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
为了准确地求解组合权重的组合系数,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)思想引入评估领域,提出一种基于MOEA/D的组合权重方法.通常,利用加权和法将组合权重模型转化为...为了准确地求解组合权重的组合系数,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)思想引入评估领域,提出一种基于MOEA/D的组合权重方法.通常,利用加权和法将组合权重模型转化为单目标模型时,模型加权系数难以准确确定.对此,引入MOEA/D算法的分解思想,将组合权重模型转化为多个单目标子模型.MOEA/D算法仅适用于无约束优化问题,而较为常用的惩罚函数法难以表达进化初期无可行解的情况,因而提出改进自适应惩罚函数(improved adaptive penalty function,IAPF),将组合权重模型转化为无约束优化模型.应用所提出方法与其他方法进行仿真实验,实验结果表明,所提出算法具有有效性.展开更多
基于分解的多目标进化算法(Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)是多目标优化算法的一个重要分支,多目标优化的关键问题是如何在算法的收敛性和散布性之间达到良好的平衡.目前主流算法的聚合函数存...基于分解的多目标进化算法(Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)是多目标优化算法的一个重要分支,多目标优化的关键问题是如何在算法的收敛性和散布性之间达到良好的平衡.目前主流算法的聚合函数存在着不同的优缺点,尤其是当使用切比雪夫方法选择个体时,经常出现个体偏离权重现象,个体和权重间得不到很好的粘合.本文基于此提出了一种新的聚合函数方法,提高了MOEA/D的性能.该聚合函数的函数形式为二次函数,种群个体在该函数下的等高线是一条二次曲线(本文称双曲线函数方法,Hyperbola Function Method,HYB),是对目前存在的聚合函数的一种泛化形式.该HYB方法相比PBI(Penalty-based Boundary Intersection)方法更强调收敛性,能更容易地在收敛性散布性之间达到平衡.本文测试了MOKP问题及DTLZ系列等测试函数,并与其他算法进行了实验对比,结果显示HYB方法更稳定有效且种群在收敛速度上有一定的提高.展开更多
Conducting reasonable weapon-target assignment( WTA) with near real time can bring the maximum awards with minimum costs which are especially significant in the modern war. A framework of dynamic WTA( DWTA) model base...Conducting reasonable weapon-target assignment( WTA) with near real time can bring the maximum awards with minimum costs which are especially significant in the modern war. A framework of dynamic WTA( DWTA) model based on a series of staged static WTA( SWTA) models is established where dynamic factors including time window of target and time window of weapon are considered in the staged SWTA model. Then,a hybrid algorithm for the staged SWTA named Decomposition-Based Dynamic Weapon-target Assignment( DDWTA) is proposed which is based on the framework of multi-objective evolutionary algorithm based on decomposition( MOEA / D) with two major improvements: one is the coding based on constraint of resource to generate the feasible solutions, and the other is the tabu search strategy to speed up the convergence.Comparative experiments prove that the proposed algorithm is capable of obtaining a well-converged and well diversified set of solutions on a problem instance and meets the time demand in the battlefield environment.展开更多
多目标进化优化是求解多目标优化问题的可行方法.但是,由于没有准确感知并充分利用问题的Pareto前沿,已有方法难以高效求解复杂的多目标优化问题.本文提出一种基于在线感知Pareto前沿划分目标空间的多目标进化优化方法,以利用感知的结果...多目标进化优化是求解多目标优化问题的可行方法.但是,由于没有准确感知并充分利用问题的Pareto前沿,已有方法难以高效求解复杂的多目标优化问题.本文提出一种基于在线感知Pareto前沿划分目标空间的多目标进化优化方法,以利用感知的结果,采用有针对性的进化优化方法求解多目标优化问题.首先,根据个体之间的拥挤距离与给定阈值的关系感知优化问题的Pareto前沿上的间断点,并基于此将目标空间划分为若干子空间;然后,在每一子空间中采用MOEA/D(Multi-objective evolutionary algorithm based on decomposition)得到一个外部保存集;最后,基于所有外部保存集生成问题的Pareto解集.将提出的方法应用于15个基准数值函数优化问题,并与NSGA-Ⅱ、RPEA、MOEA/D、MOEA/D-PBI、MOEA/D-STM和MOEA/D-ACD等比较.结果表明,提出的方法能够产生收敛和分布性更优的Pareto解集,是一种非常有竞争力的方法.展开更多
将基于分解的多目标进化算法(Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)应用于工程优化问题时,由于各目标函数在数量级及量纲上的不同,需要对目标函数进行归一化处理.首先,采用一种自适应ε约束差分进化...将基于分解的多目标进化算法(Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)应用于工程优化问题时,由于各目标函数在数量级及量纲上的不同,需要对目标函数进行归一化处理.首先,采用一种自适应ε约束差分进化算法(εConstrained Differential Evolution,εDE)寻找各个目标在Pareto前沿上的最大值和最小值,利用这些值对各目标进行归一化处理;然后,用MOEA/D进行求解,并在算法中加入了自适应ε约束处理技术;最后,采用一个标准测试问题和一个焊接梁设计优化问题对该算法进行测试,并与其他两种归一化方法进行了比较.根据提出的方法,MOEA/D能对Pareto前沿的一端进行集中优化,因而能处理一些Pareto前沿两端难以优化的问题.展开更多
摘要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.
