Standard deviations from the respective average percentage of interesting cells found by six-member teams in \n
\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
\n'}],latestNews:[{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"},{slug:"oiv-awards-recognizes-intechopen-s-editors-20201127",title:"OIV Awards Recognizes IntechOpen's Editors"},{slug:"intechopen-joins-crossref-s-initiative-for-open-abstracts-i4oa-to-boost-the-discovery-of-research-20201005",title:"IntechOpen joins Crossref's Initiative for Open Abstracts (I4OA) to Boost the Discovery of Research"},{slug:"intechopen-hits-milestone-5-000-open-access-books-published-20200908",title:"IntechOpen hits milestone: 5,000 Open Access books published!"},{slug:"intechopen-books-hosted-on-the-mathworks-book-program-20200819",title:"IntechOpen Books Hosted on the MathWorks Book Program"}]},book:{item:{type:"book",id:"3266",leadTitle:null,fullTitle:"Type 1 Diabetes",title:"Type 1 Diabetes",subtitle:null,reviewType:"peer-reviewed",abstract:"This book contains a series of up-to-date chapters that review our current knowledge of type 1 diabetes as an autoimmune disease, the problems that still remain with existing treatments, and possible solutions for the near future.",isbn:null,printIsbn:"978-953-51-1017-0",pdfIsbn:"978-953-51-7102-7",doi:"10.5772/45927",price:159,priceEur:175,priceUsd:205,slug:"type-1-diabetes",numberOfPages:626,isOpenForSubmission:!1,isInWos:1,hash:"21684525ccb8c6acd89bc43ce177f90b",bookSignature:"Alan P. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3621",title:"Silver Nanoparticles",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"silver-nanoparticles",bookSignature:"David Pozo Perez",coverURL:"https://cdn.intechopen.com/books/images_new/3621.jpg",editedByType:"Edited by",editors:[{id:"6667",title:"Dr.",name:"David",surname:"Pozo",slug:"david-pozo",fullName:"David Pozo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"64304",title:"Team Exploration of Environments Using Stochastic Local Search",doi:"10.5772/intechopen.81902",slug:"team-exploration-of-environments-using-stochastic-local-search",body:'\nAutonomous agents in complex environments may need to work together as teams to achieve desired goals. This is an important feature of most multiagent environments where individual agents lack all the required capabilities, skills, and knowledge to complete tasks alone. These environments can model real-world problem domains where agents’ knowledge and available time to complete tasks in such domains are limited. Agents may thus resort to team formation to complete tasks. Team formation or coalition formation are simple models of short-term cooperation [1, 2] where agents complete specific tasks.
\nExamples of team formation can be found in business (e.g., organizations forming teams to make more sales and hence, more profits), in academia (e.g., professors forming teams to publish articles), in search and rescue (e.g., robotic agents forming teams in large natural disaster environments to save life and property), and in network security (e.g., agents forming teams to determine critical points where checkpoints should be placed in a network to hinder adversaries’ communication or movement). Since our mundane day to day activities are not exempted from team formation, we cooperate with others to solve problems that may be otherwise difficult for us to complete alone. A number of factors can be attributed to this difficulty, including time criticality of tasks, distribution of individual skills and resources, the need for an agent’s presence in multiple work places simultaneously, and many more. An interesting number of works have employed various forms of team formation and search strategies in solving problems related to search or exploration. See for example the works of [3, 4, 5, 6, 7, 8, 9].
\nHere is a straightforward motivation for the problem we study. Consider a rescue operation in an aircraft crash site where search for survivors may be guaranteed in the first few hours of the crash. Agents neither know where survivors are located nor have enough time to explore the environment for victims. They need, preferably as teams, to devise methods that systematically explore the environment to achieve the desired goal. It is not difficult to see that this example and many other similar real-world domains can be modeled as that of search problems. This obviously raises the following important question: How can teams of agents efficiently explore relatively difficult environments using appropriate search strategies that achieve acceptable outcomes? This research provides an investigation of the use of Stochastic Local Search (SLS) technique to explore complex environments where agents’ knowledge and the time to explore such environments are limited. We model the problem as that of an instance of a search problem and develop SLS techniques that enable intelligent exploration of such relatively difficult environments by teams of agents.
