A genetic algorithm for a bi-objective capacitated arc routing problem

The capacitated arc routing problem (CARP) is a very hard vehicle routing problem for which the objective—in its classical form—is the minimization of the total cost of the routes. In addition, one can seek to minimize also the cost of the longest trip.In this paper, a multi-objective genetic algorithm is presented for this more realistic CARP. Inspired by the second version of the Non-dominated sorted genetic algorithm framework, the procedure is improved by using good constructive heuristics to seed the initial population and by including a local search procedure. The new framework and its different flavour is appraised on three sets of classical CARP instances comprising 81 files.Yet designed for a bi-objective problem, the best versions are competitive with state-of-the-art metaheuristics for the single objective CARP, both in terms of solution quality and computational efficiency: indeed, they retrieve a majority of proven optima and improve two best-known solutions.     

一种多目标优化合作型协同进化算法

基于合作型协同进化模型,提出了一种新型的多目标优化进化算法.该算法使用精英保留的思想以加快收敛速度,并采用一种新型的子群体间合作方式,提高了候选解的多样性,且避免了在一般多目标优化进化算法中难以处理的适应值分配或非支配排序过程,从而大大减小了计算资源的消耗.使用图形法和三种定量的测度将所提算法与一种经典的多目标优化进化算法NSGA-Ⅱ在一组标准测试函数上进行了比较,结果表明算法具有更高的搜索效率.     

一种求解双目标job shop问题的混合进化算法

提出一种求解双目标job shop排序问题的混合进化算法．该算法采用改进的精英复制策略,降低了计算复杂性;通过引入递进进化模式,避免了算法的早熟;通过递进过程中的非劣解邻域搜索,增强了算法局部搜索性能．采用该算法和代表性算法NSGA-Ⅱ,MOGLS对82个标准双目标job shop算例进行优化对比,所得结果验证了该算法求解双目标job shop排序问题的有效性．     

Pareto最优概念的多目标进化算法综述

群体搜索策略和群体间个体之间的信息交换是进化算法在解决多目标优化问题上的两大优势.目前,基于Pareto最优概念的多目标进化算法已成为多目标优化问题研究的主流方向.详细介绍了该领域的经典算法,特别对各种算法在种群快速收敛并均匀分布于问题的非劣最优域上所采取的策略进行了阐述,并归纳了算法性能评估中需要深入研究的问题.     

基于多目标飞蛾算法的电力系统无功优化研究

鉴于电力需求的日益增长与传统无功优化方法的桎梏,如何更加合理有效地解决电力系统的无功优化问题逐渐成为了研究的热点。提出一种多目标飞蛾扑火算法来解决电力系统多目标无功优化的问题,算法引入固定大小的外部储存机制、自适应的网格和筛选机制来有效存储和提升无功优化问题的帕累托最优解集,算法采用CEC2009标准多目标测试函数来进行仿真实验,并与两种经典算法进行性能的对比分析。此外,在电力系统IEEE 30节点上将该算法与MOPSO,NGSGA-II算法的求解结果进行比较分析的结果表明,多目标飞蛾算法具有良好的性能,并在解决电力系统多目标无功优化问题上具有良好的潜力。     

基于空间划分的进化算法应用

针对航空公司人员排班问题,提出了一种基于空间划分的进化算法。根据种群个体的分布,结合空间划分思想,对进化算法的编码方式和进化算子进行了改进,并以清洁工排班为例,验证了算法的可行性和优越性,对实际应用提供了良好的参考。     

Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.     

棒线材轧制批量调度多目标混合优化

在分析批量调度问题特征的基础上建立了精轧工序轧制批量调度的数学模型,采用混合自适应多目标进化算法进行求解．在该算法中,采用全局搜索与局部优化相结合来加快算法的收敛速度,基因修正与罚函数相结合来解决约束问题,运用免疫共享方法维护种群的多源性,根据评估结果自适应改变遗传操作的概率．应用生产实际数据进行测试,表明该调度方法能获得所需的Pareto优化前沿．     

一种求解约束多目标优化问题的线性进化算法

针对多目标优化问题,提出了一种新的基于实数编码的线性进化算法.新算法将约束优化问题的高维搜索空间通过线性变换映射到二维空间,在二维空间中探索原优化问题的解,并构造出一种线性适应度函数,重新设计了一种基于密度函数的交叉算子.对二组典型优化问题的测试表明,本算法是可行和有效的,解集分布的均匀性与多样性均较理想.     

