基于R2指标和参考向量的高维多目标进化算法

在高维多目标优化中, 不同的优化问题存在不同形状的Pareto前沿(PF), 而研究表明大多数多目标进化算法(Multi-objective evolutionary algorithms, MOEAs) 在处理不同的优化问题时普适性较差. 为了解决这个问题, 本文提出了一个基于R2指标和参考向量的高维多目标进化算法(An R2 indicator and reference vector based many-objective optimization evolutionary algorithm, R2-RVEA). R2-RVEA基于Pareto支配选取非支配解来指导种群进化, 仅当非支配解的数量超过种群规模时, 算法进一步采用种群分解策略和R2指标选择策略进行多样性管理. 通过大量的实验证明, 本文提出的算法在处理不同形状的PF时具有良好的性能.     

基于自适应参考向量和参考点的高维多目标进化算法

研究表明,现有的多目标进化算法在处理具有不同Pareto前沿的优化问题时难以有效平衡种群的收敛性与多样性.鉴于此,提出一种基于自适应参考向量和参考点的高维多目标进化算法(adaptive reference vector and reference point based many-objective evlolutionary algorithm, ARVRPMEA).ARVRPMEA主要利用种群稀疏性自适应调整参考向量和参考点以提高种群多样性,首先,生成均匀分布的参考向量子集和参考点子集,并利用该参考向量子集分解种群;然后,根据规模最大子种群中解的分布情况生成新的参考向量和参考点,直至满足参考向量集和参考点集规模;最后,为进一步提高种群收敛性,该算法结合指标进行环境选择以保存收敛性较高的个体进入下一代种群.实验结果表明,ARVRP算法在求解具有不同Pareto前沿的问题方面具有良好的性能.     

基于弱关联的自适应高维多目标进化算法

对现有的分解方法进行改进,提出一种基于弱关联的自适应高维多目标进化算法(WAEA).首先,提出一种基于夹角子空间的关联策略,使得一个解能与多个参考向量相关联;其次,提出弱关联概念,并基于此概念设计双模态标量函数,使算法能够更好地处理复杂PF问题,此外,算法通过检测参考向量子空间内解的数量,自适应调整惩罚参数大小,使其能有效处理各类多目标问题;最后,将WAEA算法与8种代表性的高维多目标算法进行比较,实验结果表明WAEA算法在处理复杂Pareto前沿的高维多目标问题时能更好地平衡Pareto最优解的收敛性与多样性.     

基于参考点选择策略的改进型NSGA-III算法

针对多目标进化算法忽视种群在决策空间的分布信息,未考虑待优化问题Pareto前沿形状的问题,文中提出基于参考点选择策略的改进型NSGA-III算法.首先,根据种群在决策空间的分布特征,借助信息论中的熵思想,计算相邻两代种群的熵差,判定种群的进化阶段.然后,根据种群在目标空间的分布特征,借助参考点关联个体数目的统计信息,评估参考点的重要性.最后,在种群进化的中后期,依据参考点的重要性特征剔除冗余的无效参考点,使保留的参考点适应种群规模与Pareto前沿面,利用筛选后的参考点引导种群进化方向,加快算法收敛及优化效率.在测试函数集上的对比实验表明,文中算法在收敛性和分布性上均较优.     

基于指标和自适应边界选择的高维多目标优化算法

多目标优化算法的主要目标是实现好的多样性和收敛性.传统的高维多目标优化算法,当目标维数增加时,选择方式难以平衡种群的收敛性与多样性.对此,提出一个基于指标和自适应边界选择的高维多目标优化算法.在环境选择中,首先计算种群中两两个体的指标Iε(x,y)作为第一选择标准;其次,提出一种自适应边界选择策略,利用种群进化信息对超...     

