The neuromuscular systems of animals are governed by extremely complex networks of control signals, sensory feedback loops, and mechanical interactions. Morphology and control are inherently intertwined. In the case of animal joints, groups of muscles work together to provide power and stability to move limbs in a coordinated manner. In contrast, many robot controllers handle both high-level planning and low-level control of individual joints. In this paper, we propose a joint-level control method, called digital muscles, that operates in a manner analogous to biological muscles, yet is abstract enough to apply to conventional robotic joints. An individual joint is controlled by multiple muscle nodes, each of which responds to a control signal according to a node-specific activation function. Evolving the physical orientation of muscle nodes and their respective activation functions enables relatively complex and coordinated gaits to be realized with simple high-level control. Even using a sinusoid as the high-level control signal, we demonstrate the evolution of effective gaits for a simulated quadruped. The proposed model realizes a control strategy for governing the behavior of individual joints, and can be coupled with a high-level controller that focuses on decision making and planning.
{"title":"Evolving joint-level control with digital muscles","authors":"Jared M. Moore, P. McKinley","doi":"10.1145/2576768.2598373","DOIUrl":"https://doi.org/10.1145/2576768.2598373","url":null,"abstract":"The neuromuscular systems of animals are governed by extremely complex networks of control signals, sensory feedback loops, and mechanical interactions. Morphology and control are inherently intertwined. In the case of animal joints, groups of muscles work together to provide power and stability to move limbs in a coordinated manner. In contrast, many robot controllers handle both high-level planning and low-level control of individual joints. In this paper, we propose a joint-level control method, called digital muscles, that operates in a manner analogous to biological muscles, yet is abstract enough to apply to conventional robotic joints. An individual joint is controlled by multiple muscle nodes, each of which responds to a control signal according to a node-specific activation function. Evolving the physical orientation of muscle nodes and their respective activation functions enables relatively complex and coordinated gaits to be realized with simple high-level control. Even using a sinusoid as the high-level control signal, we demonstrate the evolution of effective gaits for a simulated quadruped. The proposed model realizes a control strategy for governing the behavior of individual joints, and can be coupled with a high-level controller that focuses on decision making and planning.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125385791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Evolution mechanisms of different biological and social systems have inspired a variety of evolutionary computation (EC) algorithms. However, most existing EC algorithms simulate the evolution procedure at the individual-level. This paper proposes a new EC mechanism inspired by the evolution procedure at the tribe-level, namely tribal ecosystem inspired algorithm (TEA). In TEA, the basic evolution unit is not an individual that represents a solution point, but a tribe that covers a subarea in the search space. More specifically, a tribe represents the solution set locating in a particular subarea with a coding structure composed of three elements: tribal chief, attribute diversity, and advancing history. The tribal chief represents the locally best-so-far solution, the attribute diversity measures the range of the subarea, and the advancing history records the local search experience. This way, the new evolution unit provides extra knowledge about neighborhood profiles and search history. Using this knowledge, TEA introduces four evolution operators, reforms, self-advance, synergistic combination, and augmentation, to simulate the evolution mechanisms in a tribal ecosystem, which evolves the tribes from potentially promising subareas to the global optimum. The proposed TEA is validated on benchmark functions. Comparisons with three representative EC algorithms confirm its promising performance.
