改进的r支配高维多目标粒子群优化算法

高维多目标优化问题是广泛存在于实际应用中的复杂优化问题,目前的研究方法大都限于进化算法.本文利用粒子群优化算法求解高维多目标优化问题,提出了一种基于r支配的多目标粒子群优化算法.采用r支配关系进行粒子的比较与选择,并结合粒子群优化算法收敛速度快的优势,使得算法在目标个数增加时仍保持较强的搜索能力;为了弥补由此造成的群体多样性的丢失,优化非r支配阈值的取值策略;此外,引入决策空间的拥挤距离测度,并给出新的外部存储器更新方法,从而进一步防止算法陷入局部最优.对多个基准测试函数的仿真结果表明所得解集在收敛性、多样性以及围绕参考点的分布性上均优于其他两种算法.     

一种基于参考点约束支配的NSGA-III算法

针对带约束的高维多目标优化问题,设计一种基于参考点的约束支配关系(RPCDP),将可行解与不可行解作为一个整体看待,进而综合考虑它们的收敛性、多样性和可行性,并基于此提出用于解决约束高维多目标优化问题的NSGA-III算法.将所提出算法与著名的3种约束高维多目标进化算法进行对比,实验结果表明在标准测试函数集CDTLZ上,相对于其他算法,所提出算法的解集具有更好的收敛性和分布性.     

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   

基于改进K 支配排序的高维多目标进化算法

为提高4目标以上高维多目标优化问题的求解性能,提出一种基于改进K支配排序的高维多目标进化算法(KS-MODE).该算法针对K支配的支配关系和排序方法进行改进,避免循环支配并增强选择压力;设计新的全局密度估计方法提高局部密度估计精确性;设计新的精英选择策略和适应度值评价函数;采用CAO局部搜索算子加速收敛.在4～30个目标标准测试函数上的实验结果表明,KS-MODE能够在保证解集分布性的同时大幅提升收敛性和稳定性,能够有效求解高维多目标优化问题.     

基于目标迁移和条件替代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,但大多仍无法有效处理具有不规则Pareto前沿的高维多目标优化问题.鉴于此,提出基于目标迁移和条件替代的高维多目标进化算法(MaOEA-OTCR),在环境选择过程中利用目标迁移策略和条件替代准则协作逐一选择收敛性和多样性好的个体进入下一代.前者首先选择位于Pareto前沿边界的极值解进入下一代,以确定Pareto前沿的范围,同时选择收敛性最好的若干个体进入下一代,以加速种群收敛;然后迁移已选解集且利用迁移解集和未迁移解集的最大距离来选择收敛性和多样性好的个体进入下一代.后者利用基于角度和收敛性评估的条件取代准则来防止前者过度强调多样性.此外,提出一个多标准决策的匹配选择策略,旨在增加具有良好收敛性和多样性种群个体结合的概率,进一步提升算法的搜索效率.为了验证MaOEA-OTCR的有效性,在3个测试集上与8个先进的高维多目标进化算法进行对比实验.实验结果表明, MaOEA-OTCR在处理高维多目标优化问题时不仅能够获得较强的竞争性能,而且有能力处理具有不规则Pareto前沿的高维多目标优化问题.     

DAV-MOEA:一种采用动态角度向量支配关系的高维多目标进化算法

现实中不断涌现的高维多目标优化问题对传统的基于Pareto支配的多目标进化算法构成巨大挑战.一些研究者提出了若干改进的支配关系,但仍难以有效地平衡高维多目标进化算法的收敛性和多样性.提出一种动态角度向量支配关系动态地刻画进化种群在高维目标空间的分布状况,以较好地在收敛性与多样性之间取得平衡;另外,提出一种改进的基于Lp...     

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...     

基于超球形模糊支配的高维多目标粒子群优化算法

高维多目标优化问题（MAOP）会随着待优化问题维度的增加形成巨大的目标空间,导致在目标空间中非支配解的比例急剧增加,削弱了进化算法的选择压力,降低了进化算法对MAOP的求解效率。针对这一问题,提出一种以超球型支配关系降低种群中非支配解数量的粒子群优化（PSO）算法。算法以模糊支配策略来维持种群对MAOP的选择压力,并通过全局极值的选择和外部档案的维护来保持种群个体在目标空间中的分布。在标准测试集DTLZ和WFG上的仿真结果表明,所提算法在求解MAOP时具备较优的收敛性和分布性。     

