MCEDA: A novel many-objective optimization approach based on model and clustering

To solve many-objective optimization problems (MaOPs) by evolutionary algorithms (EAs), the maintenance of convergence and diversity is essential and difficult. Improved multi-objective optimization evolutionary algorithms (MOEAs), usually based on the genetic algorithm (GA), have been applied to MaOPs, which use the crossover and mutation operators of GAs to generate new solutions. In this paper, a new approach, based on decomposition and the MOEA/D framework, is proposed: model and clustering based estimation of distribution algorithm (MCEDA). MOEA/D means the multi-objective evolutionary algorithm based on decomposition. The proposed MCEDA is a new estimation of distribution algorithm (EDA) framework, which is intended to extend the application of estimation of distribution algorithm to MaOPs. MCEDA was implemented by two similar algorithm, MCEDA/B (based on bits model) and MCEDA/RM (based on regular model) to deal with MaOPs. In MCEDA, the problem is decomposed into several subproblems. For each subproblem, clustering algorithm is applied to divide the population into several subgroups. On each subgroup, an estimation model is created to generate the new population. In this work, two kinds of models are adopted, the new proposed bits model and the regular model used in RM-MEDA (a regularity model based multi-objective estimation of distribution algorithm). The non-dominated selection operator is applied to improve convergence. The proposed algorithms have been tested on the benchmark test suite for evolutionary algorithms (DTLZ). The comparison with several state-of-the-art algorithms indicates that the proposed MCEDA is a competitive and promising approach.     

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...     

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.     

一种基于分解和协同的高维多目标进化算法

现实中高维多目标优化问题普遍存在，而且其巨大的目标空间使得经典的多目标进化算法面临严峻挑战，提出一种基于分解和协同策略的高维多目标进化算法MaOEA/DCE.该算法利用混合水平正交实验设计方法产生接近于指定规模且均匀分布于聚合系数空间的权重向量，提高种群的分布性；其次，算法将差分进化算子和自适应SBX算子进行协同进化以产生高质量的子代个体，改善算法的收敛性.该算法与另外五种高性能的多目标进化算法在基准测试函数集DTLZ{1，2，4，5}上进行IGD⁺性能指标实验，结果表明MaOEA/DCE在收敛性、多样性和稳定性方面总体具有显著的性能优势.     

A hybridized angle-encouragement-based decomposition approach for many-objective optimization problems

Due to the large objective space when handling many-objective optimization problems (MaOPs), it is a challenging work for multi-objective evolutionary algorithms (MOEAs) to balance convergence and diversity during the search process. Although a number of decomposition-based MOEAs have been designed for the above purpose, some difficulties are still encountered for tackling some difficult MaOPs. As inspired by the existing decomposition approaches, a new Hybridized Angle-Encouragement-based (HAE) decomposition approach is proposed in this paper, which is embedded into a general framework of decomposition-based MOEAs, called MOEA/D-HAE. Two classes of decomposition approaches, i.e., the angle-based decomposition and the proposed encouragement-based boundary intersection decomposition, are sequentially used in HAE. The first one selects appropriate solutions for association in the feasible region of each subproblem, which is expected to well maintain the diversity of associated solutions. The second one acts as a supplement for the angle-based one under the case that no solution is located in the feasible region of subproblem, which aims to ensure the convergence and explore the boundaries. By this way, HAE can effectively combine their advantages, which helps to appropriately balance convergence and diversity in evolutionary search. To study the effectiveness of HAE, two series of well-known test MaOPs (WFG and DTLZ) are used. The experimental results validate the advantages of HAE when compared to other classic decomposition approaches and also confirm the superiority of MOEA/D-HAE over seven recently proposed many-objective evolutionary algorithms.     

MaOEA/d2:一种基于双距离构造的高维多目标进化算法

传统的基于Pareto支配关系的多目标进化算法(MOEA)难以有效求解高维多目标优化问题(MaOP). 提出一种利用PBI效用函数的双距离构造的支配关系, 且无需引入额外的参数. 其次, 利用双距离定义了一种多样性保持方法, 该方法不仅考虑了解个体的双距离, 而且还可以根据优化问题的目标数目自适应地调整多样性占比, 以较好地平衡高维目标解群的收敛性和多样性. 最后, 将基于双距离构造的支配关系和多样性保持方法嵌入到NSGA-II算法框架中, 设计了一种基于双距离的高维多目标进化算法MaOEA/d². 该算法与其他5种代表性的高维多目标进化算法一同在5-、10-、15-和20-目标的DTLZ和WFG基准测试问题上进行了IGD和HV性能测试, 结果表明, MaOEA/d²算法具有较好的收敛性和多样性. 由此表明, MaOEA/d²算法是一种颇具前景的高维多目标进化算法.     

A Line Complex-Based Evolutionary Algorithm for Many-Objective Optimization

In solving many-objective optimization problems(MaO Ps), existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure. Most candidate solutions become nondominated during the evolutionary process, thus leading to the failure of producing offspring toward Pareto-optimal front with diversity. Can we find a more effective way to select nondominated solutions and resolve this issue? To answer this critical question, this work proposes to...     

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.     

一种带规范知识引导的改进人工蜂群算法

针对数值函数优化问题,提出一种改进的人工蜂群算法.受文化算法双层进化空间的启发,利用信度空间中的规范知识引导搜索区域,自适应调整算法的搜索范围,提高算法的收敛速度和勘探能力.为保持种群多样性,设计一种种群分散策略,平衡群体的全局探索和局部开采能力,并且在各个进化阶段采用不同的方式探索新的位置.通过对多种标准测试函数进行实验并与多个近期提出的人工蜂群算法比较,结果表明该算法在收敛速度和求解质量上均取得较好的改进效果.     

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.     

自适应偏好半径划分区域的多目标进化方法

偏好多目标进化算法是一类帮助决策者找到感兴趣的Pareto最优解的算法.目前,在以参考点位置作为偏好信息载体的偏好多目标进化算法中,不合适的参考点位置往往会严重影响算法的收敛性能,偏好区域的大小难以控制,在高维问题上效果较差.针对以上问题,通过计算基于种群的自适应偏好半径,利用自适应偏好半径构造一种新的偏好关系模型,通过对偏好区域进行划分,提出基于偏好区域划分的偏好多目标进化算法.将所提算法与4种常用的以参考点为偏好信息载体的多目标进化算法g-NSGA-II、r-NSGA-II、角度偏好算法、MOEA/D-PRE进行对比实验,结果表明,所提算法具有较好的收敛性能和分布性能,决策者可以控制偏好区域大小,在高维问题上也具有较好的收敛效果.     

Many objective cooperative bat searching algorithm

In this paper, a many objective cooperative bat searching algorithm (MOCBA) is proposed to solve many-objective optimization problems by using the balanceable fitness estimation method. Similar to the particle swarm optimization (PSO) algorithm and the evolutionary algorithm (EA), the cooperative bat searching algorithm (CBA) is a recently developed swarm intelligence optimization algorithm to efficiently solve single-objective optimization problems. With the balanceable fitness estimation method, the MOCBA balances the diversity ability and convergence ability of the algorithm during searching process. Moreover, the convergence issue for MOCBA is also studied. The results on convergence in mean and convergence in probability of the MCOBA are presented. Experimental results are provided to demonstrate the effectiveness of the proposed MOCBA by comparing with fourteen state-of-the-art many-objective optimization algorithms by solving benchmark functions: DTLZ1–DTLZ5 and WFG1–WFG9. By calculating the means, standard deviations and running the Wilcoxon rank sum tests and the Friedmans tests of 100 algorithm executions, the proposed MOCBA shows superior performance among all the fifteen algorithms.     

求解约束优化问题的粒子进化变异遗传算法

设计一种求解约束优化问题的粒子进化变异遗传算法(IGA_PSE).首先,分析候选解约束条件离差统计信息与约束违反函数之间的关系及其性质,基于约束条件离差统计信息提出一种改进约束处理方法;其次,基于粒子进化策略提出3种新变异算子;然后,讨论该算法早熟收敛的3种情况,并提出相应的种群多样化维持策略;最后,通过数值实验表明所提出的算法能够有效求解约束优化问题.     

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.     

教与学信息交互粒子群优化算法

针对单一种群在解决高维问题中收敛速度较慢和多样性缺失的问题,提出了一种教与学信息交互粒子群优化(PSO)算法.根据进化过程将种群动态地划分为两个子种群,分别采用粒子群优化算法和教与学优化算法,同时粒子利用学习者阶段进行子种群之间信息交互,并通过评价收敛性和多样性指标让粒子的收敛能力和多样性在进化过程中得到平衡.与粒子群...     

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.     

区间混合性能指标优化问题的自适应遗传算法

为了解决区间混合性能指标优化问题,在此提出了一种自适应进化优化方法。首先,基于前后代最优个体的距离,计算种群的收敛进度;然后,基于种群的多样性、收敛进度,以及进化代数,计算进化种群的交叉和变异概率;最后,将所提算法应用于室内布局这一典型的区间混合性能指标优化问题,并与其他算法比较,实验结果表明,所提算法在最优解数目、性能,以及分布性等方面均具有优越性。     

基于局部协同与竞争变异的动态多种群粒子群算法

针对粒子群算法在处理复杂优化问题时,出现多样性较差、收敛精度低等问题,提出了基于局部协同与竞争变异的动态多种群粒子群算法(Dynamic Multi-population Particle Swarm Optimization Based on Local Cooperative and Competitive M utation,LC-DM PPSO).LC-DM PPSO算法设计了一种局部协同的方法,该方法划分种群成多个子种群,划分后的子种群再通过非支配排序、差分变异的方法选择出一对领导粒子.同时,对粒子的更新方法进行改进,让各个目标优化更加均衡,增强LC-DM PPSO算法的局部搜索能力,提高收敛精度.在LC-DM PPSO算法中,为了防止出现"早熟"收敛的情况,引入竞争变异来增加种群多样性.最后,通过选择一系列标准测试函数将LC-DM PPSO算法与3种进化算法进行比较,验证所提算法的有效性.实验结果显示,所提算法的多样性和收敛性比其他3种进化算法更好,优化效果更佳.