基于种群关联策略和强化解集准则的高维多目标进化算法

一般的高维多目标进化算法无法有效处理不同类型的Pareto前沿.针对这一情况,提出一种基于种群关联策略和强化解集准则的高维多目标进化算法(many-objective evolutionary algorithm based on population association strategy and enhanced solution set criterion, MaOEA/PAS-ESC).该算法在环境选择中采用种群关联策略(population association strategy, PAS)和强化解集准则(enhanced solution set criterion, ESC)协同指导种群进化. PAS利用解与参考向量的角度和欧氏距离以及种群中解之间的距离构建角度与距离联合函数(joint function of angle and distance, JFAD),选择多样性良好的解,然后ESC利用参考点与种群间的联系组成适应度函数,选择收敛性良好的解,以共同达到有效平衡多样性和收敛性的目的.实验结果表明,采用MaOEA/PAS-ESC处理高维多目标优化问题具有更强的竞...     

基于参考点的高维多目标粒子群算法

高维多目标优化问题一般指目标个数为4个 或以上时的多目标优化问题.由于种群中非支配解数量随着目标数量的增加而急剧增多,导致进化算法的进化压力严重降低,求解效率低.针对该问题,提出一种基于粒子群的高维多目标问题求解方法,在目标空间中引入一系列的参考点,根据参考点筛选出能兼顾多样性和收敛性的非支配解作为粒子的全局最优,以增大选择压力.同时,提出了基于参考点的外部档案维护策略,以保持最后所得解集的多样性.在标准测试函数DTLZ2上的仿真结果表明,所提方法在求解高维多目标问题时能够得到收敛性和分布性都较好的解集.     

进化高维多目标优化算法研究综述

首先针对常规多目标优化算法求解高维多目标优化时面临的选择压力衰减问题进行论述;然后针对该问题,按照选择机制的不同详细介绍基于Pareto支配、基于分解策略和基于性能评价指标的典型高维多目标优化算法,并分析各自的优缺点;接着立足于一种全新的性能评价指标-----R2指标,给出R2指标的具体定义,介绍基于R2指标的高维多目标优化算法,分析此类算法的本质,并按照R2指标的4个关键组成部分进行综述;最后,发掘其存在的潜在问题以及未来发展空间.     

采用放松支配关系的高维多目标微分进化算法

为了提高进化算法在求解高维多目标优化问题时的收敛性和多样性,提出了采用放松支配关系的高维多目标微分进化算法。该算法采用放松的Pareto支配关系,以增加个体的选择压力;采用群体和外部存储器协同进化的方案,并通过混合微分变异算子,生成子代群体;采用基于指标的方法计算个体的适应度并对群体进行更新;采用基于Lp范数（0相似文献   

基于指标选择和密度评估删除的高维多目标进化算法

尽管许多高维多目标进化算法已被提出,但平衡种群收敛性与多样性的困难仍然存在.对此,提出一种基于指标选择和密度评估删除的高维多目标进化算法(indicator selection and density estimation deletion-based manyobjective evolutionary algorithm, MaOEA/IS-DED).该算法在环境选择过程中采用基于Iε+(x, y)指标的选择策略和基于移动的密度评估删除机制协作逐一剔除种群中收敛性和多样性差的个体,进而使种群个体从多样性好的搜索方向上收敛于真实Pareto前沿,完成平衡收敛性与多样性.具体地,前者选择Iε+(x, y)指标值最小的一对个体,其在空间中表现为搜索方向最相似的个体;后者利用自身兼顾种群收敛性和多样性的特性,比较被选的这对个体且删除这对个体中收敛性和多样性较差的个体.实验结果表明, MaOEA/IS-DED算法在处理高维多目标优化问题时能获得较强的竞争性能.     

混合分解和强度帕累托多目标进化算法

在多目标进化优化中,使用分解策略的基于分解的多目标进化算法(MOEA/D)时间复杂度低,使用〖BP(〗强度帕累托策略的〖BP)〗强度帕累托进化算法-2(SPEA2)能得到分布均匀的解集。结合这两种策略,提出一种新的多目标进化算法用于求解具有复杂、不连续的帕累托前沿的多目标优化问题(MOP)。首先,利用分解策略快速逼近帕累托前沿;然后,利用强度帕累托策略使解集均匀分布在帕累托前沿,利用解集重置分解策略中的权重向量集,使其适配于特定的帕累托前沿;最后,利用分解策略进一步逼近帕累托前沿。使用的反向世代距离(IGD)作为度量标准,将新算法与MOEA/D、SPEA2和paλ-MOEA/D在12个基准问题上进行性能对比。实验结果表明该算法性能在7个基准问题上最优,在5个基准问题上接近于最优,且无论MOP的帕累托前沿是简单或复杂、连续或不连续的,该算法均能生成分布均匀的解集。     