基于R2指标和目标空间分解的高维多目标粒子群优化算法

基于R2指标和分解策略的多目标粒子群优化算法(R2-MOPSO)在求解2、3个目标优化问题时具有较好的收敛性和多样性,但在求解高维多目标优化问题时难度较大.对此,提出一种基于R2指标和目标空间分解的高维多目标粒子群优化算法(R2-MOPSO-II).首先借鉴R2指标和目标空间分解策略综合权衡选择过程的收敛性和多样性,设计双层档案维护策略;然后设计一种新的向导选择策略来连接目标空间和决策变量空间,进而提出一种基于双层档案的速度和位置更新策略以权衡粒子群优化算法的勘探和开采能力;最后通过引入高斯学习策略和精英学习策略防止粒子陷入局部最优前沿.数值仿真结果表明,所提出算法在求解DTLZ和WFG测试问题时具有较好的收敛性和多样性.     

基于目标分解的高维多目标并行进化优化方法

高维多目标优化问题普遍存在且难以解决, 到目前为止, 尚缺乏有效解决该问题的进化优化方法. 本文提出一种基于目标分解的高维多目标并行进化优化方法, 首先, 将高维多目标优化问题分解为若干子优化问题, 每一子优化问题除了包含原优化问题的少数目标函数之外, 还具有由其他目标函数聚合成的一个目标函数, 以降低问题求解的难度; 其次, 采用多种群并行进化算法, 求解分解后的每一子优化问题, 并在求解过程中, 充分利用其他子种群的信息, 以提高Pareto非被占优解的选择压力; 最后, 基于各子种群的非被占优解形成外部保存集, 从而得到高维多目标优化问题的Pareto 最优解集. 性能分析表明, 本文提出的方法具有较小的计算复杂度. 将所提方法应用于多个基准优化问题, 并与NSGA-II、PPD-MOEA、ε-MOEA、HypE和MSOPS等方法比较, 实验结果表明, 所提方法能够产生收敛性、分布性, 以及延展性优越的Pareto最优解集.     

A clustering-ranking method for many-objective optimization

In evolutionary multi-objective optimization, balancing convergence and diversity remains a challenge and especially for many-objective (three or more objectives) optimization problems (MaOPs). To improve convergence and diversity for MaOPs, we propose a new approach: clustering-ranking evolutionary algorithm (crEA), where the two procedures (clustering and ranking) are implemented sequentially. Clustering incorporates the recently proposed non-dominated sorting genetic algorithm III (NSGA-III), using a series of reference lines as the cluster centroid. The solutions are ranked according to the fitness value, which is considered to be the degree of closeness to the true Pareto front. An environmental selection operation is performed on every cluster to promote both convergence and diversity. The proposed algorithm has been tested extensively on nine widely used benchmark problems from the walking fish group (WFG) as well as combinatorial travelling salesman problem (TSP). An extensive comparison with six state-of-the-art algorithms indicates that the proposed crEA is capable of finding a better approximated and distributed solution set.     

A radial space division based evolutionary algorithm for many-objective optimization

In evolutionary many-objective optimization, diversity maintenance plays an important role in pushing the population towards the Pareto optimal front. Existing many-objective evolutionary algorithms mainly focus on convergence enhancement, but pay less attention to diversity enhancement, which may fail to obtain uniformly distributed solutions or fall into local optima. This paper proposes a radial space division based evolutionary algorithm for many-objective optimization, where the solutions in high-dimensional objective space are projected into the grid divided 2-dimensional radial space for diversity maintenance and convergence enhancement. Specifically, the diversity of the population is emphasized by selecting solutions from different grids, where an adaptive penalty based approach is proposed to select a better converged solution from the grid with multiple solutions for convergence enhancement. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on a variety of benchmark test problems. Experimental results demonstrate the competitiveness of the proposed algorithm in terms of both convergence enhancement and diversity maintenance.     

基于小生境的多目标进化算法

进化算法求解多目标优化问题平衡收敛性和多样性面临的主要挑战在两个方面：增强对帕累托最优前沿的选择压力和获得多样性良好的解集。然而,随着目标维数的增加,基于帕累托支配关系的选择标准无法有效地解决以上问题。因此,设计了一种基于小生境的多目标进化算法。基于小生境,提出了一种新的支配关系,其中,设计了一个聚合函数和一种采用目标向量角的密度估计方法分别度量候选解的收敛度和分布性。为了保证解集的收敛性,在同一个小生境内,仅仅收敛度最好的解是非支配解。为了维护解集的多样性,在任何两个不同的小生境内,一个小生境内兼具收敛度和分布性良好的解支配另一个小生境内收敛性和分布性均差的解,将提出的支配关系嵌入VaEA取代帕累托支配关系,设计了一种多目标进化算法VaEA-SDN。VaEA-SDN与NSGA-Ⅲ、VaEA、MSEA、NSGAII-CSDR、RPS-NSGAII以及CDR-MOEA等先进的算法在DTLZ(Deb-Thiele-Laumanns-Zitzler)和MaF(manyobjective function)基准测试系列问题上进行了广泛的对比仿真实验。仿真结果表明,VaEA-SDN平衡收敛收敛性...     

