Fuzzy-Pareto-dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization

This paper presents a fuzzy-Pareto dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization (MOPSO). This multi-objective planning model captures the possibilistic variations of the system loads using a fuzzy triangular number. The MOPSO based on the Pareto-optimality principle is used to obtain a set of non-dominated solutions representing different network structures under uncertainties in load demands and these non-dominated solutions are stored in an elite archive of limited size. Normally, choosing the candidate non-dominated solutions to be retained in the elite archive while maintaining the quality of the Pareto-approximation front as well as maintaining the diversity of solutions on this front is very much computationally demanding. In this paper, the principles of fuzzy Pareto-dominance are used to find out and rank the non-dominated solutions on the Pareto-approximation front. This ranking in turn is used to maintain the elite archive of limited size by discarding the lower ranked solutions. The two planning objectives are: (i) minimization of total installation and operational cost and (ii) minimization of risk factor. The risk factor is defined as a function of an index called contingency-load-loss index (CLLI), which captures the effect of load loss under contingencies, and the degree of network constraint violations. The minimization of the CLLI improves network reliability. The network variables that are optimized are: (i) number of feeders and their routes, and (ii) number and locations of sectionalizing switches. An MOPSO (developed by the authors), based on a novel technique for the selection and assignment of leaders/guides for efficient search of non-dominated solutions, is used as the optimization tool. The proposed planning approach is validated on a typical 100-node distribution system. Performance comparisons between the planning approaches with the possibilistic and deterministic load models are provided highlighting the relative merits and demerits. It is also verified that the proposed solution ranking scheme based on the fuzzy-Pareto dominance is very much better from both quality and computational burden point of view in comparison with the other well-known archive truncation techniques based on clustering and solution density measurement etc.     

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。     

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.     

基于不可行度和内分泌原理的多目标粒子群方法

针对有约束条件的多目标优化问题,提出了一种求解带约束的基于内分泌思想的多目标粒子群算法。利用不可行度方法和约束主导原理指导进化过程中精英种群的选择操作和约束条件的处理,根据生物体激素调节机制中促激素和释放激素间的相互作用原理,考虑当前非劣解集中的个体对其最邻近的一类群体的监督控制,引入当前粒子的类全局最优位置来反映其所属类中最好位置粒子对当前粒子的影响。为验证多目标约束优化算法的有效性,对两个典型的多目标优化问题进行了仿真实验,仿真结果表明该算法能较大概率地获得多目标约束优化问题的可行Pareto最优解。     

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.     

A novel fruit fly framework for multi-objective shape design of tubular linear synchronous motor

This paper addresses a novel multi-objective fruit fly optimization algorithm (MOFOA) for solving multi-objective optimization problems. The essence of MOFOA lies in its having two characteristic features. For the first feature, a population of random fruit flies initializes the algorithm. During this initialization phase, the dominated fruit fly is replaced by the nearest non-dominated one. Subsequently, the fruit flies undergo evolution by flying randomly around the non-dominated solution or around the reference point, i.e., the best location of the individual objectives. Afterwards, the fruit flies are updated according to the nearest location whether from the reference point or the previous non-dominated location. For the second feature, the weighted sum method is incorporated to update the previous best locations of fruit flies and the reference point to emphasize the convergence of the non-dominated solutions. To prove the capability of the proposed MOFOA, two standard benchmark problems in addition to the real world application, namely, multi-objective shape design of tubular linear synchronous motor (TLSM) are checked. The corresponding TLSM objective functions aims to maximize operating force and to minimize the flux saturation. The outcomes clearly demonstrate the effectiveness of the proposed algorithm for finding the non-dominated solutions.     

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。     

New mechanism for archive maintenance in PSO-based multi-objective feature selection

In classification problems, a large number of features are typically used to describe the problem’s instances. However, not all of these features are useful for classification. Feature selection is usually an important pre-processing step to overcome the problem of “curse of dimensionality”. Feature selection aims to choose a small number of features to achieve similar or better classification performance than using all features. This paper presents a particle swarm Optimization (PSO)-based multi-objective feature selection approach to evolving a set of non-dominated feature subsets which achieve high classification performance. The proposed algorithm uses local search techniques to improve a Pareto front and is compared with a pure multi-objective PSO algorithm, three well-known evolutionary multi-objective algorithms and a current state-of-the-art PSO-based multi-objective feature selection approach. Their performances are examined on 12 benchmark datasets. The experimental results show that in most cases, the proposed multi-objective algorithm generates better Pareto fronts than all other methods.     