{"title":"A tribal ecosystem inspired algorithm (TEA) for global optimization","authors":"Ying-biao Lin, Jingjing Li, Jun Zhang, Meng Wan","doi":"10.1145/2576768.2598253","DOIUrl":"https://doi.org/10.1145/2576768.2598253","url":null,"abstract":"Evolution mechanisms of different biological and social systems have inspired a variety of evolutionary computation (EC) algorithms. However, most existing EC algorithms simulate the evolution procedure at the individual-level. This paper proposes a new EC mechanism inspired by the evolution procedure at the tribe-level, namely tribal ecosystem inspired algorithm (TEA). In TEA, the basic evolution unit is not an individual that represents a solution point, but a tribe that covers a subarea in the search space. More specifically, a tribe represents the solution set locating in a particular subarea with a coding structure composed of three elements: tribal chief, attribute diversity, and advancing history. The tribal chief represents the locally best-so-far solution, the attribute diversity measures the range of the subarea, and the advancing history records the local search experience. This way, the new evolution unit provides extra knowledge about neighborhood profiles and search history. Using this knowledge, TEA introduces four evolution operators, reforms, self-advance, synergistic combination, and augmentation, to simulate the evolution mechanisms in a tribal ecosystem, which evolves the tribes from potentially promising subareas to the global optimum. The proposed TEA is validated on benchmark functions. Comparisons with three representative EC algorithms confirm its promising performance.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127883016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Monte Carlo Tree Search (MCTS) is applied to control the player character in a clone of the popular platform game Super Mario Bros. Standard MCTS is applied through search in state space with the goal of moving the furthest to the right as quickly as possible. Despite parameter tuning, only moderate success is reached. Several modifications to the algorithm are then introduced specifically to deal with the behavioural pathologies that were observed. Two of the modifications are to our best knowledge novel. A combination of these modifications is found to lead to almost perfect play on linear levels. Furthermore, when adding noise to the benchmark, MCTS outperforms the best known algorithm for these levels. The analysis and algorithmic innovations in this paper are likely to be useful when applying MCTS to other video games.
蒙特卡洛树搜索(Monte Carlo Tree Search, MCTS)被应用于控制热门平台游戏《超级马里奥兄弟》的克隆中的玩家角色。标准MCTS通过在状态空间中搜索来应用，目标是尽可能快地向右移动最远。尽管进行了参数调整，但只取得了中等程度的成功。然后对算法进行了一些修改，专门用于处理所观察到的行为病态。据我们所知，其中两个修改是最新颖的。我们发现，将这些修改结合在一起可以在线性关卡中获得近乎完美的玩法。此外，当向基准测试中添加噪声时，MCTS在这些级别上的性能优于最知名的算法。本文的分析和算法创新在将MCTS应用于其他视频游戏时可能是有用的。
{"title":"Monte Mario: platforming with MCTS","authors":"E. Jacobsen, R. Greve, J. Togelius","doi":"10.1145/2576768.2598392","DOIUrl":"https://doi.org/10.1145/2576768.2598392","url":null,"abstract":"Monte Carlo Tree Search (MCTS) is applied to control the player character in a clone of the popular platform game Super Mario Bros. Standard MCTS is applied through search in state space with the goal of moving the furthest to the right as quickly as possible. Despite parameter tuning, only moderate success is reached. Several modifications to the algorithm are then introduced specifically to deal with the behavioural pathologies that were observed. Two of the modifications are to our best knowledge novel. A combination of these modifications is found to lead to almost perfect play on linear levels. Furthermore, when adding noise to the benchmark, MCTS outperforms the best known algorithm for these levels. The analysis and algorithmic innovations in this paper are likely to be useful when applying MCTS to other video games.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117232944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Unix utility program wc, which stands for "word count," takes any number of files and prints the number of newlines, words, and characters in each of the files. We show that genetic programming can find programs that replicate the core functionality of the wc utility, and propose this problem as a "traditional programming" benchmark for genetic programming systems. This "wc problem" features key elements of programming tasks that often confront human programmers, including requirements for multiple data types, a large instruction set, control flow, and multiple outputs. Furthermore, it mimics the behavior of a real-world utility program, showing that genetic programming can automatically synthesize programs with general utility. We suggest statistical procedures that should be used to compare performances of different systems on traditional programming problems such as the wc problem, and present the results of a short experiment using the problem. Finally, we give a short analysis of evolved solution programs, showing how they make use of traditional programming concepts.
{"title":"Word count as a traditional programming benchmark problem for genetic programming","authors":"Thomas Helmuth, L. Spector","doi":"10.1145/2576768.2598230","DOIUrl":"https://doi.org/10.1145/2576768.2598230","url":null,"abstract":"The Unix utility program wc, which stands for \"word count,\" takes any number of files and prints the number of newlines, words, and characters in each of the files. We show that genetic programming can find programs that replicate the core functionality of the wc utility, and propose this problem as a \"traditional programming\" benchmark for genetic programming systems. This \"wc problem\" features key elements of programming tasks that often confront human programmers, including requirements for multiple data types, a large instruction set, control flow, and multiple outputs. Furthermore, it mimics the behavior of a real-world utility program, showing that genetic programming can automatically synthesize programs with general utility. We suggest statistical procedures that should be used to compare performances of different systems on traditional programming problems such as the wc problem, and present the results of a short experiment using the problem. Finally, we give a short analysis of evolved solution programs, showing how they make use of traditional programming concepts.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125464741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper describes a surrogate based multi-objective evolutionary algorithm with hyper-volume contribution-based local search. The algorithm switches between an NSGA-II phase and a local search phase. In the local search phase, a model for each of the objectives is trained and CMA-ES is used to optimize the hyper-volume contribution of each individual with respect to its two neighbors on the non-dominated front. The performance of the algorithm is evaluated using the well known ZDT and WFG benchmark suites.
{"title":"Hypervolume-based local search in multi-objective evolutionary optimization","authors":"M. Pilát, Roman Neruda","doi":"10.1145/2576768.2598332","DOIUrl":"https://doi.org/10.1145/2576768.2598332","url":null,"abstract":"This paper describes a surrogate based multi-objective evolutionary algorithm with hyper-volume contribution-based local search. The algorithm switches between an NSGA-II phase and a local search phase. In the local search phase, a model for each of the objectives is trained and CMA-ES is used to optimize the hyper-volume contribution of each individual with respect to its two neighbors on the non-dominated front. The performance of the algorithm is evaluated using the well known ZDT and WFG benchmark suites.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122319127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Bonyadi, Z. Michalewicz, M. Przybylek, A. Wierzbicki
Many real-world problems are composed of two or more problems that are interdependent on each other. The interaction of such problems usually is quite complex and solving each problem separately cannot guarantee the optimal solution for the overall multi-component problem. In this paper we experiment with one particular 2-component problem, namely the Traveling Thief Problem (TTP). TTP is composed of the Traveling Salesman Problem (TSP) and the Knapsack Problem (KP). We investigate two heuristic methods to deal with TTP. In the first approach we decompose TTP into two sub-problems, solve them by separate modules/algorithms (that communicate with each other), and combine the solutions to obtain an overall approximated solution to TTP (this method is called CoSolver ). The second approach is a simple heuristic (called density-based heuristic, DH) method that generates a solution for the TSP component first (a version of Lin-Kernighan algorithm is used) and then, based on the fixed solution for the TSP component found, it generates a solution for the KP component (associated with the given TTP). In fact, this heuristic ignores the interdependency between sub-problems and tries to solve the sub-problems sequentially. These two methods are applied to some generated TTP instances of different sizes. Our comparisons show that CoSolver outperforms DH specially in large instances.
{"title":"Socially inspired algorithms for the travelling thief problem","authors":"M. Bonyadi, Z. Michalewicz, M. Przybylek, A. Wierzbicki","doi":"10.1145/2576768.2598367","DOIUrl":"https://doi.org/10.1145/2576768.2598367","url":null,"abstract":"Many real-world problems are composed of two or more problems that are interdependent on each other. The interaction of such problems usually is quite complex and solving each problem separately cannot guarantee the optimal solution for the overall multi-component problem. In this paper we experiment with one particular 2-component problem, namely the Traveling Thief Problem (TTP). TTP is composed of the Traveling Salesman Problem (TSP) and the Knapsack Problem (KP). We investigate two heuristic methods to deal with TTP. In the first approach we decompose TTP into two sub-problems, solve them by separate modules/algorithms (that communicate with each other), and combine the solutions to obtain an overall approximated solution to TTP (this method is called CoSolver ). The second approach is a simple heuristic (called density-based heuristic, DH) method that generates a solution for the TSP component first (a version of Lin-Kernighan algorithm is used) and then, based on the fixed solution for the TSP component found, it generates a solution for the KP component (associated with the given TTP). In fact, this heuristic ignores the interdependency between sub-problems and tries to solve the sub-problems sequentially. These two methods are applied to some generated TTP instances of different sizes. Our comparisons show that CoSolver outperforms DH specially in large instances.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128155403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As an evolutionary approach to solve constrained multi-objective optimization problems (CMOPs), recently a MOEA using the two-stage non-dominated sorting and the directed mating (TNSDM) has been proposed. In TNSDM, the directed mating utilizes infeasible solutions dominating feasible solutions to generate offspring. Although the directed mating contributes to improve the search performance of TNSDM in CMOPs, there are two problems. First, since the number of infeasible solutions dominating feasible solutions in the population depends on each CMOP, the effectiveness of the directed mating also depends on each CMOP. Second, infeasible solutions utilized in the directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. To overcome these problems and further improve the effectiveness of the directed mating in TNSDM, in this work we propose an improved TNSDM introducing a method to control selection area of infeasible solutions and an archiving strategy of useful infeasible solutions for the directed mating. The experimental results on m objectives k knapsacks problems shows that the improved TNSDM improves the search performance by controlling the directionality of the directed mating and increasing the number of directed mating executions in the solution search.
