The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem d...Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.展开更多
针对未来月面着陆动力下降段轨迹规划需综合考虑多性能指标的问题,提出一种对飞行轨迹先优化后决策的多目标轨迹规划方法.在多目标进化算法MOEA/D-AWA(multi-objective evolutionary algorithm based on decomposition with adaptive we...针对未来月面着陆动力下降段轨迹规划需综合考虑多性能指标的问题,提出一种对飞行轨迹先优化后决策的多目标轨迹规划方法.在多目标进化算法MOEA/D-AWA(multi-objective evolutionary algorithm based on decomposition with adaptive weight adjustment)的框架下对轨迹规划的多个指标进行分解,得到若干个单指标的子问题.将凸优化算法作为求解单目标轨迹优化子问题的底层算法,嵌套在MOEA/D-AWA的框架中,经过迭代优化获得一组动力下降段飞行轨迹,其构成多目标轨迹规划问题的帕累托最优解集.根据模糊决策理论对各个帕累托最优解对应的多个轨迹指标逐步降阶并进行综合评估,经过决策得到多指标约束下的飞行轨迹.仿真实验表明,该轨迹规划方法能够在综合多目标的情况下,优化获得一组动力下降轨迹集合,且能够根据不同任务要求从中决策出最优的动力下降段轨迹,可有效解决月面飞行器的多目标轨迹规划问题.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)作为一种重要的多目标优化方法,已经成功地应用于解决各种多目标优化问题。然而,MOEA/D算法在解决具有高维目标和复杂帕累托前沿(Pare...基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)作为一种重要的多目标优化方法,已经成功地应用于解决各种多目标优化问题。然而,MOEA/D算法在解决具有高维目标和复杂帕累托前沿(Pareto frontier,PF)的问题时,容易陷入局部最优并难以获得可行解。本文提出一种改进的MOEA/D算法,包括3个优化策略:首先,使用拉丁超立方抽样方法代替随机方法初始化种群,得到分布均匀的初始种群,同时对权重向量关联解的策略进行优化;其次,提出一种稀疏度函数,用于计算种群中个体的稀疏度并维护外部种群;最后,提出了自适应调整权向量的方法,用于引导种群收敛到帕累托前沿,并且有效平衡种群的多样性和收敛性。将提出算法和4种对比算法在DTLZ和WFG系列问题以及多目标旅行商问题(multi-objective travel salesman problem,MOTSP)上进行对比实验,实验结果表明本文提出自适应调整权重向量的多目标进化(MOEA/D with cosine similarity adaptive weight adjustment,MOEA/D-CSAW)算法在处理具有复杂帕累托前沿和高维多目标的问题时,算法的综合性能要优于对比算法。展开更多
基金the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
文摘Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.
文摘针对未来月面着陆动力下降段轨迹规划需综合考虑多性能指标的问题,提出一种对飞行轨迹先优化后决策的多目标轨迹规划方法.在多目标进化算法MOEA/D-AWA(multi-objective evolutionary algorithm based on decomposition with adaptive weight adjustment)的框架下对轨迹规划的多个指标进行分解,得到若干个单指标的子问题.将凸优化算法作为求解单目标轨迹优化子问题的底层算法,嵌套在MOEA/D-AWA的框架中,经过迭代优化获得一组动力下降段飞行轨迹,其构成多目标轨迹规划问题的帕累托最优解集.根据模糊决策理论对各个帕累托最优解对应的多个轨迹指标逐步降阶并进行综合评估,经过决策得到多指标约束下的飞行轨迹.仿真实验表明,该轨迹规划方法能够在综合多目标的情况下,优化获得一组动力下降轨迹集合,且能够根据不同任务要求从中决策出最优的动力下降段轨迹,可有效解决月面飞行器的多目标轨迹规划问题.
