A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.     

基于多目标粒子群优化算法的装备维修任务分配

装备维修任务分配问题是典型的多约束/多目标/非线性规划问题,利用传统方法无法求解,因此提出了一种约束多目标粒子群算法,并运用该算法对装备维修任务分配问题进行了优化求解。仿真结果表明,约束多目标粒子群算法针对该问题,在不同参数和约束条件下都有很强的收敛寻优能力,能快速产生多个非支配解,是一种高效的算法,对实现装备维修任务分配的客观量化优化决策有重要作用。     

Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks

In particle swarm optimization (PSO) each particle uses its personal and global or local best positions by linear summation. However, it is very time consuming to find the global or local best positions in case of complex problems. To overcome this problem, we propose a new multi-objective variant of PSO called attributed multi-objective comprehensive learning particle swarm optimizer (A-MOCLPSO). In this technique, we do not use global or local best positions to modify the velocity of a particle; instead, we use the best position of a randomly selected particle from the whole population to update the velocity of each dimension. This method not only increases the speed of the algorithm but also searches in more promising areas of the search space. We perform an extensive experimentation on well-known benchmark problems such as Schaffer (SCH), Kursawa (KUR), and Zitzler–Deb–Thiele (ZDT) functions. The experiments show very convincing results when the proposed technique is compared with existing versions of PSO known as multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) and multi-objective particle swarm optimization (MOPSO), as well as non-dominated sorting genetic algorithm II (NSGA-II). As a case study, we apply our proposed A-MOCLPSO algorithm on an attack tree model for the security hardening problem of a networked system in order to optimize the total security cost and the residual damage, and provide diverse solutions for the problem. The results of our experiments show that the proposed algorithm outperforms the previous solutions obtained for the security hardening problem using NSGA-II, as well as MOCLPSO for the same problem. Hence, the proposed algorithm can be considered as a strong alternative to solve multi-objective optimization problems.     

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。     

基于MOPSO算法的卫星共形阵列天线多波束形成

针对共形阵列天线多波束方向图综合问题,提出一种基于最大方向性系数方法得到初始非劣解的多目标粒子群算法,求解满足多个期望波束和低副瓣要求的Pareto最优解。算法首先采用多目标分解策略,由多个单波束最优解的加权线性组合得到近最优解的非劣解。然后结合该非劣解,基于粒子空间和目标空间同时约束的局部搜寻策略,使用多目标粒子群算法优化多个波束,并降低副瓣。仿真结果表明,该算法有效地实现了卫星共形阵列天线的多波束形成和低副瓣,且能快速得到Pareto最优解分布。     

Robust optimization using multi-objective particle swarm optimization

This article proposes an algorithm to search for solutions which are robust against small perturbations in design variables. The proposed algorithm formulates robust optimization as a bi-objective optimization problem, and fi nds solutions by multi-objective particle swarm optimization (MOPSO). Experimental results have shown that MOPSO has a better performance at fi nding multiple robust solutions than a previous method using a multi-objective genetic algorithm.     

解约束规划问题的新型多目标粒子群优化算法

给出了一种求解约束规划问题的新解法。新方法将约束规划问题转化成两个目标优化问题,并对转化后的多目标优化问题设计了一种新型多目标粒子群优化算法(MOPSO)。数据实验表明该算法对带约束的规划问题求解是非常有效的。     

一种改进的多目标粒子群优化算法及其应用

为提高多目标粒子群优化 (MOPSO)算法处理多目标优化问题的性能, 降低计算复杂度, 改善算法的收敛性, 提出了一种改进的多目标粒子群优化算法。通过运用比例分布及跳数改进机制策略的方法, 使该算法不仅继承了MOPSO算法的优点, 而且具有很强的局部搜索能力和较好的鲁棒性能, 使非劣解集均匀分布, 尽可能逼近真实的非劣前沿。通过对多连杆悬架空间结构硬点的多目标优化, 进一步验证了该算法的实用性及其优越性。     

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.     

Two new meta-heuristics for a bi-objective supply chain scheduling problem in flow-shop environment

In this study, an integrated multi-objective production-distribution flow-shop scheduling problem will be taken into consideration with respect to two objective functions. The first objective function aims to minimize total weighted tardiness and make-span and the second objective function aims to minimize the summation of total weighted earliness, total weighted number of tardy jobs, inventory costs and total delivery costs. Firstly, a mathematical model is proposed for this problem. After that, two new meta-heuristic algorithms are developed in order to solve the problem. The first algorithm (HCMOPSO), is a multi-objective particle swarm optimization combined with a heuristic mutation operator, Gaussian membership function and a chaotic sequence and the second algorithm (HBNSGA-II), is a non-dominated sorting genetic algorithm II with a heuristic criterion for generation of initial population and a heuristic crossover operator. The proposed HCMOPSO and HBNSGA-II are tested and compared with a Non-dominated Sorting Genetic Algorithm II (NSGA-II), a Multi-Objective Particle Swarm Optimization (MOPSO) and two state-of-the-art algorithms from recent researches, by means of several comparing criteria. The computational experiments demonstrate the outperformance of the proposed HCMOPSO and HBNSGA-II.     