Many-objective evolutionary algorithm based on adaptive weighted decomposition

Decomposition is a representative method for handling many-objective optimization problems with evolutionary algorithms. Classical decomposition scheme relies on a set of uniformly distributed reference vectors to divide the objective space into multiple subregions. This scheme often works poorly when the problem has an irregular Pareto front due to the inconsistency between the distribution of reference vectors and the shape of Pareto fronts. We propose in this paper an adaptive weighted decomposition based many-objective evolutionary algorithm to tackle complicated many-objective problems whose Pareto fronts may or may not be regular. Unlike traditional decomposition based algorithms that use a pre-defined set of reference vectors, the reference vectors in the proposed algorithm are produced from the population during the search. The experiments show that the performance of the proposed algorithm is competitive with other state-of-the-art algorithms and is less-sensitive to the irregularity of the Pareto fronts.     

Many-objective evolutionary optimization based on reference points

Many-objective optimization problems are common in real-world applications, few evolutionary optimization methods, however, are suitable for solving them up to date due to their difficulties. A reference points-based evolutionary algorithm (RPEA) was proposed in this paper to solve many-objective optimization problems. The aim of this study is to exploit the potential of the reference points-based approach to strengthen the selection pressure towards the Pareto front while maintaining an extensive and uniform distribution among solutions. In RPEA, a series of reference points with good performances in convergence and distribution are continuously generated according to the current population to guide the evolution. Furthermore, superior individuals are selected based on the evaluation of each individual by calculating the distances between the reference points and the individual in the objective space. The proposed algorithm was applied to seven benchmark optimization problems and compared with ɛ-MOEA, HypE, MOEA/D and NSGA-III. The results empirically show that the proposed algorithm has a good adaptability to problems with irregular or degenerate Pareto fronts, whereas the other reference points-based algorithms do not. Moreover, it outperforms the other four in 8 out of 21 test instances, demonstrating that it has an advantage in obtaining a Pareto optimal set with good performances.     

Utopian point based decomposition for multi-objective optimization problems with complicated Pareto fronts

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been considered as a promising method for solving multi-objective optimization problems (MOPs). It devotes most of its effort on convergence by optimizing a set of scalar optimization subproblems in a collaborative manner, while maintaining the diversity by using a set of uniformly distributed weight vectors. However, more recent studies illustrated that MOEA/D faces difficulties on MOPs with complicated Pareto fronts, mainly because the uniformity of weight vectors no longer lead to an evenly scattered approximation of the Pareto fronts in these cases. To remedy this, we suggest replacing the ideal point in the reciprocal Tchebycheff decomposition method with a more optimistic utopian point, with the aim of alleviating the sensitivity of MOEA/D to the Pareto front shape of MOPs. Experimental studies on benchmark and real-world problems have shown that such simple modification can significantly improve the performances of MOEA/D with reciprocal Tchebycheff decomposition on MOPs with complicated Pareto fronts.     

A prediction strategy based on center points and knee points for evolutionary dynamic multi-objective optimization

In real life, there are many dynamic multi-objective optimization problems which vary over time, requiring an optimization algorithm to track the movement of the Pareto front (Pareto set) with time. In this paper, we propose a novel prediction strategy based on center points and knee points (CKPS) consisting of three mechanisms. First, a method of predicting the non-dominated set based on the forward-looking center points is proposed. Second, the knee point set is introduced to the predicted population to predict accurately the location and distribution of the Pareto front after an environmental change. Finally, an adaptive diversity maintenance strategy is proposed, which can generate some random individuals of the corresponding number according to the degree of difficulty of the problem to maintain the diversity of the population. The proposed strategy is compared with four other state-of-the-art strategies. The experimental results show that CKPS is effective for evolutionary dynamic multi-objective optimization.     

Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II

Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper introduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also proposes a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes.