一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

多目标微粒群优化算法综述

作为一种有效的多目标优化工具,微粒群优化(PSO)算法已经得到广泛研究与认可.首先对多目标优化问题进行了形式化描述,介绍了微粒群优化算法与遗传算法的区别,并将多目标微粒群优化算法(MOPSO)分为以下几类:聚集函数法、基于目标函数排序法、子群法、基于Pareto支配算法和其他方法,分析了各类算法的主要思想、特点及其代表性算法.其次,针对非支配解的选择、外部档案集的修剪、解集多样性的保持以及微粒个体历史最优解和群体最优解的选取等热点问题进行了论述,并在此基础上对各类典型算法进行了比较.最后,根据当前MOPSO算法的研究状况,提出了该领域的发展方向.     

Measuring the convergence and diversity of CDAS Multi-Objective Particle Swarm Optimization Algorithms: A study of many-objective problems

The interest for many-objective optimization has grown due to the limitations of Pareto dominance based Multi-Objective Evolutionary Algorithms when dealing with problems of a high number of objectives. Recently, some many-objective techniques have been proposed to avoid the deterioration of these algorithms' search ability. At the same time, the interest in the use of Particle Swarm Optimization (PSO) algorithms in multi-objective problems also grew. The PSO has been found to be very efficient to solve multi-objective problems (MOPs) and several Multi-Objective Particle Swarm Optimization (MOPSO) algorithms have been proposed. This work presents a study of the behavior of MOPSO algorithms in many-objective problems. The many-objective technique named control of dominance area of solutions (CDAS) is used on two Multi-Objective Particle Swarm Optimization algorithms. An empirical analysis is performed to identify the influence of the CDAS technique on the convergence and diversity of MOPSO algorithms using three different many-objective problems. The experimental results are compared applying quality indicators and statistical tests.     

基于反向学习和种群引导的多目标蝗虫优化算法

为了解决多目标优化的相关问题,提出了求解多目标的蝗虫优化算法,结合单个目标的蝗虫优化算法的搜寻机制、帕累托优势以及拥挤度策略,并在算法中应用种群引导和高斯变异算子,加入了反向学习机制。将所提出的算法与经典的MOPSO、MOCS、MOGOA和MOWOA算法进行了比较,比较结果表明,所提出的改进多目标蝗虫优化算法具有良好的鲁棒性,所求得的解分布更均匀,收敛更快速,是一种有着良好应用前景的多目标进化算法。     

混合多目标粒子群优化算法在热精轧负荷分配优化中的应用

通过对热精轧负荷分配过程的分析,选取负荷均衡、板形良好和轧制功率最低为目标,建立了热精轧负荷分配多目标优化模型.为了提高多目标优化算法解集的分布性和收敛性,提出了一种混合多目标粒子群优化算法(HMOPSO),该算法根据Pareto支配关系得到Pareto前沿进而保证种群收敛;采用分解策略维护外部存档,该策略首先根据Pareto前沿求出上界点对目标空间进行归一化处理,然后对种群进行分区处理进而保证种群的分布性能.仿真结果表明,HMOPSO的收敛性和分布性都好于MOPSO和d MOPSO;采用模糊多属性决策的方法从Pareto最优解集中选择一个Pareto最优解,通过与经验负荷分配方法相比,表明该Pareto最优解可以使轧制方案更加合理.     

Particle swarm optimization with preference order ranking for multi-objective optimization

A new optimality criterion based on preference order (PO) scheme is used to identify the best compromise in multi-objective particle swarm optimization (MOPSO). This scheme is more efficient than Pareto ranking scheme, especially when the number of objectives is very large. Meanwhile, a novel updating formula for the particle’s velocity is introduced to improve the search ability of the algorithm. The proposed algorithm has been compared with NSGA-II and other two MOPSO algorithms. The experimental results indicate that the proposed approach is effective on the highly complex multi-objective optimization problems.     