多目标资源优化分配问题的Memetic 算法

针对传统算法求解多目标资源优化分配问题收敛慢、Pareto解不能有效分布在Pareto 前沿面的问题, 提出一种新的Memetic 算法. 在遗传算法的交叉算子中引入模拟退火算法, 加强了遗传算法的局部搜索能力, 加快了收敛速度. 为了使Pareto 最优解均匀分布在Pareto 前沿面, 在染色体编码中引入禁忌表, 增加了种群的多样性, 避免了传统遗传算法后期Pareto 解集过于集中的缺点. 通过与已有的遗传算法、蚁群算法、粒子群算法进行比较, 仿真实验表明了所提出算法的有效性, 并分析了禁忌表长度和模拟退火参数对算法收敛性的影响.

     

基于均匀设计的聚类多目标粒子群优化算法

为更有效地求解多目标优化问题,提出一种基于均匀设计的聚类多目标粒子群算法UCMOPSO。采用基于均匀设计的交叉操作尽可能地获得目标空间中均匀分布的非劣解,帮助种群跳出局部最优解,并通过一种新的聚类操作选择外部存档中有代表性的非劣解,从而控制外部存档规模,降低计算复杂度。对基准函数的测试结果表明,UCMOPSO算法相比同类算法在收敛性和分布性方面具有优势。     

基于Map-Reduce模型的云资源调度方法研究

为提高Map-Reduce模型资源调度问题的求解效能,分别考虑Map和Reduce阶段的调度过程,建立带服务质量(QoS)约束的多目标资源调度模型,并提出用于模型求解的混沌多目标粒子群算法。算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均匀性;在利用Sigma方法实现快速收敛的基础上,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,避免算法陷入局部最优。实验表明,算法求解所需的迭代次数少,得到的非支配解分布均匀。Map-Reduce资源调度问题的求解过程中,在收敛性和解集的多样性方面,所提算法均明显优于传统多目标粒子群算法。     

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.     

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.     

基于动态邻居和变异因子的多目标粒子群算法*

为了克服粒子群算法求解多目标问题极易收敛到伪Pareto前沿(等价于单目标优化问题中的局部最优解)和收敛速度较慢的缺陷,提出一种合并帕累托占优概念到动态邻居和变异因子的粒子群算法(particle swarm optimizer based on dynamic neighbor topology and mutation operator,DNMPSO)来处理多目标优化问题(DNMMOPSO),该算法也合并了外部存档技术来存储每次迭代产生的非劣解。模拟结果表明,提出的算法在多目标检测问题上要优于其他算法     

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.     

多目标粒子群优化算法在柔性车间调度中的应用

将粒子群优化(Particle Swarm Optimization,PSO)算法和混沌搜索方法结合在一起,提出一种求解多目标柔性作业车间调度问题(Flexible job shop scheduling problem,FJSP)的新算法,利用混沌对PSO的参数进行自适应优化来有效平衡算法的全局搜索和局部开挖能力,并采用混沌局部优化策略来改善算法的搜索性能.此外,为了搜索到问题的所有非劣解,采用基于模糊逻辑的适应度函数来评价粒子.对于四个典型FJSP实例的实验验证了算法的可行性和有效性.     

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.     

A novel strategy of pareto-optimal solution searching in multi-objective particle swarm optimization (MOPSO)

In multi-objective particle swarm optimization (MOPSO) algorithms, finding the global optimal particle (gBest) for each particle of the swarm from a set of non-dominated solutions is very difficult yet an important problem for attaining convergence and diversity of solutions. First, a new Pareto-optimal solution searching algorithm for finding the gBest in MOPSO is introduced in this paper, which can compromise global and local searching based on the process of evolution. The algorithm is implemented and is compared with another algorithm which uses the Sigma method for finding gBest on a set of well-designed test functions. Finally, the multi-objective optimal regulation of cascade reservoirs is successfully solved by the proposed algorithm.     

基于多目标免疫系统算法的云任务调度策略

针对云计算环境下任务调度问题,为减少任务完工时间,同时降低任务执行费用,提出一种改进的基于多目标免疫系统的任务调度算法IMISA来寻找较优的可行分配方案。与传统分配适应度值不同,该算法将抗体群划分为非支配解集和支配解集,分别将非支配解的独立支配区域面积、支配解与所有非支配解所围成的多边形面积作为相应的抗体-抗原亲和力,根据相应亲和度计算克隆比例后克隆变异生成子代。在CloudSim平台上进行仿真实验,结果表明,与NSGA-Ⅱ及多目标免疫系统算法(MISA)相比,IMISA能够找到具有更短完工时间及更小的执行费用的调度方案,同时获得的Pareto解集也具有更好的分布性。     

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.