlated problems to QTSP-PIC [7, 8, 9, 10]. However, none of these explored the Multi-Strategy (MS) concept.
In the traditional ant algorithms applied to Traveling Salesman Problem (TSP), ants use the arcs’ cost as heuristic information [6]. The heuristic information adopted is called visibility. When solving the QTSP-PIC, different types of decisions must be considered: the accomplishment of the minimum quota, management of the ride requests, and minimization of travel costs. The MS idea is to use different mechanisms of visibility for the ants to improve diversification. Every ant decides which strategy to use at random with uniform distribution. The MS proposed in this study extends the original implementation proposed in [5]. MS-MMAS also incorporates RMH and MnLS and uses a memory-based technique proposed in [11] to avoid redundant work. In MS-MMAS, a hash table stores every solution constructed and used as initial solutions to a local algorithm. When the algorithm constructs a new solution, it starts the local search phase if the new solution is not in the hash table.
The benchmark for the tests consisted of 144 QTSP-PIC instances. It was proposed by Silva et al. [5]. Numerical results confirmed the effectiveness of the MS-MMAS by comparing it to other ACO variants proposed in [5].
The main contributions of this chapter are summarized in the following.
The extension of the MS concept proposed in [5] with a roulette mechanism that orients the ants to choose their heuristic information based on the best quality solutions achieved;
Improvement of the MMAS design with a memory based technique proposed in [11];
Presentation of a novel MMAS variant that combines the improved MS concept and memory-based principles and assessment of its performance;
Experiments on a set of QTSP-PIC instances ranging: 10 to 500 cities; and 30 to 10.000 travel requests. The results showed that the proposed MMAS variant is competitive regarding the other three ACO variants presented in [5] for the QTSP-PIC.
The remainder of this chapter is organized as follows. Section 2 presents the QTSP-PIC and its formulation. Section 3 presents the Ant Colony Optimization metaheuristic and the implementation design of the MS-MMAS. Section 4 presents experimental results. The performance of the proposed ant-based algorithm is discussed in Section 5. Conclusions and future research directions are outlined in Section 6.
The TSP can be formulated as a complete weighted directed graph
The QTSP-PIC is a QTSP variant in which the salesman is the driver of a vehicle and can reduce travel costs by sharing expenses with passengers. There is a travel request, associated with each person demanding a ride, consisting of a pickup and a drop off point, a budget limit, a limit for the travel duration, and penalties associated with alternative drop-off points. There is a penalty associated with each point different from the destination demanded by each person. The salesman can accept or decline travel requests. This model combines elements of ride-sharing systems [14] with alternative destinations [4], and the selective pickup and delivery problem [15].
Let
The QTSP is NP-hard [13]. It is a particular case of the QTSP-PIC, in which the list of persons demanding a ride is empty and the time spent to collect the bonus in each vertex is zero. Thus, QTSP-PIC also belongs to the NP-hard class.
Silva et al. [5] presented an integer non-linear programming model for the QTSP-PIC. They defined a solution as
In the Ant Colony Optimization, artificial ants build and share information about the quality of solutions achieved with a communication scheme similar to what occurs with some real ants species. Deneubourg et al. [16] investigated the behavior of Argentine ants and performed some experiments, where there were two bridges between the nest and a food source. He observed that the ants initially walked on the two bridges at random, depositing pheromone in the paths. Over time, due to random fluctuations, the pheromone concentration of one bridge was higher than the other. Thus, more ants were attracted to that route. Finally, the whole colony ended up converging towards the same route. The behavior of artificial ants preserves four notions of the natural behavior of ants:
Pheromone deposit on the traveled trail;
Predilection for trails with pheromone concentration;
Concentration of the amount of pheromone in shorter trails;
Communication between ants through the pheromone deposit.
Pheromone is a chemical structure of communication [17]. According to Dorigo et al. [18], pheromone enables the process of stigmergy and self-organization in which simple agents perform complex and objective-oriented behaviors. Stigmergy is a particular form of indirect communication used by social insects to coordinate their activities [18].
