偏好多目标进化算法研究综述
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摘要
多目标优化需要同时优化若干相互冲突的目标,其目的是获得均匀分布于整个Pareto前沿上的最优解集.然而在实际多目标优化问题中,决策者通常只对目标空间中部分区域内的Pareto最优解感兴趣,因此将决策者的偏好信息与多目标优化方法相结合成为进化计算领域的研究热点.偏好多目标进化算法通过引入决策者的偏好信息,将算法的搜索集中在决策者感兴趣的偏好区域,有效利用算法的计算资源,提高算法的求解效率,降低计算复杂度,同时有利于决策者高效地做出最终决策.本文从偏好的设置方法和算法性能两个角度介绍偏好多目标进化算法.在偏好的设置上,从占优关系、角度关系、权重向量和偏好集四个方面综述融入偏好信息的多目标进化算法;在算法性能上,从上述四类偏好的设置方法中各选取两种偏好算法进行仿真实验,从偏好策略的有效性、解集的整体性以及算法的复杂度三个方面进行实验对比并深入分析其优缺点.最后,总结了偏好多目标进化算法的未来发展趋势.
Multi-objective optimization needs to optimize several conflicting objective simultaneously.The aim of the optimization algorithms is to obtain the optimal solution sets which uniformly distributed on the whole Pareto front.However,decision makers usually are only interested in the Pareto optimal solutions in some regions of the objective space in practical multi-objective optimization problems.Therefore,combining decision maker's preference information with multi-objective optimization methods is gradually becoming a hot survey topic in the research field of evolutionary computing.Combining the decision maker's preference information with the multi-objective evolutionary algorithms,the search process of the algorithms can be concentrated in the preference region.This can not only use the computational resources effectively and improve the efficiency of the algorithms to solve the optimization problems,but also can reduce the computational complexity and help decision makers make the final decision efficiently.In this survey,our research team systematically describe the preference multi-objective evolutionary algorithms from two aspects:the preference setting methods and the performance of the algorithms.In the setting of preferences,we summarize the multi-objective evolutionary algorithms incorporating preference information from the four aspects:dominance relationship,angle relationship,weight vector and preference set.Firstly,we summarize the preference multi-objective evolutionary algorithms based on the dominance relationship.The core idea behind it is to modify the Pareto dominance relationship,enhance the selection pressure of the algorithms and guide the algorithms to quickly converge to the preference region.Secondly,we summarize the preference multi-objective evolutionary algorithms based on angle relationship.The core idea is to use the angle relationship between the solutions to guide the evolution of the population,while using the angle to control the range of the preference region to obtain the preference solutions.Thirdly,we summarize the preference multi-objective evolutionary algorithms based on weight vector.The core idea is to transform the decision-maker's preference information into a set of weight vectors carrying preference information,and then decompose the multi-objective optimization problem into several single-objective optimization sub-problems according to the weight vectors.We lastly introduce the preference multi-objective evolutionary algorithms based on preference sets.The core idea is coevolving a set of randomly generated preference sets together with population.Then,in the algorithm performance,two kinds of preference multi-objective evolutionary algorithms are selected from each of the four methods to perform simulation experiments.In addition,in order to verify the robustness of the eight algorithms in different preference regions.Our research team select two different reference points in the feasible region and the infeasible region for experimental comparison.Next,we carry out a systematic comparison of the eight algorithms from three aspects:the effectiveness of the preference strategy,the overall performance of the solution set,as well as the complexity of the algorithm,and analyzed their advantages and disadvantages in depth.Finally,our research team end up with discussing some potential trends in preferencebased multi-objective evolutionary algorithms' future development from the six aspects:preference information conversion, preference learning,implicit preference construction, performance indicators of preference algorithms,visualization problem and practical application.
Multi-objective optimization needs to optimize several conflicting objective simultaneously.The aim of the optimization algorithms is to obtain the optimal solution sets which uniformly distributed on the whole Pareto front.However,decision makers usually are only interested in the Pareto optimal solutions in some regions of the objective space in practical multi-objective optimization problems.Therefore,combining decision maker's preference information with multi-objective optimization methods is gradually becoming a hot survey topic in the research field of evolutionary computing.Combining the decision maker's preference information with the multi-objective evolutionary algorithms,the search process of the algorithms can be concentrated in the preference region.This can not only use the computational resources effectively and improve the efficiency of the algorithms to solve the optimization problems,but also can reduce the computational complexity and help decision makers make the final decision efficiently.In this survey,our research team systematically describe the preference multi-objective evolutionary algorithms from two aspects:the preference setting methods and the performance of the algorithms.In the setting of preferences,we summarize the multi-objective evolutionary algorithms incorporating preference information from the four aspects:dominance relationship,angle relationship,weight vector and preference set.Firstly,we summarize the preference multi-objective evolutionary algorithms based on the dominance relationship.The core idea behind it is to modify the Pareto dominance relationship,enhance the selection pressure of the algorithms and guide the algorithms to quickly converge to the preference region.Secondly,we summarize the preference multi-objective evolutionary algorithms based on angle relationship.The core idea is to use the angle relationship between the solutions to guide the evolution of the population,while using the angle to control the range of the preference region to obtain the preference solutions.Thirdly,we summarize the preference multi-objective evolutionary algorithms based on weight vector.The core idea is to transform the decision-maker's preference information into a set of weight vectors carrying preference information,and then decompose the multi-objective optimization problem into several single-objective optimization sub-problems according to the weight vectors.We lastly introduce the preference multi-objective evolutionary algorithms based on preference sets.The core idea is coevolving a set of randomly generated preference sets together with population.Then,in the algorithm performance,two kinds of preference multi-objective evolutionary algorithms are selected from each of the four methods to perform simulation experiments.In addition,in order to verify the robustness of the eight algorithms in different preference regions.Our research team select two different reference points in the feasible region and the infeasible region for experimental comparison.Next,we carry out a systematic comparison of the eight algorithms from three aspects:the effectiveness of the preference strategy,the overall performance of the solution set,as well as the complexity of the algorithm,and analyzed their advantages and disadvantages in depth.Finally,our research team end up with discussing some potential trends in preferencebased multi-objective evolutionary algorithms' future development from the six aspects:preference information conversion, preference learning,implicit preference construction, performance indicators of preference algorithms,visualization problem and practical application.
引文
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