基于最小距离和聚合策略的分解多目标进化算法

针对基于帕累托（Pareto）支配的多目标进化算法在解决高维问题时选择压力降低,以及基于分解的多目标进化算法在提高收敛性和分布性的同时降低了种群多样性的问题,提出了一种基于最小距离和聚合策略的分解多目标进化算法。首先,使用基于角度分解的技术将目标空间分解为指定个数的子空间来提高种群的多样性;然后,在生成新解的过程中加入基于聚合的交叉邻域方法,使生成的新解更接近于父代解;最后,分两阶段在每个子空间内基于最小距离和聚合策略来选择解以提高收敛性和分布性。为了验证所提算法的可行性,采用标准测试函数ZDT和DTLZ进行仿真实验,结果表明所提算法的总体性能均优于经典的基于分解的多目标进化算法（MOEA/D）、MOEA/D-DE、NSGA-Ⅲ和GrEA。可见,所提算法在提高多样性的同时可以有效平衡收敛性和多样性。     

一种改进的基于分解的多目标进化算法

利用基于分解的多目标进化算法框架(MOEA/D),将混合策略的进化算法用于求解分解后的若干单目标优化子问题,提出了一种带局部搜索的基于分解的多目标混合策略进化算法(LMS-MOEA/D)。算法利用均匀设计产生子问题的聚合权重向量,混合交叉策略能够充分利用不同交叉算子的优势;同时算法针对演化过程收敛的特点,结合局部搜索策略,获得逼近Pareto前沿的最优解集。最后通过实验验证算法在多样性和收敛性方面的有效性。     

一种基于MOEA/D的组合权重方法

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.     

一种基于多策略差分进化的分解多目标进化算法

为了提高多目标优化问题非支配解集合的分布性和收敛性,根据不同差分进化策略的特点,基于切比雪夫分解机制,提出一种基于多策略差分进化的分解多目标进化算法(MOEA/D-WMSDE).该算法首先采用切比雪夫分解机制,将多目标优化问题转化为一系列单目标优化子问题;然后引入小波基函数和正态分布实现差分进化算法的参数控制,探究一种...     

基于分解和差分进化的多目标粒子群优化算法

为了提高多目标优化算法解集的分布性和收敛性,提出一种基于分解和差分进化的多目标粒子群优化算法(dMOPSO-DE).该算法通过提出方向角产生一组均匀的方向向量,确保粒子分布的均匀性;引入隐式精英保持策略和差分进化修正机制选择全局最优粒子,避免种群陷入局部最优Pareto前沿;采用粒子重置策略保证群体的多样性.与非支配排序(NSGA-II)算法、多目标粒子群优化(MOPSO)算法、分解多目标粒子群优化(dMOPSO)算法和分解多目标进化-差分进化(MOEA/D-DE)算法进行比较,实验结果表明,所提出算法在求解多目标优化问题时具有良好的收敛性和多样性.     

基于分解的多目标花朵授粉算法

在过去几十年里，许多多目标进化算法被广泛应用于解决多目标优化问题，其中一种比较流行的多目标进化算法是基于分解的多目标进化算法(MOEA/D)。花朵授粉算法是一种启发式优化算法，但迄今为止，花朵授粉算法在基于分解的多目标进化算法领域的研究还非常少。本文在基于分解的多目标进化算法的框架下，将花朵授粉算法拓展至多目标优化领域，提出一种基于分解的多目标花朵授粉算法(MOFPA/D)。此外，为了保证非支配解的多样性，本文提出一种基于网格的目标空间分割法，该方法从找到的Pareto最优解集中筛选出一定数量且分布均匀的Pareto最优解。实验结果表明，基于分解的多目标花朵授粉算法在收敛性与多样性方面均优于基于分解的多目标进化算法。     

基于差异化邻域策略的分解多目标进化算法*

子问题邻域对基于分解的多目标进化算法性能影响较大.当邻域过大时,种群繁殖产生的新解偏离Pareto解集,在更新子问题时,新解与邻域内旧解的比较次数增多,算法的计算复杂度增加;当邻域过小时,算法容易陷入局部最优.为了解决上述问题,文中提出基于差异化邻域策略的分解多目标进化算法(MOEA/D-DN),通过分析不同大小的邻域对算法性能的影响,选择合适的参数.并根据每个子问题的权重向量与中心向量的偏角,为各子问题设置不同大小的邻域,合理分配算法资源,提高算法搜索全局最优解的速率.在2维ZDT系列和3维、5维DTLZ系列测试函数上的实验表明,MOEA/D-DN 的收敛速度与收敛性能均有明显提高,算法的计算资源分配更合理,所获解集整体质量更优.     

全局替换的自适应权重调整MOEA/D

当多目标问题的帕累托前沿形状较为复杂时,基于分解的多目标进化算法MOEA/D的解的均匀性将受到很大的影响. MOEA/D利用相邻子问题的信息来优化,但早期因为种群中的个体与子问题的关联是随机分配的,仅在邻居间更新会浪费优秀解的信息,影响收敛速度.针对这些问题,本文提出一种MOEA/D的改进算法(MOEA/DGUAW).该算法使用种群全局更新的策略,来提高收敛速度;使用自适应调整权重向量的策略来获得更均匀分布的解集.将MOEA/D-GUAW算法与现有的MOEA/D, MOEA/D-AWA, RVEA和NSGA-III算法在10个广泛应用的测试问题上进行了实验比较.实验结果表明,提出的算法在大部分问题上,反转世代距离评价指标IGD优于其他算法,收敛速度也快于其他算法.     

随机扰动不同种群变异策略的多目标进化算法

为了提高多目标优化问题非支配解集的收敛性和多样性,解决算法后期易陷入局部最优的问题,根据不同差分进化策略特点,添加随机扰动,基于改进切比雪夫机制提出了一种自适应差分进化策略的分解多目标进化算法（MOEA/D-ADE-levy）。首先使用混合水平正交实验产生均匀权重向量并应用于改进切比雪夫机制分解子问题得到均匀分布的初始种群;其次将种群分为优秀个体、中间个体和较差个体,对不同个体采用不同的变异策略,对变异因子F和交叉概率CR采用自适应机制,提高非支配解集的收敛性和多样性;最后对陷入局部最优的解集增加levy随机扰动,增大其全局搜索的能力,跳出局部最优。采用DTLZ测试函数验证算法有效性,将所提算法与NSGA2、NSGA3、MOEA\D、MOEA\D-DE等常用算法进行比较,使用GD和IGD评价指标对算法进行多样性和收敛性分析,实验结果表明,该算法在收敛性和多样性方面得到了改进与提高,能得到更优的Pareto解集。     

一种基于自适应选择策略的改进型MOEA/D算法

针对MOEA/D单纯使用邻域更新作为选择策略而造成的个体解的重复更新、缺乏全局适配性等问题,提出了一种兼及全局替换和局部更新策略的新算法,即基于自适应选择策略的改进型MOEA/D(MOEA/D-AS)。算法首先设计了一种新的基于最佳二分图匹配的选择策略(KMS),利用子问题和个体解的匹配关系,从全局角度实现精英个体集的最优选择;然后利用种群的进化信息构造一种匹配紊乱判断机制;最后利用紊乱判断机制,在综合分析邻域更新策略和KMS各自优势的基础上,使算法自适应地选择最合适的选择策略,以提高鲁棒性和优化效率。选取LZ09,DTLZ,CEC09等作为标准测试函数,将改进后的算法MOEA/D-AS与经典MOEA/D系列算法进行对比实验,并以Spread和IGD为性能评估指标。实验结果表明新算法具有更好的收敛性和分布性,验证了自适应选择策略能够有效地指导精英解的选择过程。     

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.     

基于分解的演化多目标优化算法综述

基于分解的演化多目标优化算法(MOEA/D)的基本思想是将一个多目标优化问题转化成一系列子问题(单目标或者多目标)来进行优化求解.自2007年提出以来, MOEA/D受到了国内外学者的广泛关注,已经成为最具代表性的演化多目标优化算法之一.总结过去13年中关于MOEA/D的一些研究进展,具体内容包括:(1)关于MOEA/D的算法改进;(2) MOEA/D在超多目标优化问题及约束优化问题上的研究;(3) MOEA/D在一些实际问题上的应用.然后,实验对比几个具有代表性的MOEA/D改进算法.最后,指出一些MOEA/D未来的研究方向.     

A decomposition-based multiobjective evolutionary algorithm with angle-based adaptive penalty

A multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and optimizes them in a collaborative manner. In MOEA/D, decomposition mechanisms are used to push the population to approach the Pareto optimal front (POF), while a set of uniformly distributed weight vectors are applied to maintain the diversity of the population. Penalty-based boundary intersection (PBI) is one of the approaches used frequently in decomposition. In PBI, the penalty factor plays a crucial role in balancing convergence and diversity. However, the traditional PBI approach adopts a fixed penalty value, which will significantly degrade the performance of MOEA/D on some MOPs with complicated POFs. This paper proposes an angle-based adaptive penalty (AAP) scheme for MOEA/D, called MOEA/D-AAP, which can dynamically adjust the penalty value for each weight vector during the evolutionary process. Six newly designed benchmark MOPs and an MOP in the wastewater treatment process are used to test the effectiveness of the proposed MOEA/D-AAP. Comparison experiments demonstrate that the AAP scheme can significantly improve the performance of MOEA/D.     