Considering the context of ant algorithms applied to the TSP, when moving through the graph
The base-line of the Ant Colony Optimization is the algorithm Ant System [6]. In the TSP application,
The
Eqs. (4) and (5) show the formulas used to update pheromone trails, where
The ant algorithms proposed after AS improved its implementation design with elitist pheromone update strategies and local search algorithms to improve solutions [6]. Two well-known variants of AS are the Ant Colony System (ACS) [20] and MAX-MIN Ant System [21]. Silva et al. [5] presented AS and ACS adaptations for the QTSP-PIC. Section 3.1 presents the MAX-MIN Ant System algorithm.
MMAS uses Eq. (3) to compute the probability of an ant to move from vertex
There are three possibilities for the best route (
The implementation of the MMAS for the QTSP-PIC extends the original proposal [21] with the following adaptions:
Ants start at vertex
Ants include vertices in the route up to reach the minimum quota;
Solution
Use of the MS concept.
The ants in the MMAS, use arc costs to compute heuristic information. In the MS-MMAS, ants use four sources for this task, listed in the following.
Cost oriented: uses
Time oriented: uses
Quota oriented:
Passenger oriented: the heuristic information is
In the MS concept proposed in [5], every ant decides which strategy to use at random with uniform distribution. A roulette wheel selection improves this concept. The proportion of the wheel assigned to each heuristic information is directly related to the quality of solutions achieved. So, ants learn, at each iteration, the best heuristic information. At the final iterations, ants tend to use the heuristic information that proved to be most promising.
Algorithm 1 presents the pseudo-code of the MS-MMAS. It has the following parameters: maximum number of iterations (
Algorithm 1: MS-MMAS(
1.
2. Initialize pheromone trails
3. For
4.
5. For
6. For
7.
8.
9.
10. Update(
11. If
12.
13. Store(
14. Update(
15.
16. Pheromone_update(
17. Return
The algorithm sets
This section presents the methodology for the experiments and results from the experiments. Section 4.1 presents the methodology. Section 4.2 presents the parameters used in the MS-MMAS algorithm. Section 4.3 presents the results.
The experiments were executed on a computer with an Intel Core i5, 2.6 GHz processor, Windows 10, 64-bit, and 6GB RAM memory. The algorithms were implemented in C ++ lan and compiled with GNU g++ version 4.8.4. The benchmark set proposed in [5] was used to test the effectiveness of the MS-MMAS. The sizes of those instances range from 10 to 500 vertices. Small instances have up to 40 vertices, medium up to 100, and large more than 100 vertices. The instances are available for download at
The best, average results, and average processing times (in seconds) are reported from 20 independent executions of the MS-MMAS. Experiments are conducted to report the distance between the best-known solutions and the best results provided by the MS-MMAS. The variability in which the MS-MMAS achieved the best-known solutions stated in the benchmark set is also calculated. With these experiments, it is possible to conclude if the MS-MMAS algorithm was able to find the best-known solution of each instance and with what variability this happens.
The Friedman test [23] with the Nemenyi post-hoc procedure [24] are applied, with a significance level 0.05, to conclude about significant differences among the results of the MS-MMAS and the other three ACO variants proposed in this [5]. The instances were grouped according to their sizes (number of vertices) for the Friedman test. There are eight groups of symmetric (asymmetric) instances, each of them contains nine instances, called
The IRACE software was used, presented by [22], to tune the parameters of the MS-MMAS algorithm. 20 symmetric and 20 asymmetric instances were submitted to adjust the parameters. Those instances were selected at random. The IRACE uses the
For the asymmetric instance set, the parameters were defined as follows:
In this section, the results of the MS-MMAS are tested and compared to those produced by the other three ACO variants proposed in [5]: AS, ACS, and MS-ACS.
Table 1 presents the comparison between the ant algorithms. The best results obtained by MS-MMAS were compared with those achieved by each ant algorithm proposed in [5]. The results are in the
Asymmetric | Symmetric | |||||
---|---|---|---|---|---|---|
AS | ACS | MS-ACS | AS | ACS | MS-ACS | |
MS-MMAS | 68 x 0 | 68 x 1 | 45 x 17 | 66 x 1 | 68 x 2 | 48 x 14 |
Comparison between the ant algorithms.