\nSLS algorithms have made significant success in solving many hard problems [10] which involve search of well-defined solutions spaces (or states). A model of SLS algorithms is defined to include a neighborhood and an evaluation function—both of which are specific to different problems. The goal of an agent using SLS algorithm is to seek a state \n
We model the problem described in the motivation above by using three different two-dimensional grids to represent environments that agents need to explore. Some cells within the grids are referred to as being “interesting,” such as possibly having victims in them. We then randomly distribute goals among the interesting cells. Goals in this work represent some desirable situation that we want agents to achieve. In the motivation above, the presence of a victim in an interesting cell will represent a goal. The three environments are further constrained such that not all interesting cells contain goals, thus agents do not have background knowledge of the environments. Agents in our model are required to devise techniques to search and find as many goals within a limited amount of time steps. The performance of agents in these environment are evaluated based on a number of factors, including the amount of goals found with respect to the number of agents in teams, type, and size of environments. The main contributions of this work are as follows:
We provide a formalization of the concept of state and neighborhood in three different simulated random, clumped, and linear environments described in [12].
We provide agents performance evaluation in the three environments using the number of interesting cells found by teams as done in [12] and our previous work [13]. We further modify the environments to include limited number of goals that are randomly distributed among the interesting cells. Agents in this case are thus required to search for goals rather than interesting cells as done in [12, 13].
We model agents, their methods of movements in the environments, and provide a clever design of an evaluation function that agents can use to navigate the three environments.
Finally, we provide an implementation of a model that allows agents to operate on these environments using the proposed evaluation function.
Several simulations to mimic real-world environments were completed using different dimensions of the three environments and varying agents’ team sizes. The results of these simulations compare favorably with those of a previous work that was used as a benchmark. In particular, the proposed model avoids such expensive cost of extensive time requirements of evolutionary learning by agents. This is made possible as agents in this model are not subjected to training before being deployed to the testing environments. They only conduct local searches of the environments from their current locations using two important features from the SLS algorithms: neighborhood and evaluation function.
\nSLS algorithms have been successfully applied to many hard problems including Traveling Salesman Problem, Graph Coloring Problem, Satisfiability Problem in Propositional Logic, and more [10, 14]. Common SLS algorithms include simulated annealing, hill climbing, and evolutionary inspired genetic algorithms [15]. As highlighted in the previous section, the definitions of a neighborhood and its associated evaluation function in SLS algorithms are specific to the problem domain. The real novelty in the employment of SLS techniques to construct an algorithm comes from how elegant the neighborhood and the evaluation function are defined for the problem domain such that the algorithm is well-guided towards feasible solutions within a short period of time.
\nSoule and Heckendorn [12] describe three environments on which their work is based. We reproduce these environments and their descriptions since we have used them to evaluate our proposed SLS technique. Each of the three environments is composed of two-dimensional grids of \n
The environments are named according to how the number of interesting cells are distributed in the grids. They are referred to as random, clumped, and linear. Figures 1–3 depict sample schematic views of random, clumped, and linear environments for a \n
A schematic view of a random environment for a \n\n45\n×\n45\n\n two-dimensional grid.
A schematic view of a clumped environment for a \n\n45\n×\n45\n\n two-dimensional grid.
A schematic view of a linear environment for a \n\n45\n×\n45\n\n two-dimensional grid.
Soule and Heckendorn use evolutionary algorithms to implement a multiagent team training algorithm called Orthogonal Evolution of Teams (OET) to evolve teams of agents. The three environments above alternatively serve as both the training and testing environments to evaluate the performance of their OET algorithm. They consider evolution of heterogeneous multiagent teams (i.e., teams of agents with specialized roles). There are two types of specialized agents in their work: scouts and investigators. The scouts and investigators are respectively responsible for finding as much as possible interesting cells and marking them as investigated. Unlike our approach however, where all agents are limited to moves of length one in a single time step in the environments, the scouts are allowed a move of length two in a single time step. Results from our work using SLS technique to explore different environments compare with those of Soule and Heckendorn’s with performances within similar ranges. However, it is not yet clear how fair that comparison can be justified since their work employs evolutionary algorithm which come with extensive time requirements of evolutionary learning and huge time and costs of training for agents before they are deployed to actual testing environments.
\nGiven any of the three environments (i.e., random, linear, and clumped) described in the previous section and a number of autonomous agents (each with a limited knowledge of the environments), the problem we attempt to solve is to form teams of agents that intelligently explore as much as possible interesting cells and/or goals in the grids within a limited amount of time. Our attempt in solving this problem uses a model that employs techniques from SLS algorithms. We provide in this section, a formalization of the framework and implementation details for state and neighborhood, evaluation function, and a description of the simulation employed in our research.
\nWe present our framework of the concept of state and neighborhood in any of the three environments. Denote by \n A state \n
It is clear from Definition 3.1 that a state is composed of a \n The neighborhood \n
A view of a state (with reference cell \n\n\nc\nij\n\n\n), denoted \n\ns\n\n, and a neighborhood \n\nN\n\ns\n\n\n for \n\ns\n\n. \n\nN\n\ns\n\n=\n\n\ns\n1\n\n\ns\n2\n\n\ns\n3\n\n\ns\n4\n\n\n.\n\n
Figure 4 shows an example of a neighborhood \n
A schematic view of some possible neighborhoods for different states with reference cells, \n\n\nc\nij\n\n\n.