均衡分布性和收敛性的多目标粒子群优化方法

粒子群优化（PSO）算法是一种基于群体演化且非常有效的求解多目标优化问题的方法,但因经典算法中粒子进化存在趋同性导致算法易陷入局部Pareto最优前沿,使得解集收敛性和分布性不理想。为此提出了一种均衡分布性和收敛性的多目标粒子群优化（DWMOPSO）算法,算法中每个粒子根据自身在进化过程中记忆的个体最好适应度值构建进化速度,由进化速度的快慢动态调整各粒子惯性权重,增加粒子的多样性,从而提高粒子跳出局部最优解的概率。通过在5个标准测试函数上进行仿真实验,结果表明,与Coello的多目标粒子群优化(MOPSO)算法相比,DWMOPSO算法获得的解集在与真实解集的逼近性和解集的分布性两个方面都有了很大的提高。     

基于Pareto邻域交叉算子的多目标粒子群优化算法

针对粒子群优化（PSO）算法局部搜索能力不足的问题,提出一种基于Pareto邻域交叉算子的多目标粒子群优化算法(MPSOP)。该算法利用粒子群优化算法和Pareto邻域交叉算子相结合的策略产生新种群,并利用尺度因子在线调节粒子群优化算法和Pareto邻域交叉算子的贡献量。数值实验选取6个常用测试函数并对NSGA-Ⅱ、SPEA2、MOPSO三个多目标算法进行比较,数值实验结果表明MPSOP算法的有效性。     

基于粒子群算法求解多目标优化问题

粒子群优化算法自提出以来，由于其容易理解、易于实现，所以发展很快，在很多领域得到了应用．通过对粒子群算法全局极值和个体极值选取方式的改进，提出了一种用于求解多目标优化问题的算法，实现了对多目标优化问题的非劣最优解集的搜索，实验结果证明了算法的有效性．     

解多目标优化问题的新粒子群优化算法

通过定义的粒子序值方差和U-度量方差,把对任意多个目标函数的优化问题转化成为两个目标函数的优化问题。继而把Pareto最优与粒子群优化(PSO)算法相结合,对转化后的优化问题提出了一种新的多目标粒子群优化算法,并证明了其收敛性。新方法用较少计算量便可以求出一组在最优解集合中分布均匀且数量充足的最优解。计算机仿真表明该算法对不同的试验函数均可用较少计算量求出在最优解集合中分布均匀且数量充足的最优解。     

Simple heuristics-based selection of guides for multi-objective PSO with an application to electrical distribution system planning

In multi-objective particle swarm optimization (MOPSO), a proper selection of local guides significantly influences detection of non-dominated solutions in the objective/solution space and, hence, the convergence characteristics towards the Pareto-optimal set. This paper presents an algorithm based on simple heuristics for selection of local guides in MOPSO, named as HSG-MOPSO (Heuristics-based-Selection-of-Guides in MOPSO). In the HSG-MOPSO, the set of potential guides (in a PSO iteration) consists of the non-dominated solutions (which are normally stored in an elite archive) and some specifically chosen dominated solutions. Thus, there are two types of local guides in the HSG-MOPSO, i.e., non-dominated and dominated guides; they are named so as to signify whether the chosen guide is a non-dominated or a dominated solution. In any iteration, a guide, from the set of available guides, is suitably selected for each population member. Some specified proportion of the current population members follow their respective nearest non-dominated guides and the rest follow their respective nearest dominated guides. The proposed HSG-MOPSO is firstly evaluated on a number of multi-objective benchmark problems along with investigations on the controlling parameters of the guide selection algorithm. The performance of the proposed method is compared with those of two well-known guide selection methods for evolutionary multi-objective optimization, namely the Sigma method and the Strength Pareto Evolutionary Algorithm-2 (SPEA2) implemented in PSO framework. Finally, the HSG-MOPSO is evaluated on a more involved real world problem, i.e., multi-objective planning of electrical distribution system. Simulation results are reported and analyzed to illustrate the viability of the proposed guide selection method for MOPSO.     