Table 1 shows that the MS-MMAS was the algorithm that reported the best solution for most instances. This algorithm performed best than other ACO variants due to its enhanced pheromone update procedures. The MS implementation with roulette wheel selection proved to be effective at finding the best heuristic information used by the ants during the run. Table 1 also shows that the MS-MMAS provides results with better quality than the MS-ACS in the most symmetric cases. The MS-ACS was superior to the MS-MMAS in seventeen asymmetric cases and fourteen symmetric instances. Was observed that the pseudo-random action choice rule of MS-ACS [20], which allows for a greedier solution construction, proved to be a good algorithmic strategy for solving large instances.
Tables 2 and 3 shows the ranks of the ant algorithms based on the Friedman test [23] with the Nemenyi [24] post-hoc test. The first column of this Tables presents the subsets of instances grouped according to their sizes. The other columns of this Tables present the p-values of the Friedman test and the ranks from the Nemenyi post-hoc test. In the post-hoc test, the order ranks from
Asymmetric | |||||
---|---|---|---|---|---|
Subset | p-value | AS | ACS | MS-ACS | MS-MMAS |
0.003159 | b | b | a | a | |
0.000040 | b | c | a | a | |
0.000017 | c | c | a | a | |
0.000024 | b | c | a | a | |
0.000048 | c | c | b | a | |
0.000045 | b | c | a | a | |
0.000031 | b | c | a | a | |
0.000037 | c | b | a | a |
Results of Friedman’s test and Nemenyi post-hoc test over asymmetric instances set.
Symmetric | |||||
---|---|---|---|---|---|
Subset | p-value | AS | ACS | MS-ACS | MS-MMAS |
0.003543 | b | b | a | a | |
0.000205 | b | c | a | a | |
0.000045 | c | c | b | a | |
0.000059 | b | c | a | a | |
0.000035 | b | b | a | a | |
0.000024 | b | b | a | a | |
0.000045 | c | b | a | a | |
0.000098 | c | b | a | a |
Results of Friedman’s test and Nemenyi post-hoc test over symmetric instances set.
The p-values presented in Tables 2 and 3 show that the performance of the ant algorithms was not similar, i.e., the null hypothesis [24] is rejected in all cases. In these Tables, can be observed that MS-MMAS ranks higher than AS and ACS for all subsets. The ranks of MS-ACS and MS-MMAS were the same in the most cases. This implies that the performance of only these two algorithms where similar, i. e., the relative distance between the results achieved by these two algorithms are short.
To analyze the variability of the results provided by each ant algorithm compared to the best results so far for the benchmark set, three metrics regarding the results produced by the experiments were adopted. The first metric,
Asymmetric | ||||
---|---|---|---|---|
Metric | AS | ACS | MS-ACS | MS-MMAS |
4.30 | 2.56 | 6.8 | 11.84 | |
0.2075333 | 0.2773624 | 0.0541799 | 0.0054741 | |
0.2835401 | 0.4023659 | 0.1754952 | 0.5854892 |
Variability of the ants algorithms for asymmetric instances.
Symmetric | ||||
---|---|---|---|---|
Metric | AS | ACS | MS-ACS | MS-MMAS |
2.01 | 0.69 | 8.75 | 9.05 | |
0.2169756 | 0.2285948 | 0.0547890 | 0.0113889 | |
0.3017957 | 0.3620682 | 0.1656022 | 0.6432748 |
Variability of the ants algorithms for symmetric instances.
It can be observed from Tables 4 and 5 that the MS-MMAS is the best one concerning the
Tables 8 and 9 present the average processing time (in seconds) spent by each heuristic. Instances are grouped by the number of vertices. From these tables, it can be conclude that the MS-MMAS was the ant algorithm that demanded more processing time. Tables 6 and 7 (1) present detailed results concerning the average time required by the MS-MMAS. Data regarding the time consumption of the other ACO variants can be seen in [5].
