基于模糊的多目标粒子群优化算法及应用

粒子群优化算法的思想来源于人工生命和进化计算理论,由于其容易理解、易于实现,在很多领域得到了应用.由于传统的粒子群优化算法无法对多目标优化问题进行求解,因此文中利用模糊理论中的隶属度函数和给定的最优解评估选取原则,提出了一种适合求解约束型多目标优化问题的模糊粒子群算法(FPSO).模糊粒子群算法很好地解决了汽车零部件可靠性稳健优化设计的求解问题,仿真结果证明,该算法可行而有效,同时也拓展了粒子群算法的应用领域.     

一类新的粒子群算法

提出一种新的模糊粒子群优化算法--收敛模糊粒子群优化算法.重点研究了收敛因子的确定和模糊隶属度函数的选择对算法性能的影响,在考虑计算效率的同时,提高了算法的精度.利用4个基准函数测试了收敛模糊粒子群优化算法的性能,并与模糊粒子群优化算法、收敛粒子群优化算法以及基本粒子群优化算法进行了对比.实验结果表明,新算法具有很好的性能.     

Fuzzy particle swarm optimization algorithms for the open shortest path first weight setting problem

The open shortest path first (OSPF) routing protocol is a well-known approach for routing packets from a source node to a destination node. The protocol assigns weights (or costs) to the links of a network. These weights are used to determine the shortest paths between all sources to all destination nodes. Assignment of these weights to the links is classified as an NP-hard problem. The aim behind the solution to the OSPF weight setting problem is to obtain optimized routing paths to enhance the utilization of the network. This paper formulates the above problem as a multi-objective optimization problem. The optimization metrics are maximum utilization, number of congested links, and number of unused links. These metrics are conflicting in nature, which motivates the use of fuzzy logic to be employed as a tool to aggregate these metrics into a scalar cost function. This scalar cost function is then optimized using a fuzzy particle swarm optimization (FPSO) algorithm developed in this paper. A modified variant of the proposed PSO, namely, fuzzy evolutionary PSO (FEPSO), is also developed. FEPSO incorporates the characteristics of the simulated evolution heuristic into FPSO. Experimentation is done using 12 test cases reported in literature. These test cases consist of 50 and 100 nodes, with the number of arcs ranging from 148 to 503. Empirical results have been obtained and analyzed for different values of FPSO parameters. Results also suggest that FEPSO outperformed FPSO in terms of quality of solution by achieving improvements between 7 and 31 %. Furthermore, comparison of FEPSO with various other algorithms such as Pareto-dominance PSO, weighted aggregation PSO, NSGA-II, simulated evolution, and simulated annealing algorithms revealed that FEPSO performed better than all of them by achieving best results for two or all three objectives.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

A particle swarm optimization based memetic algorithm for dynamic optimization problems

Recently, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are dynamic. This paper investigates a particle swarm optimization (PSO) based memetic algorithm that hybridizes PSO with a local search technique for dynamic optimization problems. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as the global search operator and a fuzzy cognition local search method is proposed as the local search technique. In addition, a self-organized random immigrants scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in the search space. Experimental study over the moving peaks benchmark problem shows that the proposed PSO-based memetic algorithm is robust and adaptable in dynamic environments.     

Fuzzy C-means and fuzzy swarm for fuzzy clustering problem

Fuzzy clustering is an important problem which is the subject of active research in several real-world applications. Fuzzy c-means (FCM) algorithm is one of the most popular fuzzy clustering techniques because it is efficient, straightforward, and easy to implement. However, FCM is sensitive to initialization and is easily trapped in local optima. Particle swarm optimization (PSO) is a stochastic global optimization tool which is used in many optimization problems. In this paper, a hybrid fuzzy clustering method based on FCM and fuzzy PSO (FPSO) is proposed which make use of the merits of both algorithms. Experimental results show that our proposed method is efficient and can reveal encouraging results.     