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。     

人工免疫系统中免疫细胞的分离演化策略

免疫细胞是人工免疫系统最关键的组件,它在整个生命周期的演变过程将直接决定免疫系统的性能。文章针对免疫细胞的浓度和系统识别效率这两个相互制约的约束条件,分析了免疫细胞在不同阶段的差异,提出了一个免疫细胞的进化策略。论文采用不同的适应方法,控制细胞群体的演化方向。并充分考虑单个细胞的覆盖能力和免疫细胞群体对资源的占用问题,采用多目标优化策略,使免疫系统的有效性得到明显改善。     

Multi-objective evolution of fuzzy systems

Fuzzy systems comprise one of the models best suited to function approximation problems, but due to the non linear dependencies between the parameters that define the system rules, the solution search space for this type of problems contains many local optima. Another important issue is the identification of the optimum structure for the fuzzy system. Depending on the complexity of the model, different solutions can be found with different compromises between their approximation error and their generalization properties. Thus, the problem becomes a multi-objective problem with two clearly competing objectives, the complexity of the model and its approximation error.The algorithms proposed in the literature to construct fuzzy systems from examples usually refine iteratively a unique model until a compromise between its complexity and its approximation error is found. This is not an adequate approach for this problem because there exists a set of Pareto-optimum solutions that can be considered equivalent. Thus, we propose the use of multi-objective evolutionary algorithms because, as they maintain a population of potential solutions for the problem, they are able to optimize both objectives simultaneously. We also incorporate some new expert evolutionary operators that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm.The proposed algorithm is tested with some target functions widely used in the literature and the results obtained are compared to other approaches.     

Plateaus can be harder in multi-objective optimization

In recent years a lot of progress has been made in understanding the behavior of evolutionary computation methods for single- and multi-objective problems. Our aim is to analyze the diversity mechanisms that are implicitly used in evolutionary algorithms for multi-objective problems by rigorous runtime analyses. We show that, even if the population size is small, the runtime can be exponential where corresponding single-objective problems are optimized within polynomial time. To illustrate this behavior we analyze a simple plateau function in a first step and extend our result to a class of instances of the well-known SetCover problem.     

Non-additive multi-objective robot coalition formation

Manifold increase in the complexity of robotic tasks has mandated the use of robotic teams called coalitions that collaborate to perform complex tasks. In this scenario, the problem of allocating tasks to teams of robots (also known as the coalition formation problem) assumes significance. So far, solutions to this NP-hard problem have focused on optimizing a single utility function such as resource utilization or the number of tasks completed. We have modeled the multi-robot coalition formation problem as a multi-objective optimization problem with conflicting objectives. This paper extends our recent work in multi-objective approaches to robot coalition formation, and proposes the application of the Pareto Archived Evolution Strategy (PAES) algorithm to the coalition formation problem, resulting in more efficient solutions. Simulations were carried out to demonstrate the relative diversity in the solution sets generated by PAES as compared to previously studied methods. Experiments also demonstrate the relative scalability of PAES. Finally, three different selection strategies were implemented to choose solutions from the Pareto optimal set. Impact of the selection strategies on the final coalitions formed has been shown using Player/Stage.     

基于多点非均匀变异的多目标极值优化算法研究

多目标进化算法因其在解决含有多个矛盾目标函数的多目标优化问题中的强大处理能力,正受到越来越多的关注与研究。极值优化作为一种新型的进化算法,已在各种离散优化、连续优化测试函数以及工程优化问题中得到了较为成功的应用,但有关多目标EO算法的研究却十分有限。本文将采用Pareto优化的基本原理引入到极值优化算法中,提出一种求解连续多目标优化问题的基于多点非均匀变异的多目标极值优化算法。通过对六个国际公认的连续多目标优化测试函数的仿真实验结果表明：本文提出算法相比NSGA-II、 PAES、SPEA和SPEA2等经典多目标优化算法在收敛性和分布性方面均具有优势。