摘要为了准确地求解组合权重的组合系数,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)思想引入评估领域,提出一种基于MOEA/D的组合权重方法.通常,利用加权和法将组合权重模型转化为单目标模型时,模型加权系数难以准确确定.对此,引入MOEA/D算法的分解思想,将组合权重模型转化为多个单目标子模型.MOEA/D算法仅适用于无约束优化问题,而较为常用的惩罚函数法难以表达进化初期无可行解的情况,因而提出改进自适应惩罚函数(improved adaptive penalty function,IAPF),将组合权重模型转化为无约束优化模型.应用所提出方法与其他方法进行仿真实验,实验结果表明,所提出算法具有有效性.
摘要基于分解的多目标进化算法(Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)是多目标优化算法的一个重要分支,多目标优化的关键问题是如何在算法的收敛性和散布性之间达到良好的平衡.目前主流算法的聚合函数存在着不同的优缺点,尤其是当使用切比雪夫方法选择个体时,经常出现个体偏离权重现象,个体和权重间得不到很好的粘合.本文基于此提出了一种新的聚合函数方法,提高了MOEA/D的性能.该聚合函数的函数形式为二次函数,种群个体在该函数下的等高线是一条二次曲线(本文称双曲线函数方法,Hyperbola Function Method,HYB),是对目前存在的聚合函数的一种泛化形式.该HYB方法相比PBI(Penalty-based Boundary Intersection)方法更强调收敛性,能更容易地在收敛性散布性之间达到平衡.本文测试了MOKP问题及DTLZ系列等测试函数,并与其他算法进行了实验对比,结果显示HYB方法更稳定有效且种群在收敛速度上有一定的提高.
摘要Conducting reasonable weapon-target assignment( WTA) with near real time can bring the maximum awards with minimum costs which are especially significant in the modern war. A framework of dynamic WTA( DWTA) model based on a series of staged static WTA( SWTA) models is established where dynamic factors including time window of target and time window of weapon are considered in the staged SWTA model. Then,a hybrid algorithm for the staged SWTA named Decomposition-Based Dynamic Weapon-target Assignment( DDWTA) is proposed which is based on the framework of multi-objective evolutionary algorithm based on decomposition( MOEA / D) with two major improvements: one is the coding based on constraint of resource to generate the feasible solutions, and the other is the tabu search strategy to speed up the convergence.Comparative experiments prove that the proposed algorithm is capable of obtaining a well-converged and well diversified set of solutions on a problem instance and meets the time demand in the battlefield environment.
摘要多目标进化优化是求解多目标优化问题的可行方法.但是,由于没有准确感知并充分利用问题的Pareto前沿,已有方法难以高效求解复杂的多目标优化问题.本文提出一种基于在线感知Pareto前沿划分目标空间的多目标进化优化方法,以利用感知的结果,采用有针对性的进化优化方法求解多目标优化问题.首先,根据个体之间的拥挤距离与给定阈值的关系感知优化问题的Pareto前沿上的间断点,并基于此将目标空间划分为若干子空间;然后,在每一子空间中采用MOEA/D(Multi-objective evolutionary algorithm based on decomposition)得到一个外部保存集;最后,基于所有外部保存集生成问题的Pareto解集.将提出的方法应用于15个基准数值函数优化问题,并与NSGA-Ⅱ、RPEA、MOEA/D、MOEA/D-PBI、MOEA/D-STM和MOEA/D-ACD等比较.结果表明,提出的方法能够产生收敛和分布性更优的Pareto解集,是一种非常有竞争力的方法.
摘要将基于分解的多目标进化算法(Multi-objective Evolutionary Algorithm Based on Decomposition,MOEA/D)应用于工程优化问题时,由于各目标函数在数量级及量纲上的不同,需要对目标函数进行归一化处理.首先,采用一种自适应ε约束差分进化算法(εConstrained Differential Evolution,εDE)寻找各个目标在Pareto前沿上的最大值和最小值,利用这些值对各目标进行归一化处理;然后,用MOEA/D进行求解,并在算法中加入了自适应ε约束处理技术;最后,采用一个标准测试问题和一个焊接梁设计优化问题对该算法进行测试,并与其他两种归一化方法进行了比较.根据提出的方法,MOEA/D能对Pareto前沿的一端进行集中优化,因而能处理一些Pareto前沿两端难以优化的问题.