We present implementation details of the framework developed in the previous section. We provide abstraction of state and neighborhood in an environment using the Java programming language. The following Java classes, \n
We first consider how to locate a state in an environment. Using the Agent class above, an agent is always aware of its current location. All agents start exploration of an environment from some locations that are determined randomly. These locations correspond to certain reference cells in the environment’s grid. No two agents are allowed to start from the same reference cell. Since a state is made up of a \n
Thus, it is straightforward to determine the states that all the cells in the grid of an environment belongs. Given a reference cell for a state, the following provides an implementation that returns the start indices of the state.
When a state has been explored by an agent, the state is marked as investigated. A state is considered visited if the reference cell for the state and all of its immediate cells have been marked as investigated. Since agents are always aware of their locations, we implement this functionality for each agent using the following method:
Parameter refCell is the reference cell of the state, gridSize is the size of the grid, and visitedCell is a boolean \n
Given the reference cell of a state, the method getNeighborhood above provides an implementation that determines the neighborhood of that state. The method first checks the location of the reference cell to determine the size of the neighborhood, then returns the appropriate states in the neighborhood as demonstrated in Figure 5. For the part of the code shown in the method, the reference cell of the state, say, \n
Agents in our model use an evaluation function to guide selection of successor states to transit into. The evaluation function depends on the framework of the state and neighborhood we developed in the previous section. Algorithm 1 gives the pseudocode of our evaluation function.
\nAlgorithm 1: \n | \n
---|
Input: Agent \n Output: A successor state \n 1: procedure \n 2: \n 3: for each state \n 4: if \n 5: if there exists no other agent \n 6: \n 7: if \n 8: randomly select an \n 9: else 10: randomly select an \n 11: return \n 12: end procedure | \n
Algorithm 1 i.e., SuccessorState \n
Suppose an agent \n
Observe that the number of attempts required by the evaluation function until any one of the three states in \n
We form teams consisting of a certain number of agents. One of the team’s members is designated as a leader. We assume that the leader has some additional computational power than other members. The leader is responsible for maintaining an updated status (i.e., visited states) and communicates same to other members when requested. The leader answers the following queries from members: Has a given state been visited? and Is there an agent in a given state? These are the queries that are used by the evaluation function. The leader agent does not participate in the actual exploration of individual states. Other agents are responsible for locating and visiting interesting cells and as well as finding goals in the grids. All visited cells, either interesting or not, and whether goals are found or not are marked as investigated. An agent can move from her current location in only one of four directions (i.e., north, east, west, and south) and is limited to moves of length one in a single time step. The following three actions, goForward, turnLeft, and turnRight are made available to all agents except the leader.
\nWhen starting, all agents (except the leader) are randomly distributed in the environment. We describe the procedure used by agents to explore the environments next. Imagine an agent \n
Figure 6(a) provides a simple illustration of an agent currently in a state with reference cell \n
Exhaustive search of a state by agents. (a) Agent exits reference cell \n\nx\n\n, search current state in the direction of the arrows, and transits into \n\n\ns\n4\n\n\n with reference \n\ny\n\n. (b) Agent exits reference cell \n\nx\n\n, search current state in the direction of arrows, and transits into \n\n\ns\n1\n\n\n with reference cell \n\ny\n\n.
Figure 7 shows an example of a random environment with an initial deployment of six agents (red pictures with arrow heads) in the environment. There are also currently ten goals (diamond pictures in yellow) that are also randomly distributed across the grid. The agents will search the environment using the evaluation function and the concept of neighborhood proposed in this work to guide their search. A snapshot of what the search area looks like after few time steps of exploration is shown in Figure 8. The highlighted areas covered in green have been explored by agents, while the white areas are yet to be explored. Also, the rectangle of agents shown together illustrate an exhaustive search of that state by an agent. We make the rectangle of agents disappear in the real simulation when the agent complete exploration of the state.
\nRandom environment showing initial deployment of agents (red) and goals (yellow).
Random environment showing partial search of the environment by agents. The highlighted areas covered in green have been explored by agents.
We present results of our extensive simulations in this section. Our findings are based on two different sets of experiments—first, on the percentage of interesting cells found by agents, and second, on the average number of goals found by agents in the three environments. For our study, we use a different set of parameters to include number of agents in teams, size, and type (random, linear, and clumped) of environments.
