一种基于最小生成树的多目标进化算法

怎样保证朝Pareto最优解的方向搜索和如何获得均匀分布且范围广泛的非支配解是多目标进化算法(MOEA)设计时的两个关键问题,它们很大程度上取决于适应度赋值和外部种群维护这两个重要部分.提出了一种基于最小生成树的多目标进化算法(MST_MOEA).在考虑了个体间支配关系的基础上,利用个体与非支配集的距离和不同等级个体的树聚集密度来对适应度赋值;在外部种群的非支配解个数超过规定的种群规模时,用树的度数和树聚集密度对其进行修剪.将其应用于不同维数下9个测试函数,并与NSGA-II,SPEA2进行对比,结果证实了算法良好的收敛性和分布性.     

一种求解约束多目标问题的协作进化算法

针对约束多目标进化算法求解约束多目标问题时难以平衡收敛性、多样性和可行性的问题,提出一种协作进化算法(ConMOEA).将自适应形状估计进化算法(AGE-MOEA)和非支配排序遗传算法(NSGA-II)优势融合,采用Deb约束支配原则非支配排序组合种群实现个体优选,在临界层中根据最大拥挤距离或生存值选择所需个体,最终形成新种群,实现种群快速接近Pareto前沿并具有良好分布性.为验证所提出算法的性能,对近期提出的一组DOC基准函数进行仿真计算,采用反世代距离(IGD)和超体积(HV)两个通用评价指标,与NSGA-II-CDP、C-TAEA、PPS、ToP、A-NSGA-III、AGE-MOEA约束多目标算法进行比较分析,实验结果证明ConMOEA具有更优的收敛性和多样性.     

一种基于混合高斯模型的多目标进化算法

目前,大多数多目标进化算法采用为单目标优化所设计的重组算子.通过证明或实验分析了几个典型的单目标优化重组算子并不适合某些多目标优化问题.提出了基于分解技术和混合高斯模型的多目标优化算法（multiobjective evolutionary algorithm based on decomposition and mixture Gaussian models,简称MOEA/D-MG）.该算法首先采用一个改进的混合高斯模型对群体建模并采样产生新个体,然后利用一个贪婪策略来更新群体.针对具有复杂Pareto前沿的多目标优化问题的测试结果表明,对给定的大多数测试题,该算法具有良好的效果.     

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.     

An effective model of multiple multi-objective evolutionary algorithms with the assistance of regional multi-objective evolutionary algorithms: VIPMOEAs

Division of the evolutionary search among multiple multi-objective evolutionary algorithms (MOEAs) is a recent advantage in MOEAs design, particularly in effective parallel and distributed MOEAs. However, most these algorithms rely on such a central (re) division that affects the algorithms’ efficiency. This paper first proposes a local MOEA that searches on a particular region of objective space with its novel evolutionary selections. It effectively searches for Pareto Fronts (PFs) inside the given polar-based region, while nearby the region is also explored, intelligently. The algorithm is deliberately designed to adjust its search direction to outside the region – but nearby – in the case of a region with no Pareto Front. With this contribution, a novel island model is proposed to run multiple forms of the local MOEA to improve a conventional MOEA (e.g. NSGA-II or MOEA/D) running along – in another island. To dividing the search, a new division technique is designed to give particular regions of objective space to the local MOEAs, frequently and effectively. Meanwhile, the islands benefit from a sophisticated immigration strategy without any central (re) collection, (re) division and (re) distribution acts. Results of three experiments have confirmed that the proposed island model mostly outperforms to the clustering MOEAs with similar division technique and similar island models on DTLZs. The model is also used and evaluated on a real-world combinational problem, flexible logistic network design problem. The model definitely outperforms to a similar island model with conventional MOEA (NSGA-II) used in each island.     

一种求解多目标优化问题的进化算法混合框架

为了提高多目标优化算法的求解性能,提出一种启发式的基于种群的全局搜索与局部搜索相结合的多目标进化算法混合框架.该框架采用模块化、系统化的设计思想,不同模块可以采用不同策略构成不同的算法.采用经典的改进非支配排序遗传算法(NSGA-II)和基于分解的多目标进化算法(MOEA/D)作为进化算法的模块算法来验证所提混合框架的有效性.数值实验表明,所提混合框架具有良好性能,可以兼顾算法求解的多样性和收敛性,有效提升现有多目标进化算法的求解性能.     