{"title":"Controlling selection area of useful infeasible solutions and their archive for directed mating in evolutionary constrained multiobjective optimization","authors":"Minami Miyakawa, K. Takadama, Hiroyuki Sato","doi":"10.1145/2576768.2598313","DOIUrl":"https://doi.org/10.1145/2576768.2598313","url":null,"abstract":"As an evolutionary approach to solve constrained multi-objective optimization problems (CMOPs), recently a MOEA using the two-stage non-dominated sorting and the directed mating (TNSDM) has been proposed. In TNSDM, the directed mating utilizes infeasible solutions dominating feasible solutions to generate offspring. Although the directed mating contributes to improve the search performance of TNSDM in CMOPs, there are two problems. First, since the number of infeasible solutions dominating feasible solutions in the population depends on each CMOP, the effectiveness of the directed mating also depends on each CMOP. Second, infeasible solutions utilized in the directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. To overcome these problems and further improve the effectiveness of the directed mating in TNSDM, in this work we propose an improved TNSDM introducing a method to control selection area of infeasible solutions and an archiving strategy of useful infeasible solutions for the directed mating. The experimental results on m objectives k knapsacks problems shows that the improved TNSDM improves the search performance by controlling the directionality of the directed mating and increasing the number of directed mating executions in the solution search.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133956435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article proposes an innovative solution for reducing polluting gas emissions from road traffic in modern cities. It is based on our new Red Swarm architecture which is composed of a series of intelligent spots with WiFi connections that can suggest a customized route to drivers. We have tested our proposal in four different case studies corresponding to actual European smart cities. To this end, we first import the city information from OpenStreetMap into the SUMO road traffic micro-simulator, propose a Red Swarm architecture based on intelligent spots located at traffic lights, and then optimize the resulting system in terms of travel times and gas emissions by using an evolutionary algorithm. Our results show that an important quantitative reduction in gas emissions as well as in travel times can be achieved when vehicles are rerouted according to our Red Swarm indications. This represents a promising result for the low cost implementation of an idea that could engage the interest of both citizens and municipal authorities.
{"title":"Eco-friendly reduction of travel times in european smart cities","authors":"Daniel Stolfi, E. Alba","doi":"10.1145/2576768.2598317","DOIUrl":"https://doi.org/10.1145/2576768.2598317","url":null,"abstract":"This article proposes an innovative solution for reducing polluting gas emissions from road traffic in modern cities. It is based on our new Red Swarm architecture which is composed of a series of intelligent spots with WiFi connections that can suggest a customized route to drivers. We have tested our proposal in four different case studies corresponding to actual European smart cities. To this end, we first import the city information from OpenStreetMap into the SUMO road traffic micro-simulator, propose a Red Swarm architecture based on intelligent spots located at traffic lights, and then optimize the resulting system in terms of travel times and gas emissions by using an evolutionary algorithm. Our results show that an important quantitative reduction in gas emissions as well as in travel times can be achieved when vehicles are rerouted according to our Red Swarm indications. This represents a promising result for the low cost implementation of an idea that could engage the interest of both citizens and municipal authorities.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131463909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Passive solar building design considers the effect that sunlight has on energy usage. The goal is to reduce the need for artificial cooling and heating devices, thereby saving energy costs. A number of competing design objectives can arise. Window heat gain during winter requires large windows. These same windows, however, reduce energy efficiency during nights and summers. Other model requirements add further complications, which creates a challenging optimization problem. We use genetic programming for passive solar building design. The EnergyPlus system is used to evaluate energy consumption. It considers factors ranging from model construction (shape, windows, materials) to location particulars (latitude/longitude, weather, time of day/year). We use a strongly typed design language to build 3D models, and multi-objective fitness to evaluate the multiple design objectives. Experimental results showed that balancing window heat gain and total energy use is challenging, although our multi-objective strategy could find interesting compromises. Many factors (roof shape, material selection) were consistently optimized by evolution. We also found that geographic aspects of the location play a critical role in the final building design.