广义粒子群优化模型

粒子群优化算法提出至今一直未能有效解决的离散及组合优化问题．针对这个问题,文中首先回顾了粒子群优化算法在整数规划问题的应用以及该算法的二进制离散优化模型,并分析了其缺陷．然后,基于传统算法的速度一位移更新操作,在分析粒子群优化机理的基础上提出了广义粒子群优化模型（GPSO）,使其适用于解决离散及组合优化问题．GPSO模型本质仍然符合粒子群优化机理,但是其粒子更新策略既可根据优化问题的特点设计,也可实现与已有方法的融合．该文以旅行商问题（TSP）为例,针对遗传算法（GA）解决该问题的成功经验,使用遗传操作作为GPSO模型中的更新算子,进一步提出基于遗传操作的粒子群优化模型,并以Inverover算子作为模型中具体的遗传操作设计了基于GPSO模型的TSP算法．与采用相同遗传操作的GA比较,基于GPSO模型的算法解的质量与收敛稳定性提高,同时计算费用显著降低．     

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。     

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.     

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.     

星型结构的多目标粒子群算法求解多模态多目标问题

首先,根据多目标粒子群算法中的粒子结构信息,利用非支配解集构造粒子个体邻域之间的拓扑结构,提出星型结构的多目标粒子群算法用于求解多模态多目标问题。其次,针对多目标粒子群中全局最优个体选择困难,提出一种非支配解集分布均匀程度的评价方法,评价结果用于确定当前粒子对应的全局最优个体。最后,结合2种方法提出带均匀计算方法的星型拓扑结构多目标粒子群优化算法STMOPSONCMIU。通过测试函数分析算法的收敛性,表明改进的算法比原来的算法收敛速度快。实验结果表明,该算法可以较好地兼顾问题的目标空间和决策空间的分布,有效解决多模态多目标问题。     

Intelligent identification and control using improved fuzzy particle swarm optimization

This paper presents a novel improved fuzzy particle swarm optimization (IFPSO) algorithm to the intelligent identification and control of a dynamic system. The proposed algorithm estimates optimally the parameters of system and controller by minimizing the mean of squared errors. The particle swarm optimization is enhanced intelligently by using a fuzzy inertia weight to rationally balance the global and local exploitation abilities. In the proposed IFPSO, every particle dynamically adjusts inertia weight according to particles best memories using a nonlinear fuzzy model. As a result, the IFPSO algorithm has a faster convergence speed and a higher accuracy. The performance of IFPSO algorithm is compared with advanced algorithms such as Real-Coded Genetic Algorithm (RCGA), Linearly Decreasing Inertia Weight PSO (LDWPSO) and Fuzzy PSO (FPSO) in terms of parameter accuracy and convergence speed. Simulation results demonstrate the effectiveness of the proposed algorithm.     

An improved particle swarm optimization algorithm for flowshop scheduling problem

The flowshop scheduling problem has been widely studied and many techniques have been applied to it, but few algorithms based on particle swarm optimization (PSO) have been proposed to solve it. In this paper, an improved PSO algorithm (IPSO) based on the “alldifferent” constraint is proposed to solve the flow shop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnate, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that the proposed IPSO algorithm is more effective and better than the other compared algorithms. It can be used to solve large scale flow shop scheduling problem effectively.     

PSO优化在模糊联合补充问题中的应用

对用PSO算法解决需求为不确定的联合补充问题进行了研究。运用模糊规划方法处理需求为模糊变量的联合补充问题,得到了作为求解目标的模糊数学模型;采用PSO思想对该模型进行分析,转化为PSO问题模型,制定出算法流程,并用数值实例验证了提出的粒子群优化模型和求解算法的有效性;对随机生成的大量数据进行处理,结果证明问题规模相同时该算法较遗传算法具有更高的效率。     