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.     

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...     

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.     

基于多目标进化算法的MOEA/D权重向量产生方法

在进化多目标优化研究领域,多目标优化是指对含有2个及以上目标的多目标问题的同时优化,其在近些年来受到越来越多的关注。随着MOEA/D的提出,基于聚合的多目标进化算法得到越来越多的研究,对MOEA/D算法的改进已有较多成果,但是很少有成果研究MOEA/D中权重的产生方法。提出一种使用多目标进化算法产生任意多个均匀分布的权重向量的方法,将其应用到MOEA/D,MSOPS和NSGA-III中,对这3个经典的基于聚合的多目标进化算法进行系统的比较研究。通过该类算法在DTLZ测试集、多目标旅行商问题MOTSP上的优化结果来分别研究该类算法在连续性问题、组合优化问题上的优化能力,以及使用矩形测试问题使得多目标进化算法的优化结果在决策空间可视化。实验结果表明,没有一个算法能适用于所有特性的问题。然而,MOEA/D采用不同聚合函数的两个算法MOEA/D_Tchebycheff和MOEA/D_PBI在多数情况下的性能比MSOPS和NSGA-III更好。     

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.     

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.     

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.     

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。     

MOEA/D线性插入方向向量策略研究

MOEA/D具有良好的收敛性、均匀的分布性、求解效率高等优点,普遍应用于求解多目标优化问题.然而对于Pareto前端复杂的多目标优化问题,预先设定均匀的权重向量并不能够维持Pareto最优解集的良好分布性.本文,首先分析均匀分布的权重向量、均匀分布的搜索方向二者与均匀分布的解集之间的关系,提出一种新的权重向量设置方式;其次基于进化过程中解集的分布,提出线性插入搜索方向策略,并将其转换为对应的权重向量,同时在MOEA/D中周期性应用该策略调整搜索方向,获取分布均匀的解集;最后将该算法在WFG系列测试问题上进行性能测试,并采用世代距离指标(GD)、Spacing指标(S)、超体积指标(HV)对算法收敛性和多样性进行对比分析,实验结果表明,与原始的MOEA/D、使用均匀分布的搜索方向MOEA/D、使用预处理的M OEA/D、M OEA/D-DU相比,改进的算法求出解集的多样性极大提高,收敛性明显增强,解集的整体质量显著提高.     

Multiobjective memetic algorithm based on decomposition

In recent years, hybridization of multi-objective evolutionary algorithms (MOEAs) with traditional mathematical programming techniques have received significant attention in the field of evolutionary computing (EC). The use of multiple strategies with self-adaptation manners can further improve the algorithmic performances of decomposition-based evolutionary algorithms. In this paper, we propose a new multiobjective memetic algorithm based on the decomposition approach and the particle swarm optimization (PSO) algorithm. For brevity, we refer to our developed approach as MOEA/D-DE+PSO. In our proposed methodology, PSO acts as a local search engine and differential evolution works as the main search operator in the whole process of optimization. PSO updates the position of its solution with the help of the best information on itself and its neighboring solution. The experimental results produced by our developed memtic algorithm are more promising than those of the simple MOEA/D algorithm, on most test problems. Results on the sensitivity of the suggested algorithm to key parameters such as population size, neighborhood size and maximum number of solutions to be altered for a given subproblem in the decomposition process are also included.     

基于聚类的快速多目标遗传算法

多目标遗传算法非常适合于求解多目标优化问题．讨论了进化个体之间的支配关系及有关性质，论证了可以用快速排序的方法对进化群体中的个体进行分类，同时探讨了用聚类方法来保持群体的多样性，具体讨论了基于层次凝聚距离的聚类，在此基础上提出了用分类和聚类的方法构造新的进化群体．理论分析与实验结果表明，所讨论的方法比较国际上已有的方法具有更快的收敛速度．     

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.     

Multiobjective evolutionary algorithms for electric power dispatch problem

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.