基于多目标粒子群算法的混合流水车间调度方法研究

混合流水车间调度问题HFSP是一种具有很强应用背景的生产调度问题。本文给出了一种HFSP多目标调度模型,提出了一种针对该类问题的多目标粒子群算法。该算法采用基于Pareto支配关系的极值更新策略;采取对自适应惯性权重递减和对种群变异的方法以保持种群多样性;设置Pareto解池保存计算中出现的Pareto最优解,并提出了一种基于适应度拥挤度的聚类算法优化解的分布特性。实验结果表明,本文算法是求解HFSP问题的一种有效方法。     

Handling multi-objective optimization problems with a multi-swarm cooperative particle swarm optimizer

This paper presents a new multi-objective optimization algorithm in which multi-swarm cooperative strategy is incorporated into particle swarm optimization algorithm, called multi-swarm cooperative multi-objective particle swarm optimizer (MC-MOPSO). This algorithm consists of multiple slave swarms and one master swarm. Each slave swarm is designed to optimize one objective function of the multi-objective problem in order to find out all the non-dominated optima of this objective function. In order to produce a well distributed Pareto front, the master swarm is developed to cover gaps among non-dominated optima by using a local MOPSO algorithm. Moreover, in order to strengthen the capability locating multiple optima of the PSO, several improved techniques such as the Pareto dominance-based species technique and the escape strategy of mature species are introduced. The simulation results indicate that our algorithm is highly competitive to solving the multi-objective optimization problems.     

基于多目标蝗虫优化算法的移动机器人路径规划

在静态多障碍物环境下的移动机器人路径规划问题中，粒子群算法存在容易产生早熟收敛和局部寻优能力较差等缺点，导致机器人路径规划精度低。为此，提出一种多目标蝗虫优化算法（MOGOA）来解决这一问题。根据移动机器人路径规划要求将路径长度、平滑度和安全性作为路径优化的目标，建立相应的多目标优化问题的数学模型。在种群的搜索过程中，引入曲线自适应策略以提高算法收敛速度，并使用Pareto最优准则来解决三个目标之间的共存问题。实验结果表明：所提出的算法在解决上述问题中寻找到的路径更短，表现出更好的收敛性。该算法与多目标粒子群（MOPSO）算法相比路径长度减少了约2.01%，搜索到最小路径的迭代次数减少了约19.34%。     

基于Pareto的多目标优化免疫算法

免疫算法具有搜索效率高、避免过早收敛、群体优化、保持个体多样性等优点。将其应用于多目标优化问题,建立了一种新型的基于Pareto的多目标优化免疫算法(MOIA)。算法中,将优化问题的可行解对应抗体,优化问题的目标函数对应抗原,Pareto最优解被保存在记忆细胞集中,并利用有别于聚类的邻近排挤算法对其进行不断更新,进而获得分布均匀的Pareto最优解。文章最后,对MOIA算法与文献[3]中SPEA算法进行仿真,通过比较两者的收敛性和分布性,得到了MOIA优于SPEA的结论。     

求解机械优化的Pareto多目标中心粒子群算法

针对基于权重法的多目标算法无法求解约束多目标问题的缺陷,将中心粒子群算法与Pareto解集搜索算法相结合,提出一种Pareto多目标中心粒子群算法。将此方法用来优化气门弹簧的模型,实验结果表明,该优化方法能够快速准确地收敛于Pareto解集,并且使其对应的目标域均匀地分布于Pareto最优目标域。     

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.     

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

一种基于拟态物理学优化的多目标优化算法

提出一种使用拟态物理学优化(APO)解决多目标优化问题的算法(MOAPO).根据多目标优化问题的特点,借鉴聚集函数法的思想,利用APO算法实现了对多目标优化问题中Pareto最优解集的搜索,并且在搜索过程中动态调整惯性权重与引力因子,以增强非劣解的多样性.实验结果表明了将APO应用于多目标优化问题的有效性.通过与基于微粒群优化(PSO)的多目标优化算法及NSGA-Ⅱ算法的比较,表明了MOAPO算法具有较好的分布性.     

A multi-objective artificial physics optimization algorithm based on ranks of individuals

This paper proposes a multi-objective artificial physics optimization algorithm based on individuals’ ranks. Using a Pareto sorting based technique and incorporating the concept of neighborhood crowding degree, evolutionary individuals in the search space are evaluated at first. Then each individual is assigned a unique serial number in terms of its performance, which affects the mass of the individual. Thereby, the population evolves towards the direction of the Pareto-optimal front. Synchronously, the presented approach has good diversity, such that the population is spread evenly on the Pareto front. Results of simulation on a number of difficult test problems show that the proposed algorithm, with less evolutionary generations, is able to find a better spread of solutions and better convergence near the true Pareto-optimal front compared to classical multi-objective evolutionary algorithms (NSGA, SPEA, MOPSO) and to simple multi-objective artificial physics optimization algorithm.