A novel adaptive control strategy for decomposition-based multiobjective algorithm

Recently, evolutionary algorithm based on decomposition (MOEA/D) has been found to be very effective and efficient for solving complicated multiobjective optimization problems (MOPs). However, the selected differential evolution (DE) strategies and their parameter settings impact a lot on the performance of MOEA/D when tackling various kinds of MOPs. Therefore, in this paper, a novel adaptive control strategy is designed for a recently proposed MOEA/D with stable matching model, in which multiple DE strategies coupled with the parameter settings are adaptively conducted at different evolutionary stages and thus their advantages can be combined to further enhance the performance. By exploiting the historically successful experience, an execution probability is learned for each DE strategy to perform adaptive adjustment on the candidate solutions. The proposed adaptive strategies on operator selection and parameter settings are aimed at improving both of the convergence speed and population diversity, which are validated by our numerous experiments. When compared with several variants of MOEA/D such as MOEA/D, MOEA/D-DE, MOEA/D-DE+PSO, ENS-MOEA/D, MOEA/D-FRRMAB and MOEA/D-STM, our algorithm performs better on most of test problems.     

MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives

To extend multiobjective evolutionary algorithm based on decomposition (MOEA/D) in higher dimensional objective spaces, this paper proposes a new version of MOEA/D with uniform design, named the uniform design multiobjective evolutionary algorithm based on decomposition (UMOEA/D), and compares the proposed algorithm with MOEA/D and NSGA-II on some scalable test problems with three to five objectives. UMOEA/D adopts the uniform design method to set the aggregation coefficient vectors of the subproblems. Compared with MOEA/D, distribution of the coefficient vectors is more uniform over the design space, and the population size neither increases nonlinearly with the number of objectives nor considers a formulaic setting. The experimental results indicate that UMOEA/D outperforms MOEA/D and NSGA-II on almost all these many-objective test instances, especially on problems with higher dimensional objectives and complicated Pareto set shapes. Experimental results also show that UMOEA/D runs faster than NSGA-II for the problems used in this paper. In additional, the results obtained are very competitive when comparing UMOEA/D with some other algorithm on the multiobjective knapsack problems.     

Decomposing the user-preference in multiobjective optimization

Preference information (such as the reference point) of the decision maker (DM) is often used in multiobjective optimization; however, the location of the specified reference point has a detrimental effect on the performance of multiobjective evolutionary algorithms (MOEAs). Inspired by multiobjective evolutionary algorithm-based decomposition (MOEA/D), this paper proposes an MOEA to decompose the preference information of the reference point specified by the DM into a number of scalar optimization subproblems and deals with them simultaneously (called MOEA/D-PRE). This paper presents an approach of iterative weight to map the desired region of the DM, which makes the algorithm easily obtain the desired region. Experimental results have demonstrated that the proposed algorithm outperforms two popular preference-based approaches, g-dominance and r-dominance, on continuous multiobjective optimization problems (MOPs), especially on many-objective optimization problems. Moreover, this study develops distinct models to satisfy different needs of the DM, thus providing a new way to deal with preference-based multiobjective optimization. Additionally, in terms of the shortcoming of MOEA/D-PRE, an improved MOEA/D-PRE that dynamically adjusts the size of the preferred region is proposed and has better performance on some problems.     

采用新邻居模型的多目标分解进化算法

在通常的基于分解的多目标进化算法中,繁殖计算时使用的解从基于子问题定义的邻居集合中选择,当目标函数存在多峰等复杂特征时,它们在决策空间的距离可能较远,这会导致算法性能变差。为了解决这一问题,提出了一种采用新邻居模型的多目标分解进化算法MOEA/D-NN。该算法重新设计了繁殖计算中使用的邻居模型,利用解在决策空间上的距离计算邻居,进而为每个子问题维护相应的邻居集合,在此基础上对邻居集合进行定时更新,实现了基于新邻居模型的繁殖计算。通过在公开测试集上的实验结果表明,提出的算法与几种经典的多目标进化算法相比,在大多数测试集上表现更优。     

The effects of asymmetric neighborhood assignment in the MOEA/D algorithm

The Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) is a very efficient multiobjective evolutionary algorithm introduced in recent years. This algorithm works by decomposing a multiobjective optimization problem to many scalar optimization problems and by assigning each specimen in the population to a specific subproblem. The MOEA/D algorithm transfers information between specimens assigned to the subproblems using a neighborhood relation.In this paper it is shown that parameter settings commonly used in the literature cause an asymmetric neighbor assignment which in turn affects the selective pressure and consequently causes the population to converge asymmetrically. The paper contains theoretical explanation of how this bias is caused as well as an experimental verification. The described effect is undesirable, because a multiobjective optimizer should not introduce asymmetries not present in the optimization problem. The paper gives some guidelines on how to avoid such artificial asymmetries.     

一种新的基于进化策略的多目标优化算法

用进化策略求解多目标优化问题时,为了提高解在决策变量空间中的搜索能力和保证Pareto前沿的多样性,提出了一种新的基于进化策略的多目标优化算法。运用自适应变异步长的进化策略,使解在决策变量空间中进行全局和局部搜索;并引入非劣解按一定比例进入下一代的方法,使完全被占优的个体有机会参与到下一代的繁殖,保持了解在Pareto前沿的多样性。该算法在保证解在决策空间多样性的同时,也保持了Pareto前沿的多样性。仿真实验表明,该算法具有良好的搜索性能。