Multi-criterion Pareto based particle swarm optimized polynomial neural network for classification: A review and state-of-the-art

In this paper, we proposed a multi-objective Pareto based particle swarm optimization (MOPPSO) to minimize the architectural complexity and maximize the classification accuracy of a polynomial neural network (PNN). To support this, we provide an extensive review of the literature on multi-objective particle swarm optimization and PNN. Classification using PNN can be considered as a multi-objective problem rather than as a single objective one. Measures like classification accuracy and architectural complexity used for evaluating PNN based classification can be thought of as two different conflicting criterions. Using these two metrics as the criteria of classification problem, the proposed MOPPSO technique attempts to find out a set of non-dominated solutions with less complex PNN architecture and high classification accuracy. An extensive experimental study has been carried out to compare the importance and effectiveness of the proposed method with the chosen state-of-the-art multi-objective particle swarm optimization (MOPSO) algorithm using several benchmark datasets. A comprehensive bibliography is included for further enhancement of this area.     

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。     

基于模糊物元模型的高维多目标FJSP研究*

为解决高维多目标柔性作业车间调度问题,提出了一种基于模糊物元模型与粒子群算法的模糊粒子群算法（Fuzzy Particle Swarm Optimization,FPSO）。该算法以模糊物元分析理论为依据,采用复合模糊物元与基准模糊物元之间的欧式贴近度作为适应度值引导粒子群算法的进化,并引入具有容量限制的外部存储器保留较优的Pareto非支配解以供决策者选择。此外,构建了优化目标为最大完工时间、设备总负荷、加工成本、最大设备负荷与加工质量的高维多目标优化模型,并以Kacem基准问题与实际生产数据为例进行仿真模拟与对比分析。结果表明,该算法具有良好的收敛性且搜索到的非支配解分布性较好,能够有效地应用于求解高维多目标柔性作业车间调度问题。     

改进的约束多目标粒子群算法

在约束优化问题搜索空间分析的基础上提出了一种改进的约束多目标粒子群算法（CMOPSO）。提出一种动态ε不可行度许可约束支配关系作为主要约束的处理方法,提高了算法的边缘搜索能力和跨越非联通可行区域的能力。设计了一种新的密集距离度量方法用于外部档案维护,提高了算法的效率;提出了新的全局向导选取策略,使算法获得了更好的收敛性和多样性。数值仿真实验结果表明约束多目标粒子群算法算法可得到分布性、均匀性及逼近性都较好的Pareto最优解。     

多目标粒子群算法在交叉培训规划中的应用

为了进一步提高人力资源交叉培训规划的实用性,增加了对于员工学习行为的考虑,提出了在保证任务覆盖水平的基础上,获得员工满意度最大和学习效率最高的多目标优化模型.本文针对问题的特征,采用多目标粒子群(MOPSO)算法对多目标优化模型进行了求解,并设计了多种算法策略,以适应不同的问题环境.通过数值实验,分析了不同问题规模下,针对不同性能指标算法参数和策略的适用性.最后,以柔性单元装配生产线为例,进行了数值实验,实验结果表明了模型的有效性和合理性.     

基于混沌多目标粒子群优化算法的云服务选择

随着云计算环境中各种服务数量的急剧增长,如何从功能相同或相似的云服务中选择满足用户需求的服务成为云计算研究中亟待解决的关键问题。为此,建立带服务质量约束的多目标服务组合优化模型,针对传统多目标粒子群优化(MOPSO)算法中解的多样性差、易陷入局部最优等缺点,设计基于混沌多目标粒子群优化(CMOPSO)算法的云服务选择方法。采用信息熵理论来维护非支配解集,以保持解的多样性和分布的均匀性。当种群多样性丢失时,引入混沌扰动机制,以提高种群多样性和算法全局寻优能力,避免陷入局部最优。实验结果表明,与MOPSO算法相比,CMOPSO算法的收敛性和解集多样性均得到改善,能够更好地解决云计算环境下服务动态选择问题。     

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。     

基于多目标优化模型的电动汽车增程器油耗及排放优化

针对增程式电动汽车油耗和排放优化问题,首先综合考虑增程器的油-电转换效率特性、HC排放特性、CO排放特性以及NOx排放特性,构造了增程器油耗和排放多目标优化模型,同时结合实际增程器工作中的机械和电气约束特征,分析了多目标优化模型的3种转速、转矩约束条件.然后采用多目标粒子群算法和加权尺度法对增程器油耗和排放多目标优化模型进行了离线优化,得出了增程器的最优全局工作点和各功率值下的多目标最优工作曲线.最后,采用NEDC,FTP和HWFET3种测试工况在AVL Puma Open发动机测试台架上进行了实验,并和基于最佳制动燃油消耗率(BSFC)的油耗单目标优化模型进行了比较.结果表明,本文提出的方法能够以微弱的油耗增加为代价,有效的改善整车的HC,CO和NOx排放.     

多目标微粒群优化算法及其应用研究进展*

多目标微粒群优化(MOPSO)算法是一类基于群体智能的新型全局多目标优化方法,已受到广泛关注,并在许多领域得到应用。针对近几年来MOPSO算法及其应用的进展进行了综述和评论。首先描述了MOPSO算法的基本框架;接着对MOPSO算法进行了分类和分析,并给出了MOPSO算法的一些改进策略;然后介绍了MOPSO算法的应用进展;最后,展望了MOPSO算法值得进一步研究的方向。