Asymmetric | Symmetric | |||||||
---|---|---|---|---|---|---|---|---|
Instance | Best | Average | Time | Percentage | Best | Average | Time | Percentage |
A-10-3 | 478.42 | 863.13 | 0.15 | 100 | 545.92 | 996.34 | 0.15 | 25 |
A-10-4 | 523.57 | 1069.33 | 0.14 | 80 | 460.00 | 838.84 | 0.18 | 20 |
A-10-5 | 482.60 | 690.08 | 0.14 | 5 | 371.93 | 658.97 | 0.19 | 10 |
A-20-3 | 519.67 | 936.47 | 0.35 | 5 | 679.75 | 1363.59 | 0.32 | 20 |
A-20-4 | 458.10 | 1145.88 | 0.38 | 0 | 346.30 | 661.82 | 0.43 | 35 |
A-20-5 | 398.75 | 669.82 | 0.35 | 10 | 351.50 | 1006.24 | 0.48 | 5 |
A-30-3 | 618.33 | 1180.70 | 0.48 | 10 | 574.33 | 1469.68 | 0.50 | 5 |
A-30-4 | 401.20 | 805.32 | 1.28 | 5 | 654.80 | 1202.15 | 0.40 | 5 |
A-30-5 | 475.83 | 1033.91 | 0.58 | 10 | 464.05 | 911.56 | 0.66 | 5 |
A-40-3 | 692.00 | 1060.67 | 2.83 | 5 | 718.25 | 1399.04 | 0.72 | 10 |
A-40-4 | 658.95 | 1088.41 | 2.52 | 5 | 570.98 | 961.13 | 2.95 | 5 |
A-40-5 | 460.90 | 900.51 | 3.11 | 5 | 441.22 | 836.52 | 2.89 | 5 |
B-10-3 | 729.50 | 925.35 | 0.13 | 5 | 834.67 | 1485.47 | 0.20 | 20 |
B-10-4 | 306.90 | 421.35 | 0.13 | 15 | 493.58 | 757.45 | 0.16 | 10 |
B-10-5 | 434.75 | 835.01 | 0.18 | 55 | 726.35 | 1160.97 | 0.23 | 5 |
B-20-3 | 805.42 | 1251.39 | 0.28 | 10 | 950.00 | 1666.22 | 0.45 | 5 |
B-20-4 | 848.62 | 1366.69 | 0.35 | 5 | 822.82 | 1386.67 | 0.49 | 5 |
B-20-5 | 895.17 | 1275.78 | 0.28 | 70 | 660.22 | 1215.12 | 0.35 | 5 |
B-30-3 | 747.75 | 1316.96 | 1.31 | 5 | 718.67 | 1358.11 | 0.93 | 5 |
B-30-4 | 723.27 | 1301.57 | 1.51 | 5 | 650.35 | 1272.86 | 0.69 | 5 |
B-30-5 | 700.75 | 1205.96 | 1.39 | 5 | 504.68 | 1091.11 | 0.89 | 5 |
B-40-3 | 964.42 | 1574.00 | 2.02 | 0 | 889.83 | 1682.76 | 1.97 | 5 |
B-40-4 | 1195.62 | 2134.73 | 1.20 | 5 | 743.82 | 1508.16 | 2.09 | 0 |
B-40-5 | 819.28 | 1537.71 | 1.11 | 10 | 749.82 | 1351.64 | 0.85 | 5 |
C-10-3 | 359.25 | 604.70 | 0.17 | 55 | 597.83 | 697.51 | 0.05 | 0 |
C-10-4 | 307.10 | 514.66 | 0.20 | 5 | 408.45 | 514.65 | 0.15 | 85 |
C-10-5 | 566.58 | 783.35 | 0.17 | 10 | 409.60 | 846.51 | 0.23 | 10 |
C-20-3 | 650.25 | 978.84 | 0.46 | 10 | 629.92 | 1063.99 | 0.36 | 0 |
C-20-4 | 563.78 | 938.50 | 0.72 | 5 | 441.65 | 1019.96 | 1.06 | 10 |
C-20-5 | 739.22 | 1056.77 | 1.02 | 0 | 711.87 | 1095.84 | 0.63 | 5 |
C-30-3 | 837.58 | 1198.09 | 1.05 | 5 | 830.17 | 1221.65 | 0.61 | 10 |
C-30-4 | 754.10 | 1144.99 | 2.47 | 5 | 745.92 | 1096.55 | 1.16 | 5 |
C-30-5 | 560.18 | 998.28 | 2.29 | 10 | 490.80 | 931.81 | 2.21 | 5 |
C-40-3 | 1008.00 | 1541.54 | 2.59 | 5 | 607.00 | 946.57 | 3.45 | 10 |
C-40-4 | 695.30 | 1172.76 | 2.06 | 10 | 699.80 | 1136.17 | 2.25 | 0 |
C-40-5 | 623.33 | 1097.22 | 3.24 | 10 | 475.67 | 898.80 | 7.82 | 0 |
Results of the MS-MMAS executions for small instances.