\nFigure 9 shows the average percentage of interesting cells found by six-member teams of agents for \n
Average percentage of interesting cells found by six-member teams in \n\n45\n×\n45\n\n grid environments.
\n | Random | \nClumped | \nLinear | \n
---|---|---|---|
Standard deviation | \n\n\n | \n\n\n | \n\n\n | \n
Standard deviations from the respective average percentage of interesting cells found by six-member teams in \n
The average percentage of interesting cells found by agents’ teams using the SLS model provides a measure of the level of difficulty of the three environments for the teams. This conversely implies a measure of the relative performance of the teams in each of the environments. Figure 7 shows that the relative performance of the teams in the random environment (\n
An implication of the closeness of the level of difficulty of the three environments is that the SLS model’s performance has less reliance on these environments. Contrarily, Soule and Heckendorn [12] have shown that the performance of the evolved teams by their model depends on both the training and testing environments. They show that training in either the random or clumped environment is a good training for the other environment, but neither is as good of a training environment for the linear environment. In fact, the performance of the evolved teams when they are trained in either of random or clumped, and later deployed in linear environment, is poor in comparison with when they are deployed in either the random or clumped environment. Recall also that agents in our model are not subjected to training before being deployed to the testing environments. They only conduct local searches of their environments using two important features from SLS algorithms: neighborhood and evaluation function.
\nFor the next set of experiments, we evaluate the effectiveness of the SLS model by measuring the average percentage of interesting cells found by agents’ teams, varying the number of agents in the teams, and the grid sizes in the three environments. Figure 10 shows the average percentage of interesting cells found by agents’ teams of different sizes in \n
Average percentage of interesting cells found by agents’ teams of different sizes in \n\n45\n×\n45\n\n grid environments.
The six-member teams always discover more than \n
Increasing the number of agents in the teams beyond ten does not appear to improve average performance of agents. We noticed marginal decrease in the average performance of larger teams—as teams’ sizes increase past \n
Figure 11 shows the average percentage of interesting cells found by six-member teams for different grid sizes in the three environments. The \n
Average percentage of interesting cells found by six-member teams for different grid sizes of environments.
The results show, perhaps not too surprising that in general, the average performance of the teams degrade for the three environments as the dimension of the grids increases. A partial explanation for this is that fixing the team size while increasing the dimension of the environments makes members of the teams to be sparsely distributed in the environments. Thus, it will then be more difficult for agents to cooperate as they now require several time steps to move closer to one another in order to cover different parts of the grids. Nonetheless, even at higher dimensions of the grids, agents’ teams are still able to achieve some reasonable level of performance. For instance, when the grid size is \n
This second part of the experiments is based on the average number of goals found by agents’ teams. We set the number of goals that are randomly distributed in the environments to be \n
Average number of goals found by agents’ teams for different grid sizes in the random environment.
Average number of goals found by agents’ teams for different grid sizes in the clumped environment.
Average number of goals found by agents’ teams for different grid sizes in the linear environment.
The results we observe from the figures suggest that the performance of agents’ teams in the three environments are similar and consistent for agents’ teams, environment types, as well as for the various grid sizes. It is interesting to see that all teams of agents were able to find on average all the \n
We are interested in the lessons to be learnt from these experiments, as well as the implications of the similarity and consistency of the results across the three environments. The outcomes from these experiments suggest that our proposed SLS method is independent of the three environments, thus, agents using our search procedures are expected to perform about the same in any of the environments. This is also a confirmation of the results for agents’ teams in the three environments when they are expected to find as many interesting cells from the previous section.
\nWe consider an investigation of the use of Stochastic Local Search (SLS) technique to explore complex environments where agents’ knowledge and the time to explore such environments are limited. We model the problem as that of an instance of a search problem and develop a SLS technique that enables efficient exploration of such relatively difficult environments by teams of agents. Thus, we provide extensions to the work of Soule and Heckendorn [12] that uses evolutionary algorithms in evolving multiagent teams in the three different simulated random, clumped, and linear environments described in their work. We first provide a formalization of the concept of state and neighborhood in these environments and provide agents’ performance evaluations in the three environments using the number of interesting cells found by teams as done in [12] and our previous work [13]. We further modify the environments to include a limited number of goals that are randomly distributed among the interesting cells. Agents in this case are thus required to search for goals rather than interesting cells.
