Estimation of distribution algorithms are a class of evolutionary optimization algorithms based on probability distribution model. In this article, a Pareto-based multi-objective estimation of distribution algorithm w...Estimation of distribution algorithms are a class of evolutionary optimization algorithms based on probability distribution model. In this article, a Pareto-based multi-objective estimation of distribution algorithm with multivariate T-copulas is proposed. The algorithm employs Pareto-based approach and multivariate T-copulas to construct probability distribution model. To estimate joint distribution of the selected solutions, the correlation matrix of T-copula is firstly estimated by estimating Kendall’s tau and using the relationship of Kendall’s tau and correlation matrix. After the correlation matrix is estimated, the degree of freedom of T-copula is estimated by using the maximum likelihood method. Afterwards, the Monte Carte simulation is used to generate new individuals. An archive with maximum capacity is used to maintain the non-dominated solutions. The Pareto optimal solutions are selected from the archive on the basis of the diversity of the solutions, and the crowding-distance measure is used for the diversity measurement. The archive gets updated with the inclusion of the non-dominated solutions from the combined population and current archive, and the archive which exceeds the maximum capacity is cut using the diversity consideration. The proposed algorithm is applied to some well-known benchmark. The relative experimental results show that the algorithm has better performance and is effective.展开更多
Multi-Objective Evolutionary Algorithms(MOEAs)have significantly advanced the domain of MultiObjective Optimization(MOO),facilitating solutions for complex problems with multiple conflicting objectives.This review exp...Multi-Objective Evolutionary Algorithms(MOEAs)have significantly advanced the domain of MultiObjective Optimization(MOO),facilitating solutions for complex problems with multiple conflicting objectives.This review explores the historical development of MOEAs,beginning with foundational concepts in multi-objective optimization,basic types of MOEAs,and the evolution of Pareto-based selection and niching methods.Further advancements,including decom-position-based approaches and hybrid algorithms,are discussed.Applications are analyzed in established domains such as engineering and economics,as well as in emerging fields like advanced analytics and machine learning.The significance of MOEAs in addressing real-world problems is emphasized,highlighting their role in facilitating informed decision-making.Finally,the development trajectory of MOEAs is compared with evolutionary processes,offering insights into their progress and future potential.展开更多
文摘Estimation of distribution algorithms are a class of evolutionary optimization algorithms based on probability distribution model. In this article, a Pareto-based multi-objective estimation of distribution algorithm with multivariate T-copulas is proposed. The algorithm employs Pareto-based approach and multivariate T-copulas to construct probability distribution model. To estimate joint distribution of the selected solutions, the correlation matrix of T-copula is firstly estimated by estimating Kendall’s tau and using the relationship of Kendall’s tau and correlation matrix. After the correlation matrix is estimated, the degree of freedom of T-copula is estimated by using the maximum likelihood method. Afterwards, the Monte Carte simulation is used to generate new individuals. An archive with maximum capacity is used to maintain the non-dominated solutions. The Pareto optimal solutions are selected from the archive on the basis of the diversity of the solutions, and the crowding-distance measure is used for the diversity measurement. The archive gets updated with the inclusion of the non-dominated solutions from the combined population and current archive, and the archive which exceeds the maximum capacity is cut using the diversity consideration. The proposed algorithm is applied to some well-known benchmark. The relative experimental results show that the algorithm has better performance and is effective.
文摘Multi-Objective Evolutionary Algorithms(MOEAs)have significantly advanced the domain of MultiObjective Optimization(MOO),facilitating solutions for complex problems with multiple conflicting objectives.This review explores the historical development of MOEAs,beginning with foundational concepts in multi-objective optimization,basic types of MOEAs,and the evolution of Pareto-based selection and niching methods.Further advancements,including decom-position-based approaches and hybrid algorithms,are discussed.Applications are analyzed in established domains such as engineering and economics,as well as in emerging fields like advanced analytics and machine learning.The significance of MOEAs in addressing real-world problems is emphasized,highlighting their role in facilitating informed decision-making.Finally,the development trajectory of MOEAs is compared with evolutionary processes,offering insights into their progress and future potential.