{"title":"Passive solar building design using genetic programming","authors":"M. Gholami, B. Ross","doi":"10.1145/2576768.2598211","DOIUrl":"https://doi.org/10.1145/2576768.2598211","url":null,"abstract":"Passive solar building design considers the effect that sunlight has on energy usage. The goal is to reduce the need for artificial cooling and heating devices, thereby saving energy costs. A number of competing design objectives can arise. Window heat gain during winter requires large windows. These same windows, however, reduce energy efficiency during nights and summers. Other model requirements add further complications, which creates a challenging optimization problem. We use genetic programming for passive solar building design. The EnergyPlus system is used to evaluate energy consumption. It considers factors ranging from model construction (shape, windows, materials) to location particulars (latitude/longitude, weather, time of day/year). We use a strongly typed design language to build 3D models, and multi-objective fitness to evaluate the multiple design objectives. Experimental results showed that balancing window heat gain and total energy use is challenging, although our multi-objective strategy could find interesting compromises. Many factors (roof shape, material selection) were consistently optimized by evolution. We also found that geographic aspects of the location play a critical role in the final building design.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131742634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many multi-objective algorithms use volume based quality indicators to approximate the Pareto front. Amongst these, the hypervolume is the most widely used. The distribution of solution sets of finite size μ that maximize the hypervolume have been investigated theoretically. But nearly all results are limited to the bi-objective case. In this paper, many of these results are extended to higher dimensions and a theoretical analysis and characterization of optimal $mu$-distributions is done. We investigate monotonic Pareto curves that are embedded in three and higher dimensions that keep the property of the bi-objective case that only few points are determining the hypervolume contribution of a point. For finite μ, we consider the influence of the choice of the reference point and determine sufficient conditions that assure the extreme points of the Pareto curves to be included in an optimal μ- distribution. We state conditions about the slope of the front that makes it impossible to include the extremes. Furthermore, we prove more specific results for three dimensional linear Pareto fronts. It is shown that the equispaced property of an optimal distribution for a line in two dimensions does not hold in higher dimensions. We additionally investigate hypervolume in general dimensions and problems with cone domination structures.
{"title":"A theoretical analysis of volume based Pareto front approximations","authors":"P. Shukla, Nadja Doll, H. Schmeck","doi":"10.1145/2576768.2598348","DOIUrl":"https://doi.org/10.1145/2576768.2598348","url":null,"abstract":"Many multi-objective algorithms use volume based quality indicators to approximate the Pareto front. Amongst these, the hypervolume is the most widely used. The distribution of solution sets of finite size μ that maximize the hypervolume have been investigated theoretically. But nearly all results are limited to the bi-objective case. In this paper, many of these results are extended to higher dimensions and a theoretical analysis and characterization of optimal $mu$-distributions is done. We investigate monotonic Pareto curves that are embedded in three and higher dimensions that keep the property of the bi-objective case that only few points are determining the hypervolume contribution of a point. For finite μ, we consider the influence of the choice of the reference point and determine sufficient conditions that assure the extreme points of the Pareto curves to be included in an optimal μ- distribution. We state conditions about the slope of the front that makes it impossible to include the extremes. Furthermore, we prove more specific results for three dimensional linear Pareto fronts. It is shown that the equispaced property of an optimal distribution for a line in two dimensions does not hold in higher dimensions. We additionally investigate hypervolume in general dimensions and problems with cone domination structures.","PeriodicalId":123241,"journal":{"name":"Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127627690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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