Asymmetric | Symmetric | |||||||
---|---|---|---|---|---|---|---|---|
Instance | Best | Average | Time | Percentage | Best | Average | Time | Percentage |
A-50-3 | 1058.33 | 2128.68 | 2.31 | 5 | 1000.33 | 1943.13 | 2.91 | 5 |
A-50-4 | 774.93 | 1473.57 | 4.48 | 5 | 783.40 | 1345.19 | 3.53 | 5 |
A-50-5 | 673.42 | 1314.54 | 4.16 | 5 | 583.08 | 1008.33 | 2.59 | 0 |
A-100-3 | 1431.42 | 2046.96 | 53.44 | 5 | 1514.08 | 2292.08 | 15.66 | 20 |
A-100-4 | 1456.47 | 2705.07 | 23.12 | 5 | 1165.90 | 1595.91 | 37.11 | 5 |
A-100-5 | 1106.17 | 1778.38 | 40.57 | 10 | 980.28 | 1366.09 | 58.20 | 5 |
A-200-3 | 2806.75 | 3610.22 | 424.60 | 0 | 2793.33 | 3272.00 | 257.42 | 0 |
A-200-4 | 2388.88 | 3196.15 | 381.07 | 0 | 2199.45 | 2807.06 | 79.32 | 10 |
A-200-5 | 1753.00 | 2286.08 | 1380.26 | 10 | 2086.82 | 3237.85 | 55.37 | 10 |
A-500-3 | 6878.42 | 7165.39 | 1641.92 | 33 | 6331.75 | 7679.65 | 732.94 | 10 |
A-500-4 | 5572.42 | 5637.26 | 4939.84 | 0 | 5030.48 | 5080.66 | 913.82 | 0 |
A-500-5 | 4389.92 | 4539.44 | 16990.77 | 50 | 4610.95 | 4696.91 | 73.97 | 33 |
B-50-3 | 1338.42 | 2356.24 | 5.82 | 10 | 966.42 | 1770.88 | 4.60 | 5 |
B-50-4 | 951.87 | 1757.61 | 5.00 | 5 | 772.67 | 1490.01 | 1.47 | 5 |
B-50-5 | 1083.18 | 1943.22 | 3.91 | 5 | 692.42 | 1342.78 | 4.74 | 5 |
B-100-3 | 1781.00 | 3115.78 | 30.96 | 5 | 1803.33 | 3258.90 | 15.11 | 5 |
B-100-4 | 1409.65 | 2467.02 | 61.76 | 5 | 1648.58 | 3360.93 | 11.00 | 5 |
B-100-5 | 1361.20 | 2734.24 | 39.89 | 5 | 1018.37 | 1536.34 | 99.02 | 5 |
B-200-3 | 3302.83 | 4840.94 | 317.37 | 0 | 3016.67 | 4267.17 | 56.62 | 0 |
B-200-4 | 2536.80 | 3477.13 | 681.75 | 0 | 2326.97 | 3139.57 | 81.34 | 10 |
B-200-5 | 2127.88 | 2814.24 | 906.74 | 0 | 1893.67 | 2506.64 | 102.33 | 10 |
B-500-3 | 6994.84 | 7203.61 | 3857.77 | 0 | 6433.92 | 6475.67 | 126.51 | 0 |
B-500-4 | 5419.87 | 5730.97 | 24183.87 | 100 | 5191.77 | 5276.98 | 267.72 | 0 |
B-500-5 | 4546.28 | 4643.03 | 21118.98 | 0 | 4379.43 | 4494.11 | 164.08 | 33 |
C-50-3 | 1201.92 | 1801.68 | 3.12 | 5 | 829.75 | 1482.86 | 2.82 | 5 |
C-50-4 | 937.25 | 1651.11 | 7.96 | 5 | 901.40 | 1605.24 | 6.16 | 10 |