\nExperiments using agents’ teams of different sizes implementing our model in different problem environments show the effectiveness of our technique. In most cases of the problem instances, teams of agents were able to complete exploration of more than \n
We also evaluate the performance of agents’ teams in another set of experiments requiring agents to search for goals in the three environments. It is interesting to note that all teams of agents were able to find on average all the goals in the three environments when the size of the grid is \n
There are several areas of ongoing research on this problem. Here are some directions for future work. A drawback of Soule and Heckendorn’s model is the unlimited vision of the environments by all agents in their work. We avoid this problem by ensuring that agents in our model have only limited vision of the environments except the team leader that still has unlimited vision of the environments. We plan to address this issue in future work. Our proposed SLS model in this work still has some limitations. The search approach by the model is uninformed, thus, agents exhaustively search all states by slowly branching out of their neighborhood from their starting locations. We have commenced improvement of our model by allowing agents to do more informed search of the environments by using cleverly designed and admissible heuristics to guide the search. The expectation is that agents will now have direction of the search towards the goals in the environments at every new time step.
\nAutonomous agents in complex environments may need to work together as teams to achieve desired goals. This is an important feature of most multiagent environments where individual agents lack all the required capabilities, skills, and knowledge to complete tasks alone. These environments can model real-world problem domains where agents’ knowledge and available time to complete tasks in such domains are limited. Agents may thus resort to team formation to complete tasks. Team formation or coalition formation are simple models of short-term cooperation [1, 2] where agents complete specific tasks.
\nExamples of team formation can be found in business (e.g., organizations forming teams to make more sales and hence, more profits), in academia (e.g., professors forming teams to publish articles), in search and rescue (e.g., robotic agents forming teams in large natural disaster environments to save life and property), and in network security (e.g., agents forming teams to determine critical points where checkpoints should be placed in a network to hinder adversaries’ communication or movement). Since our mundane day to day activities are not exempted from team formation, we cooperate with others to solve problems that may be otherwise difficult for us to complete alone. A number of factors can be attributed to this difficulty, including time criticality of tasks, distribution of individual skills and resources, the need for an agent’s presence in multiple work places simultaneously, and many more. An interesting number of works have employed various forms of team formation and search strategies in solving problems related to search or exploration. See for example the works of [3, 4, 5, 6, 7, 8, 9].
\nHere is a straightforward motivation for the problem we study. Consider a rescue operation in an aircraft crash site where search for survivors may be guaranteed in the first few hours of the crash. Agents neither know where survivors are located nor have enough time to explore the environment for victims. They need, preferably as teams, to devise methods that systematically explore the environment to achieve the desired goal. It is not difficult to see that this example and many other similar real-world domains can be modeled as that of search problems. This obviously raises the following important question: How can teams of agents efficiently explore relatively difficult environments using appropriate search strategies that achieve acceptable outcomes? This research provides an investigation of the use of Stochastic Local Search (SLS) technique to explore complex environments where agents’ knowledge and the time to explore such environments are limited. We model the problem as that of an instance of a search problem and develop SLS techniques that enable intelligent exploration of such relatively difficult environments by teams of agents.
\nSLS algorithms have made significant success in solving many hard problems [10] which involve search of well-defined solutions spaces (or states). A model of SLS algorithms is defined to include a neighborhood and an evaluation function—both of which are specific to different problems. The goal of an agent using SLS algorithm is to seek a state \n
We model the problem described in the motivation above by using three different two-dimensional grids to represent environments that agents need to explore. Some cells within the grids are referred to as being “interesting,” such as possibly having victims in them. We then randomly distribute goals among the interesting cells. Goals in this work represent some desirable situation that we want agents to achieve. In the motivation above, the presence of a victim in an interesting cell will represent a goal. The three environments are further constrained such that not all interesting cells contain goals, thus agents do not have background knowledge of the environments. Agents in our model are required to devise techniques to search and find as many goals within a limited amount of time steps. The performance of agents in these environment are evaluated based on a number of factors, including the amount of goals found with respect to the number of agents in teams, type, and size of environments. The main contributions of this work are as follows:
We provide a formalization of the concept of state and neighborhood in three different simulated random, clumped, and linear environments described in [12].
We provide agents performance evaluation in the three environments using the number of interesting cells found by teams as done in [12] and our previous work [13]. We further modify the environments to include limited number of goals that are randomly distributed among the interesting cells. Agents in this case are thus required to search for goals rather than interesting cells as done in [12, 13].
We model agents, their methods of movements in the environments, and provide a clever design of an evaluation function that agents can use to navigate the three environments.
Finally, we provide an implementation of a model that allows agents to operate on these environments using the proposed evaluation function.
Several simulations to mimic real-world environments were completed using different dimensions of the three environments and varying agents’ team sizes. The results of these simulations compare favorably with those of a previous work that was used as a benchmark. In particular, the proposed model avoids such expensive cost of extensive time requirements of evolutionary learning by agents. This is made possible as agents in this model are not subjected to training before being deployed to the testing environments. They only conduct local searches of the environments from their current locations using two important features from the SLS algorithms: neighborhood and evaluation function.
