Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system

The main objective of this paper is to solve the bi-objective reliability redundancy allocation problem for series-parallel system where reliability of the system and the corresponding designing cost are considered as two different objectives. In their formulation, reliability of each component is considered as a triangular fuzzy number. In order to solve the problem, developed fuzzy model is converted to a crisp model by using expected values of fuzzy numbers and taking into account the preference of decision maker regarding cost and reliability goals. Finally the obtained crisp optimization problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Examples are shown to illustrate the method. Finally statistical simulation has been performed for supremacy the approach.     

混合人工生命系统与粒子群算法的优化算法

提出-种混合人工生命系统和粒子群算法的优化算法.算法包括两个阶段,第1阶段创建人工生命系统,系统中的人工生物有感知系统,它们可以发现所需要的资源,并新陈代谢,人工生物之间互相交互,导致整个系统出现突现集群现象.通过人工生命系统形成的突现集群给粒子群算法提供优良的初始位置.第2阶段使用粒子群算法进一步寻找优化的最佳结果.最后以著名的Rosenbrock函数为例来证明该算法的优化能力,实验数据表明,该优化算法是有效的.     

Identification using ANFIS with intelligent hybrid stable learning algorithm approaches

This paper suggests novel hybrid learning algorithm with stable learning laws for adaptive network based fuzzy inference system (ANFIS) as a system identifier and studies the stability of this algorithm. The new hybrid learning algorithm is based on particle swarm optimization (PSO) for training the antecedent part and gradient descent (GD) for training the conclusion part. Lyapunov stability theory is used to study the stability of the proposed algorithm. This paper, studies the stability of PSO as an optimizer in training the identifier, for the first time. Stable learning algorithms for the antecedent and consequent parts of fuzzy rules are proposed. Some constraints are obtained and simulation results are given to validate the results. It is shown that instability will not occur for the leaning rate and PSO factors in the presence of constraints. The learning rate can be calculated on-line and will provide an adaptive learning rate for the ANFIS structure. This new learning scheme employs adaptive learning rate that is determined by input–output data.     

求解TSP问题的模糊自适应粒子群算法

由于惯性权值的设置对粒子群优化（PSO）算法性能起着关键的作用，本文通过引入模糊技术，给出了一种惯性权值的模糊自适应调整模型及其相应的粒子群优化算法，并用于求解旅行商（TSP）问题。实验结果表明了改进算法在求解组合优化问题中的有效性，同时提高了算法的性能，并具有更快的收敛速度。     

模拟生物理想自由分布模型的粒子群算法

在分析生物觅食行为中资源斑块选择理想自由分布模型的基础上,提出一种新型的粒子群算法——理想自由分布粒子群优化算法（IFDPSO）．该算法将所有粒子中3个不重叠的个体最优位置的适应度视为资源斑块的食物质量,根据理想自由分布模型随机分配相应数量的粒予到各资源斑块中．为保证群体的多样性,各资源斑块的群体最优位置保持随迭代次数增加而线性递减的距离．在间隔一定的迭代次数后,将各资源斑块的粒子重新组合．标准测试函数的仿真结果表明了IFDPSO算法的有效性．     

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.     

一种催化粒子群算法及其性能分析

针对粒子群算法（PSO）在解决高维、多模复杂问题时容易陷入局部最优的问题,提出了一种新颖的混合算法—催化粒子群算法（CPSO）。在CPSO优化过程中,种群中的粒子始终保持其个体历史最优值pbests。CPSO种群更新由改造PSO、横向交叉以及垂直交叉三个搜索算子交替进行,其中,每个算子产生的中庸解均通过贪婪思想产生占优解pbests,并作为下一个算子的父代种群。在CPSO中,纵横交叉算法（CSO）作为PSO的加速催化剂,一方面通过横向交叉改善PSO的全局收敛性能,另一方面通过纵向交叉维持种群的多样性。对6个典型benchmark函数的仿真结果表明,相比其它主流PSO变体,CPSO在全局收敛能力和收敛速率方面具有明显优势。     

基于模糊文化算法的自适应粒子群优化

为解决粒子群优化中惯性权重的调整机制在具体优化问题中的自适应问题,本文建立了一种全新的基于模糊文化算法的自适应粒子群优化算法;利用模糊规则表示个体粒子在演化过程中获取的经验,经验共享形成群体文化,并利用遗传算法来实现文化的进化;通过信念空间中以模糊规则表示的知识建立模糊系统来逼近与实际问题相适应的惯性权
权重控制器。在测试函数集上的仿真实验对比结果证明,该算法相对于现有算法有优势。     

An Integer Linear Programming approach to the single and bi-objective Next Release Problem

ContextThe Next Release Problem involves determining the set of requirements to implement in the next release of a software project. When the problem was first formulated in 2001, Integer Linear Programming, an exact method, was found to be impractical because of large execution times. Since then, the problem has mainly been addressed by employing metaheuristic techniques.ObjectiveIn this paper, we investigate if the single-objective and bi-objective Next Release Problem can be solved exactly and how to better approximate the results when exact resolution is costly.MethodsWe revisit Integer Linear Programming for the single-objective version of the problem. In addition, we integrate it within the Epsilon-constraint method to address the bi-objective problem. We also investigate how the Pareto front of the bi-objective problem can be approximated through an anytime deterministic Integer Linear Programming-based algorithm when results are required within strict runtime constraints. Comparisons are carried out against NSGA-II. Experiments are performed on a combination of synthetic and real-world datasets.FindingsWe show that a modern Integer Linear Programming solver is now a viable method for this problem. Large single objective instances and small bi-objective instances can be solved exactly very quickly. On large bi-objective instances, execution times can be significant when calculating the complete Pareto front. However, good approximations can be found effectively.ConclusionThis study suggests that (1) approximation algorithms can be discarded in favor of the exact method for the single-objective instances and small bi-objective instances, (2) the Integer Linear Programming-based approximate algorithm outperforms the NSGA-II genetic approach on large bi-objective instances, and (3) the run times for both methods are low enough to be used in real-world situations.     

A hybrid multi-objective PSO–EDA algorithm for reservoir flood control operation

Reservoir flood control operation (RFCO) is a complex multi-objective optimization problem (MOP) with interdependent decision variables. Traditionally, RFCO is modeled as a single optimization problem by using a certain scalar method. Few works have been done for solving multi-objective RFCO (MO-RFCO) problems. In this paper, a hybrid multi-objective optimization approach named MO-PSO–EDA which combines the particle swarm optimization (PSO) algorithm and the estimation of distribution algorithm (EDA) is developed for solving the MO-RFCO problem. MO-PSO–EDA divides the particle population into several sub-populations and builds probability models for each of them. Based on the probability model, each sub-population reproduces new offspring by using PSO based and EDA methods. In the PSO based method, a novel global best position selection method is designed. With the help of the EDA based reproduction, the algorithm can lean linkage between decision variables and hence have a good capability of solving complex multi-objective optimization problems, such as the MO-RFCO problem. Experimental studies on six benchmark problems and two typical multi-objective flood control operation problems of Ankang reservoir have indicated that the proposed MO-PSO–EDA performs as well as or superior to the other three competitive multi-objective optimization algorithms. MO-PSO–EDA is suitable for solving MO-RFCO problems.     

哈夫曼编码的协同粒子群优化算法

针对粒子群优化（PSO）算法在优化问题过程中易陷入局部最优的问题,提出一种基于哈夫曼编码的协同粒子群优化（HC PSO）算法。采用哈夫曼编码将种群划分成2个子种群并对2个子种群进行独立优化,同时,2子种群之间协同完成搜索种群的全局最优解。采用6个标准测试函数来测试算法性能。实验结果表明,该算法可以有效地避免种群陷入局部最优,具有较好的优化性能和稳定性,收敛精度得到了显著的提高。     

二阶卡尔曼滤波分布估计算法

分布估计算法由于其较强的理论基础已成为进化计算研究的新热点．从卡尔曼滤波的角度来看，它的作甩实际上是一个递归滤波器，但作用在一个种群上的分布估计算法相当于只有一个信息源．因此，该文利用信息融合的思想，将种群分成若干子种群，各子种群独立地使用二阶分布估计算法来估计其状态，这样就可从多个信息源获得信息．然后用卡尔曼滤波器将这多个信息源的信息相融合，以产生更准确的估计，并将估计信息反馈到各子种群中．实验结果表明，相对于已有的二阶分布估计算法，该文算法的稳定性和全局搜索能力都得到了很大提高，从而说明了该文算法的有效性．     

Multi-objective rule mining using a chaotic particle swarm optimization algorithm

In this paper, classification rule mining which is one of the most studied tasks in data mining community has been modeled as a multi-objective optimization problem with predictive accuracy and comprehensibility objectives. A multi-objective chaotic particle swarm optimization (PSO) method has been introduced as a search strategy to mine classification rules within datasets. The used extension to PSO uses similarity measure for neighborhood and far-neighborhood search to store the global best particles found in multi-objective manner. For the bi-objective problem of rule mining of high accuracy/comprehensibility, the multi-objective approach is intended to allow the PSO algorithm to return an approximation to the upper accuracy/comprehensibility border, containing solutions that are spread across the border. The experimental results show the efficiency of the algorithm.     

基于种群规模动态减小的混合微粒群优化算法研究

针对基本微粒群优化(PSO,particle swarm optimization)算法存在早熟、易陷入局部极值等缺点,提出了一种改进的PSO优化算法。该算法分为全局搜索和局部搜索两个阶段。在全局搜索阶段采用基本PSO算法快速收缩搜索范围;在局部搜索阶段将PSO算法与模拟退火(SA,simulated annealing)算法结合,通过产生部分变异微粒确保算法能够跳出局部极值。同时为提高搜索效率,动态地减少种群规模。仿真结果表明,该算法具有较好的优化性能以及较高的执行效率。     

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.     

A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic

This paper considers the problem of sequence-dependent setup time hybrid flowshop scheduling with the objectives of minimizing the makespan and sum of the earliness and tardiness of jobs, and present a multi-phase method. In initial phase, the population will be decomposed into several subpopulations. In this phase we develop a random key genetic algorithm and the goal is to obtain a good approximation of the Pareto-front. In the second phase, for improvement the Pareto-front, non-dominant solutions will be unified as one big population. In this phase, based on the local search in Pareto space concept, we propose multi-objective hybrid metaheuristic. Finally in phase 3, we propose a novel method using e-constraint covering hybrid metaheuristic to cover the gaps between the non-dominated solutions and improve Pareto-front. Generally in three phases, we consider appropriate combinations of multi-objective methods to improve the total performance. The hybrid algorithm used in phases 2 and 3 combines elements from both simulated annealing and a variable neighborhood search. The aim of using a hybrid metaheuristic is to raise the level of generality so as to be able to apply the same solution method to several problems. Furthermore, in this study to evaluate non-dominated solution sets, we suggest several new approaches. The non-dominated sets obtained from each phase and global archive sub-population genetic algorithm presented previously in the literature are compared. The results obtained from the computational study have shown that the multi-phase algorithm is a viable and effective approach.     

SELF-GENERATION FUZZY MODELING SYSTEMS THROUGH HIERARCHICAL RECURSIVE-BASED PARTICLE SWARM OPTIMIZATION

ABSTRACT

In this article, fuzzy modeling systems are automatically developed by Hierarchical Recursive-Based Particle Swarm Optimization (HRPSO). HRPSO, which contains Fuzzy C-Mean (FCM) clustering, Particle Swarm Optimization (PSO), and recursive least-squares technology, self constructs adjustable parameters for approximating a nonlinear function and a discrete dynamic system. In general, the heuristic PSO is an evolutional computing technology when solving complex and global problems. However, the necessary training time is unsuitable for large population sizes and many adjustable parameters. To quickly approximate the actual output of nonlinear functions, the input-output training data is initially clustered by an FCM algorithm. From there favorable features are extracted from the training data and some fuzzy structures with fewer adjustable parameters will be collected as the initial population of the PSO. The FCM procedure is used to directly extract necessary small populations of PSO from training samples. After that, the recursive-based PSO is proposed to tune some adjustable parameters to quickly construct the desired fuzzy modeling system. Therefore, the proposed HRPSO determines fuzzy modeling systems with a small number of fuzzy rules to approach high accuracy within a short training time. Simulation results demonstrate the efficiency of our fuzzy model systems to solve two nonlinear problems.     

A discrete version of particle swarm optimization for flowshop scheduling problems

Particle swarm optimization (PSO) is a novel metaheuristic inspired by the flocking behavior of birds. The applications of PSO to scheduling problems are extremely few. In this paper, we present a PSO algorithm, extended from discrete PSO, for flowshop scheduling. In the proposed algorithm, the particle and the velocity are redefined, and an efficient approach is developed to move a particle to the new sequence. To verify the proposed PSO algorithm, comparisons with a continuous PSO algorithm and two genetic algorithms are made. Computational results show that the proposed PSO algorithm is very competitive. Furthermore, we incorporate a local search scheme into the proposed algorithm, called PSO-LS. Computational results show that the local search can be really guided by PSO in our approach. Also, PSO-LS performs well in flowshop scheduling with total flow time criterion, but it requires more computation times.     

基于多种群粒子群算法和布谷鸟搜索的联合寻优算法

为了提高动态多种群粒子群(DMS-PSO) 算法的全局搜索能力, 将布谷鸟搜索算法(CS) 引入DMS-PSO 算法中, 提出DMS-PSO-CS 算法. 采用中位数聚类算法将整个种群动态划分为若干小种群, 各个小种群作为底层种群通过PSO 算法进行寻优, 再将每个小种群中的最优粒子作为高层种群的粒子通过CS 算法进行深度优化. 将所提出算法应用于CEC 2014 测试函数, 并与CS 算法和其他改进的PSO 算法进行比较. 实验结果表明, 所提出算法能够显著提高全局搜索能力和算法效率.

     

一种新型的动态粒子群优化算法

为了改进标准粒子群优化算法全局搜索性能,提出了一种种群动态变化的多种群粒子群优化算法。当算法搜索停滞时,把种群分裂成2个子种群,通过子种群粒子随机初始化及个体替代机制增强种群多样性,两个子种群并行搜索一定代数后,通过混合子种群来完成不同子种群中粒子的信息交流。收敛性分析表明,本文算法能以概率1收敛到全局最优解。实验结果表明,本文算法具有较好的全局寻优能力和较快的收敛速度。