C-50-5 | 609.60 | 1127.99 | 16.58 | 5 | 766.48 | 1366.58 | 7.43 | 5 |
C-100-3 | 1496.58 | 2001.76 | 47.62 | 0 | 1364.00 | 1819.03 | 14.21 | 10 |
C-100-4 | 1352.85 | 2458.82 | 32.32 | 5 | 1099.00 | 1445.29 | 23.98 | 0 |
C-100-5 | 1022.70 | 1466.42 | 127.11 | 0 | 991.12 | 1472.23 | 35.21 | 5 |
C-200-3 | 2629.00 | 3197.13 | 478.90 | 10 | 2510.50 | 3171.66 | 65.07 | 10 |
C-200-4 | 2184.85 | 2648.38 | 710.70 | 10 | 2141.40 | 2741.11 | 52.59 | 0 |
C-200-5 | 1881.03 | 2296.53 | 486.62 | 0 | 1713.17 | 2127.84 | 126.85 | 10 |
C-500-3 | 6528.08 | 6618.16 | 2484.52 | 0 | 6023.42 | 6087.14 | 138.12 | 33 |
C-500-4 | 5139.54 | 5298.21 | 8188.46 | 0 | 4942.28 | 4958.64 | 65.19 | 33 |
C-500-5 | 4286.45 | 4278.49 | 6061.78 | 0 | 4167.67 | 4178.10 | 302.79 | 0 |
Results of the MS-MMAS executions for medium and large instances.
n | AS | ACS | MS-ACS | MS-MMAS |
---|---|---|---|---|
10 | 0.05 | 0.06 | 0.12 | 0.15 |
20 | 0.10 | 0.13 | 0.26 | 0.46 |
30 | 0.20 | 0.30 | 1.92 | 1.37 |
40 | 0.34 | 0.48 | 2.29 | 2.29 |
50 | 0.41 | 2.20 | 5.77 | 5.92 |
100 | 6.68 | 28.85 | 32.69 | 50.75 |
200 | 31.81 | 270.94 | 409.72 | 640.89 |
500 | 41.72 | 3477.13 | 3545.20 | 9940.87 |
Average time spent by the ant algorithms for the set of asymmetric instances.
n | AS | ACS | MS-ACS | MS-MMAS |
---|---|---|---|---|
10 | 0.05 | 0.06 | 0.12 | 0.17 |
20 | 0.10 | 0.13 | 0.27 | 0.51 |
30 | 0.18 | 0.24 | 0.49 | 0.89 |
40 | 0.28 | 0.38 | 0.73 | 2.78 |
50 | 0.40 | 0.56 | 5.41 | 4.02 |
100 | 8.13 | 13.51 | 29.17 | 34.93 |
200 | 22.94 | 51.92 | 112.58 | 97.43 |
500 | 40.53 | 75.72 | 127.83 | 309.46 |
Average time spent by the ant algorithms for the set of symmetric instances.
The purpose of this study was to adapt MMAS to the QTSP-PIC and compare its performance with the ACO variants proposed in [5]. As expected, MS-MMAS proved to be competitive regarding the other ACO variants proposed to solve QTSP-PIC. Similarities and differences that were observed in the results are discussed in section 5.1. The limitations of the study are discussed in Section 5.2.
The ACO algorithms proposed by Silva et al. [5] showed to be a viable method for solving QTSP-PIC. Yet, the performance of AS and ACS algorithms, when compared to MS-MMAS, was rather poor for the benchmark set studied. MS-MMAS improved the results achieved by AS in 134 instances. Compared to ACS, MS-MMAS performed better in 136 instances. The results achieved by MS-MMAS improved those produced by MS-ACS in 93 instances. It is interesting to note that the MS-ACS algorithm performed slightly better on the large instances than the MS-MMAS. The Friedman test and Nemenyi post-hoc ranked these two ACO algorithms with the same scale for the most instance groups, which means that difference between the results achieved by the MS-ACS and MS-MMAS was significantly small.
These observations are also supported by the variability results of each ACO algorithm. Metric
Results presented in this study showed that the MS-MMAS algorithm is better suited than the other three ACO variants proposed in [5] to solve QTSP-PIC. This suggests a positive impact of the implementation design proposed in this study and a contribution to the MAX-MIN Ant System state of the art.
Due to limited time, parallel computing techniques could not be tested to improve the performance of MS-MMAS. A previous study done by Skinderowicz [10] investigated the potential effectiveness of a GPU-based parallel MAX-MIN Ant System in solving the TSP. In this study, the most promising MMAS variant was able to generate over 1 million candidate solutions per second when solving a large instance of the TSP benchmark set. Other techniques can improve the MS-MMAS design and could not be tested due to the lack of time:
This work dealt with a recently proposed variant of the Traveling Salesman Problem named The Quota Traveling Salesman Problem with Passengers, Incomplete Ride, and Collection Time. In this problem, the salesman uses a flexible ride-sharing system to minimize travel costs while visiting some vertices to satisfy a pre-established quota. He must respect the budget limitations and the maximum travel time of every passenger. Each passenger can be transported directly to the desired destination or an alternate destination. The alternative destination idea suggests that when sharing a ride, pro-environmental or money-saving concerns can induce persons to agree to fulfill their needs at a similar destination. Operational constraints regarding vehicle capacity and travel time were also considered.
The Multi-Strategy MAX-MIN Ant System, a variant from the Ant Colony Optimization (ACO) family of algorithms, was presented. This algorithm uses the MS concept improved with roulette wheel selection and memory-based principles to avoid redundant executions of the local search algorithm. The results of MS-MMAS were compared with those produced by the ACO algorithms presented in [5]. To support MS-MMAS, the ride-matching heuristic and the local search heuristic based on multiple neighborhood operators proposed by [5] were reused.
The computational experiments reported in this study comprised one hundred forty-four instances. The experimental results show that the proposed ant algorithm variant could update the best-known solutions for this benchmark set according to the statistical results. The comparison results with three other ACO variants proposed in [5] showed that MS-MMAS improved the best results of MS-ACS for ninety-three instances, and a significant superiority of MS-MMAS over AS and ACS.
The presented work may be extended in multiple directions. First, it would be interesting to investigate if the application of the pseudo-random action choice rule [20] could improve the MS-MMAS results. Another further promising idea is the use of pheromone update rule based on ants ranking [25]. Extension of the MS-MMAS implementation design with parallel computing techniques [10] and hybridization with other meta-heuristics [26, 27, 28] is other interesting opportunity for the future research.
MaaS | Mobility as a Service |
QTSP-PIC | Quota Traveling Salesman Problem with Passengers, Incomplete Ride and Collection Time |
ACO | Ant Colony Optimization |
RMH | Ride-Matching Heuristic |
MnLS | Multi-neighborhood Local Search |
MS-ACS | Multi-Strategy Ant Colony System |
MMAS | MAX-MIN Ant System |
MS-MMAS | Multi-Strategy MAX-MIN Ant System |
MS | Multi-Strategy |
TSP | Traveling Salesman Problem |
QTSP | Quota Traveling Salesman Problem |
AS | Ant System |
ACS | Ant Colony System |
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