A new decomposition based evolutionary algorithm with uniform designs for many-objective optimization

For many-objective optimization problems, how to get a set of solutions with good convergence and diversity is a difficult and challenging work. In this paper, a new decomposition based evolutionary algorithm with uniform designs is proposed to achieve the goal. The proposed algorithm adopts the uniform design method to set the weight vectors which are uniformly distributed over the design space, and the size of the weight vectors neither increases nonlinearly with the number of objectives nor considers a formulaic setting. A crossover operator based on the uniform design method is constructed to enhance the search capacity of the proposed algorithm. Moreover, in order to improve the convergence performance of the algorithm, a sub-population strategy is used to optimize each sub-problem. Comparing with some efficient state-of-the-art algorithms, e.g., NSGAII-CE, MOEA/D and HypE, on six benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence.     

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.     

An angle based evolutionary algorithm with infeasibility information for constrained many-objective optimization

Recently, angle-based approaches have shown promising for unconstrained many-objective optimization problems (MaOPs), but few of them are extended to solve constrained MaOPs (CMaOPs). Moreover, due to the difficulty in searching for feasible solutions in high-dimensional objective space, the use of infeasible solutions comes to be more important in solving CMaOPs. In this paper, an angle based evolutionary algorithm with infeasibility information is proposed for constrained many-objective optimization, where different kinds of infeasible solutions are utilized in environmental selection and mating selection. To be specific, an angle-based constrained dominance relation is proposed for non-dominated sorting, which gives infeasible solutions with good diversity the same priority to feasible solutions for escaping from the locally feasible regions. As for diversity maintenance, an angle-based density estimation is developed to give the infeasible solutions with good convergence a chance to survive for next generation, which is helpful to get across the large infeasible barrier. In addition, in order to utilize the potential of infeasible solutions in creating high-quality offspring, a modified mating selection is designed by considering the convergence, diversity and feasibility of solutions simultaneously. Experimental results on two constrained many-objective optimization test suites demonstrate the competitiveness of the proposed algorithm in comparison with five existing constrained many-objective evolutionary algorithms for CMaOPs. Moreover, the effectiveness of the proposed algorithm on a real-world problem is showcased.     

基于全局排序的高维多目标优化研究

目标数超过4的高维多目标优化是目前进化多目标优化领域求解难度最大的问题之一,现有的多目标进化算法求解该类问题时,存在收敛性和解集分布性上的缺陷,难以满足实际工程优化需求.提出一种基于全局排序的高维多目标进化算法GR-MODE,首先,采用一种新的全局排序策略增强选择压力,无需用户偏好及目标主次信息,且避免宽松Pareto支配在排序结果合理性与可信性上的损失;其次,采用Harmonic平均拥挤距离对个体进行全局密度估计,提高现有局部密度估计方法的精确性;最后,针对高维多目标复杂空间搜索需求,设计新的精英选择策略及适应度值评价函数.将该算法与国内外现有的5种高性能多目标进化算法在标准测试函数集DTLZ{1,2, 4,5}上进行对比实验,结果表明,该算法具有明显的性能优势,大幅提升了4~30维高维多目标优化的收敛性和分布性.     

Indicator-based set evolution particle swarm optimization for many-objective problems

Multi-objective particle swarm optimization (MOPSO) has been well studied in recent years. However, existing MOPSO methods are not powerful enough when tackling optimization problems with more than three objectives, termed as many-objective optimization problems (MaOPs). In this study, an improved set evolution multi-objective particle swarm optimization (S-MOPSO, for short) is proposed for solving many-objective problems. According to the proposed framework of set evolution MOPSO (S-MOPSO), including quality indicators-based objective transformation, the Pareto dominance on sets, and the particle swarm operators for set evolution, an enhanced S-MOPSO method is developed by updating particles hierarchically, i.e., a set of solutions is first regarded as a particle to be updated and then the solutions in a selected set are further evolved by a modified PSO. In the set evolutionary stage, the strategy for efficiently updating the set particle is proposed. When further evolving a single solution in the initial decision space of the optimized MaOP, the global and local best particles are dynamically determined based on those ideal reference points. The performance of the proposed algorithm is empirically demonstrated by applying it to several scalable benchmark many-objective problems.