\nSLS algorithms have been successfully applied to many hard problems including Traveling Salesman Problem, Graph Coloring Problem, Satisfiability Problem in Propositional Logic, and more [10, 14]. Common SLS algorithms include simulated annealing, hill climbing, and evolutionary inspired genetic algorithms [15]. As highlighted in the previous section, the definitions of a neighborhood and its associated evaluation function in SLS algorithms are specific to the problem domain. The real novelty in the employment of SLS techniques to construct an algorithm comes from how elegant the neighborhood and the evaluation function are defined for the problem domain such that the algorithm is well-guided towards feasible solutions within a short period of time.
\nSoule and Heckendorn [12] describe three environments on which their work is based. We reproduce these environments and their descriptions since we have used them to evaluate our proposed SLS technique. Each of the three environments is composed of two-dimensional grids of \n
The environments are named according to how the number of interesting cells are distributed in the grids. They are referred to as random, clumped, and linear. Figures 1–3 depict sample schematic views of random, clumped, and linear environments for a \n
A schematic view of a random environment for a \n\n45\n×\n45\n\n two-dimensional grid.
A schematic view of a clumped environment for a \n\n45\n×\n45\n\n two-dimensional grid.
A schematic view of a linear environment for a \n\n45\n×\n45\n\n two-dimensional grid.
Soule and Heckendorn use evolutionary algorithms to implement a multiagent team training algorithm called Orthogonal Evolution of Teams (OET) to evolve teams of agents. The three environments above alternatively serve as both the training and testing environments to evaluate the performance of their OET algorithm. They consider evolution of heterogeneous multiagent teams (i.e., teams of agents with specialized roles). There are two types of specialized agents in their work: scouts and investigators. The scouts and investigators are respectively responsible for finding as much as possible interesting cells and marking them as investigated. Unlike our approach however, where all agents are limited to moves of length one in a single time step in the environments, the scouts are allowed a move of length two in a single time step. Results from our work using SLS technique to explore different environments compare with those of Soule and Heckendorn’s with performances within similar ranges. However, it is not yet clear how fair that comparison can be justified since their work employs evolutionary algorithm which come with extensive time requirements of evolutionary learning and huge time and costs of training for agents before they are deployed to actual testing environments.
\nGiven any of the three environments (i.e., random, linear, and clumped) described in the previous section and a number of autonomous agents (each with a limited knowledge of the environments), the problem we attempt to solve is to form teams of agents that intelligently explore as much as possible interesting cells and/or goals in the grids within a limited amount of time. Our attempt in solving this problem uses a model that employs techniques from SLS algorithms. We provide in this section, a formalization of the framework and implementation details for state and neighborhood, evaluation function, and a description of the simulation employed in our research.
\nWe present our framework of the concept of state and neighborhood in any of the three environments. Denote by \n A state \n
It is clear from Definition 3.1 that a state is composed of a \n The neighborhood \n
A view of a state (with reference cell \n\n\nc\nij\n\n\n), denoted \n\ns\n\n, and a neighborhood \n\nN\n\ns\n\n\n for \n\ns\n\n. \n\nN\n\ns\n\n=\n\n\ns\n1\n\n\ns\n2\n\n\ns\n3\n\n\ns\n4\n\n\n.\n\n
Figure 4 shows an example of a neighborhood \n
A schematic view of some possible neighborhoods for different states with reference cells, \n\n\nc\nij\n\n\n.
We present implementation details of the framework developed in the previous section. We provide abstraction of state and neighborhood in an environment using the Java programming language. The following Java classes, \n
We first consider how to locate a state in an environment. Using the Agent class above, an agent is always aware of its current location. All agents start exploration of an environment from some locations that are determined randomly. These locations correspond to certain reference cells in the environment’s grid. No two agents are allowed to start from the same reference cell. Since a state is made up of a \n
Thus, it is straightforward to determine the states that all the cells in the grid of an environment belongs. Given a reference cell for a state, the following provides an implementation that returns the start indices of the state.
When a state has been explored by an agent, the state is marked as investigated. A state is considered visited if the reference cell for the state and all of its immediate cells have been marked as investigated. Since agents are always aware of their locations, we implement this functionality for each agent using the following method:
Parameter refCell is the reference cell of the state, gridSize is the size of the grid, and visitedCell is a boolean \n
Given the reference cell of a state, the method getNeighborhood above provides an implementation that determines the neighborhood of that state. The method first checks the location of the reference cell to determine the size of the neighborhood, then returns the appropriate states in the neighborhood as demonstrated in Figure 5. For the part of the code shown in the method, the reference cell of the state, say, \n
Agents in our model use an evaluation function to guide selection of successor states to transit into. The evaluation function depends on the framework of the state and neighborhood we developed in the previous section. Algorithm 1 gives the pseudocode of our evaluation function.
\nAlgorithm 1: \n | \n
---|
Input: Agent \n Output: A successor state \n 1: procedure \n 2: \n 3: for each state \n 4: if \n 5: if there exists no other agent \n 6: \n 7: if \n 8: randomly select an \n 9: else 10: randomly select an \n 11: return \n 12: end procedure | \n
Algorithm 1 i.e., SuccessorState \n
Suppose an agent \n
Observe that the number of attempts required by the evaluation function until any one of the three states in \n
We form teams consisting of a certain number of agents. One of the team’s members is designated as a leader. We assume that the leader has some additional computational power than other members. The leader is responsible for maintaining an updated status (i.e., visited states) and communicates same to other members when requested. The leader answers the following queries from members: Has a given state been visited? and Is there an agent in a given state? These are the queries that are used by the evaluation function. The leader agent does not participate in the actual exploration of individual states. Other agents are responsible for locating and visiting interesting cells and as well as finding goals in the grids. All visited cells, either interesting or not, and whether goals are found or not are marked as investigated. An agent can move from her current location in only one of four directions (i.e., north, east, west, and south) and is limited to moves of length one in a single time step. The following three actions, goForward, turnLeft, and turnRight are made available to all agents except the leader.
\nWhen starting, all agents (except the leader) are randomly distributed in the environment. We describe the procedure used by agents to explore the environments next. Imagine an agent \n
Figure 6(a) provides a simple illustration of an agent currently in a state with reference cell \n
Exhaustive search of a state by agents. (a) Agent exits reference cell \n\nx\n\n, search current state in the direction of the arrows, and transits into \n\n\ns\n4\n\n\n with reference \n\ny\n\n. (b) Agent exits reference cell \n\nx\n\n, search current state in the direction of arrows, and transits into \n\n\ns\n1\n\n\n with reference cell \n\ny\n\n.
Figure 7 shows an example of a random environment with an initial deployment of six agents (red pictures with arrow heads) in the environment. There are also currently ten goals (diamond pictures in yellow) that are also randomly distributed across the grid. The agents will search the environment using the evaluation function and the concept of neighborhood proposed in this work to guide their search. A snapshot of what the search area looks like after few time steps of exploration is shown in Figure 8. The highlighted areas covered in green have been explored by agents, while the white areas are yet to be explored. Also, the rectangle of agents shown together illustrate an exhaustive search of that state by an agent. We make the rectangle of agents disappear in the real simulation when the agent complete exploration of the state.
\nRandom environment showing initial deployment of agents (red) and goals (yellow).
Random environment showing partial search of the environment by agents. The highlighted areas covered in green have been explored by agents.
We present results of our extensive simulations in this section. Our findings are based on two different sets of experiments—first, on the percentage of interesting cells found by agents, and second, on the average number of goals found by agents in the three environments. For our study, we use a different set of parameters to include number of agents in teams, size, and type (random, linear, and clumped) of environments.
\nFigure 9 shows the average percentage of interesting cells found by six-member teams of agents for \n
Average percentage of interesting cells found by six-member teams in \n\n45\n×\n45\n\n grid environments.
\n | Random | \nClumped | \nLinear | \n
---|---|---|---|
Standard deviation | \n\n\n | \n\n\n | \n\n\n | \n
Standard deviations from the respective average percentage of interesting cells found by six-member teams in \n
The average percentage of interesting cells found by agents’ teams using the SLS model provides a measure of the level of difficulty of the three environments for the teams. This conversely implies a measure of the relative performance of the teams in each of the environments. Figure 7 shows that the relative performance of the teams in the random environment (\n
An implication of the closeness of the level of difficulty of the three environments is that the SLS model’s performance has less reliance on these environments. Contrarily, Soule and Heckendorn [12] have shown that the performance of the evolved teams by their model depends on both the training and testing environments. They show that training in either the random or clumped environment is a good training for the other environment, but neither is as good of a training environment for the linear environment. In fact, the performance of the evolved teams when they are trained in either of random or clumped, and later deployed in linear environment, is poor in comparison with when they are deployed in either the random or clumped environment. Recall also that agents in our model are not subjected to training before being deployed to the testing environments. They only conduct local searches of their environments using two important features from SLS algorithms: neighborhood and evaluation function.
\nFor the next set of experiments, we evaluate the effectiveness of the SLS model by measuring the average percentage of interesting cells found by agents’ teams, varying the number of agents in the teams, and the grid sizes in the three environments. Figure 10 shows the average percentage of interesting cells found by agents’ teams of different sizes in \n
Average percentage of interesting cells found by agents’ teams of different sizes in \n\n45\n×\n45\n\n grid environments.
The six-member teams always discover more than \n
Increasing the number of agents in the teams beyond ten does not appear to improve average performance of agents. We noticed marginal decrease in the average performance of larger teams—as teams’ sizes increase past \n
Figure 11 shows the average percentage of interesting cells found by six-member teams for different grid sizes in the three environments. The \n
Average percentage of interesting cells found by six-member teams for different grid sizes of environments.
The results show, perhaps not too surprising that in general, the average performance of the teams degrade for the three environments as the dimension of the grids increases. A partial explanation for this is that fixing the team size while increasing the dimension of the environments makes members of the teams to be sparsely distributed in the environments. Thus, it will then be more difficult for agents to cooperate as they now require several time steps to move closer to one another in order to cover different parts of the grids. Nonetheless, even at higher dimensions of the grids, agents’ teams are still able to achieve some reasonable level of performance. For instance, when the grid size is \n
This second part of the experiments is based on the average number of goals found by agents’ teams. We set the number of goals that are randomly distributed in the environments to be \n
Average number of goals found by agents’ teams for different grid sizes in the random environment.
Average number of goals found by agents’ teams for different grid sizes in the clumped environment.
Average number of goals found by agents’ teams for different grid sizes in the linear environment.
The results we observe from the figures suggest that the performance of agents’ teams in the three environments are similar and consistent for agents’ teams, environment types, as well as for the various grid sizes. It is interesting to see that all teams of agents were able to find on average all the \n
We are interested in the lessons to be learnt from these experiments, as well as the implications of the similarity and consistency of the results across the three environments. The outcomes from these experiments suggest that our proposed SLS method is independent of the three environments, thus, agents using our search procedures are expected to perform about the same in any of the environments. This is also a confirmation of the results for agents’ teams in the three environments when they are expected to find as many interesting cells from the previous section.
\nWe consider an investigation of the use of Stochastic Local Search (SLS) technique to explore complex environments where agents’ knowledge and the time to explore such environments are limited. We model the problem as that of an instance of a search problem and develop a SLS technique that enables efficient exploration of such relatively difficult environments by teams of agents. Thus, we provide extensions to the work of Soule and Heckendorn [12] that uses evolutionary algorithms in evolving multiagent teams in the three different simulated random, clumped, and linear environments described in their work. We first provide a formalization of the concept of state and neighborhood in these environments and provide agents’ performance evaluations in the three environments using the number of interesting cells found by teams as done in [12] and our previous work [13]. We further modify the environments to include a limited number of goals that are randomly distributed among the interesting cells. Agents in this case are thus required to search for goals rather than interesting cells.
\nExperiments using agents’ teams of different sizes implementing our model in different problem environments show the effectiveness of our technique. In most cases of the problem instances, teams of agents were able to complete exploration of more than \n
We also evaluate the performance of agents’ teams in another set of experiments requiring agents to search for goals in the three environments. It is interesting to note that all teams of agents were able to find on average all the goals in the three environments when the size of the grid is \n
There are several areas of ongoing research on this problem. Here are some directions for future work. A drawback of Soule and Heckendorn’s model is the unlimited vision of the environments by all agents in their work. We avoid this problem by ensuring that agents in our model have only limited vision of the environments except the team leader that still has unlimited vision of the environments. We plan to address this issue in future work. Our proposed SLS model in this work still has some limitations. The search approach by the model is uninformed, thus, agents exhaustively search all states by slowly branching out of their neighborhood from their starting locations. We have commenced improvement of our model by allowing agents to do more informed search of the environments by using cleverly designed and admissible heuristics to guide the search. The expectation is that agents will now have direction of the search towards the goals in the environments at every new time step.
\nIntechOpen is the first native scientific publisher of Open Access books, with more than 116,000 authors worldwide, ranging from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery. Established in Europe with the new headquarters based in London, and with plans for international growth, IntechOpen is the leading publisher of Open Access scientific books. The values of our business are based on the same ones that any scientist applies to their research -- we have created a culture of respect, collegiality and collaboration within an atmosphere that’s relaxed, friendly and progressive.
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\n\nThe Social Media Community Manager and Marketing Assistant will report to the Senior Marketing Manager. They will work alongside the Marketing and Corporate Communications team, supporting the preparation of all marketing programs, assisting in the development of scientific marketing and communication deliverables, and creating content for social media outlets, as well as managing international social communities.
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\n\nEssential Skills:
\n\nDesired Skills:
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\n\nTo apply, please email a copy of your CV and covering letter to hogan@intechopen.com stating your salary expectations.
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