改进型粒子群算法及其在选址问题中的应用

为了解决基本粒子群算法不易跳出局部最优的问题,提出了一种协同粒子群优化算法。在算法中通过加入权值递减的惯性因子和变异算子以克服基本PSO易早熟、不易收敛以及缺乏多样性的不足。将算法应用于极小极大选址问题的实验结果表明,算法能够有效地求解极小极大选址问题,具有较好的应用价值。     

求解TSP的改进自组织PSO算法

针对粒子群算法（PSO）的早熟收敛现象,从种群多样性出发,基于自组织临界性特点改进PSO 算法的参数设置,采用自组织的惯性权重和加速系数,并增加了变异算子。借鉴交换子和交换序概念,设计出了能直接在离散域进行搜索的改进的自组织PSO算法。用于旅行商问题（TSP）的求解,并与基本及其他典型改进PSO算法进行性能比较。实验结果证实改进的自组织PSO算法是有效的。     

基于多目标粒子群优化的虚拟网络映射算法

在虚拟网络映射中,多数研究只考虑一个映射目标,不能体现多方的利益。为此,将多目标算法和粒子群算法结合,提出了一种基于多目标粒子群优化（PSO）的虚拟网络映射算法（VNE-MOPSO）。首先,在基本的粒子群算法中引入交叉算子,扩大了种群优化的搜索空间;其次,在多目标优化算法中引入非支配排序、拥挤距离排序,从而加快种群的收敛;最后,以同时最小化成本和节点负载均衡度为虚拟网络映射目标函数,采用多目标粒子群优化算法求解虚拟网络映射问题（VNMP）。实验结果表明,采用该算法求解虚拟网络映射问题,在网络请求接受率、平均成本、平均节点负载均衡度、基础设施提供商的收益等方面具有优势。     

Development of Granular Fuzzy Relation Equations Based on a Subset of Data

Developing and optimizing fuzzy relation equations are of great relevance in system modeling, which involves analysis of numerous fuzzy rules. As each rule varies with respect to its level of influence, it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance. In this study, we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules. The subset of rules is selected by maximizing their performance of the obtained solutions. The originality of this study is conducted in the following ways. Starting with developing granular fuzzy relation equations, an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules (the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations), which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency. Then, the particle swarm optimization (PSO) is implemented to solve a multi-objective optimization problem, in which not only an optimal subset of rules is selected but also a parameter ε for specifying a level of information granularity is determined. A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance. A visible improvement of particle swarm optimization (about 78.56% of the encoding mechanism of particle swarm optimization, or 90.42% of particle swarm optimization with an exploration operator) is gained over the method conducted without using the particle swarm optimization algorithm.      

Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max–min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.     

MPI-based parallel synchronous vector evaluated particle swarm optimization for multi-objective design optimization of composite structures

This paper presents a decentralized/peer-to-peer architecture-based parallel version of the vector evaluated particle swarm optimization (VEPSO) algorithm for multi-objective design optimization of laminated composite plates using message passing interface (MPI). The design optimization of laminated composite plates being a combinatorially explosive constrained non-linear optimization problem (CNOP), with many design variables and a vast solution space, warrants the use of non-parametric and heuristic optimization algorithms like PSO. Optimization requires minimizing both the weight and cost of these composite plates, simultaneously, which renders the problem multi-objective. Hence VEPSO, a multi-objective variant of the PSO algorithm, is used. Despite the use of such a heuristic, the application problem, being computationally intensive, suffers from long execution times due to sequential computation. Hence, a parallel version of the PSO algorithm for the problem has been developed to run on several nodes of an IBM P720 cluster. The proposed parallel algorithm, using MPI's collective communication directives, establishes a peer-to-peer relationship between the constituent parallel processes, deviating from the more common master-slave approach, in achieving reduction of computation time by factor of up to 10. Finally we show the effectiveness of the proposed parallel algorithm by comparing it with a serial implementation of VEPSO and a parallel implementation of the vector evaluated genetic algorithm (VEGA) for the same design problem.