A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables

This paper presents a new multi-objective optimization algorithm called FC-MOPSO for optimal design of engineering problems with a small number of function evaluations. The proposed algorithm expands the main idea of the single-objective particle swarm optimization (PSO) algorithm to deal with constrained and unconstrained multi-objective problems (MOPs). FC-MOPSO employs an effective procedure in selection of the leader for each particle to ensure both diversity and fast convergence. Fifteen benchmark problems with continuous design variables are used to validate the performance of the proposed algorithm. Finally, a modified version of FC-MOPSO is introduced for handling discrete optimization problems. Its performance is demonstrated by optimizing five space truss structures. It is shown that the FC-MOPSO can effectively find acceptable approximations of Pareto fronts for structural MOPs within very limited number of function evaluations.     

On convergence of the multi-objective particle swarm optimizers

Several variants of the particle swarm optimization (PSO) algorithm have been proposed in recent past to tackle the multi-objective optimization (MO) problems based on the concept of Pareto optimality. Although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of PSO as a single-objective optimizer, till date, to the best of our knowledge, no such analysis exists for the multi-objective PSO (MOPSO) algorithms. This paper presents a first, simple analysis of the general Pareto-based MOPSO and finds conditions on its most important control parameters (the inertia factor and acceleration coefficients) that govern the convergence behavior of the algorithm to the optimal Pareto front in the objective function space. Computer simulations over benchmark MO problems have also been provided to substantiate the theoretical derivations.     

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.     

A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation

Engineering design problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive design problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional design problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test problems: (i) a set of 9 unconstrained problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) problems. We also explore the applicability of this algorithm to a large scale engineering design problem—-wind farm layout optimization.     

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．     

Hybrid sliding level Taguchi-based particle swarm optimization for flowshop scheduling problems

A hybrid sliding level Taguchi-based particle swarm optimization (HSLTPSO) algorithm is proposed for solving multi-objective flowshop scheduling problems (FSPs). The proposed HSLTPSO integrates particle swarm optimization, sliding level Taguchi-based crossover, and elitist preservation strategy. The novel contribution of the proposed HSLTPSO is the use of a PSO to explore the optimal feasible region in macro-space, the use of a systematic reasoning mechanism of the sliding level Taguchi-based crossover to exploit the better solution in micro-space, and the use of the elitist preservation strategy to retain the best particles of multi-objective population for next iteration. The sliding level Taguchi-based crossover is embedded in the PSO to find the best solutions and consequently enhance the PSO. Using the systematic reasoning way of the Taguchi-based crossover with considering the influence of tuning factors α, β and γ is presented in this study to solve the conflicting problem of non-feasible solutions and to find the better particles. As a result, it exhibits a significant improvement in Pareto best solutions of the FSP. By combining the advantages of exploration and exploitation, from the computational experiments of the six test problems, the HSLTPSO provides better results compared to the existing methods reported in the literature when solving multi-objective FSPs. Therefore, the HSLTPSO is an effective approach in solving multi-objective FSPs.     

网格环境下基于Weka4WS的分布式聚类算法*

Weka4WS采用WSRF技术用于执行远程的数据挖掘和管理分布式计算,支持分布式数据挖掘任务。基于Weka4WS和网格环境,尝试了一种新的分布式聚类方法,并成功地将其嵌入到Weka4WS框架中,借助Weka Library实现分布式数据挖掘算法,同时引入了距离代价和混合概率的概念,将网格与Web服务技术融合,以分布式问题求解环境和开源数据挖掘类库Weka为底层支持环境,构建了网格环境下面向服务的分布式数据挖掘体系,并以基于Weka4WS的分布式聚类算法验证了算法的有效性和体系结构的可行性。     

一种多目标优化问题的理想灰色粒子群算法*

针对逼近理想解的排序方法对Pareto前端的距离跟踪以及灰色关联度能够很好地分析非劣解集曲线与Pareto最优解集曲线的相似性,提出了一种求解多目标优化问题的理想灰色粒子群算法。该算法利用理想解理论与灰色关联度理论来求解粒子与理想解之间的相对适应度和灰色关联度系数,把两者的和定义为相对理想度,通过相对理想度来判别粒子的优劣,以确定个体极值和全局极值。通过四组不同类型的基准函数测试算法性能,并与目标加权法和灰色粒子群算法比较分析,结果表明该算法能够较好地收敛到Pareto最优解集,不但具有较好的收敛性和分布     

免疫标准化正规化约束方法及其应用

为了加快准化正规化约束(normalized normal constraint,简称NNC)方法求解多目标优化问题的速度,将免疫算法与NNC方法相结合提出了基于免疫算法的NNC方法,简称免疫NNC(IANNC)方法.该方法利用免疫算法中的免疫接种技术,从相邻的乌托邦面上的点对应的单目标优化问题的优化过程中提取疫苗,对初始抗体群进行疫苗接种;使用克隆选择算法求解NNC方法中的单目标优化问题,进而使IANNC方法能够更快的获得多目标优化问题的Pareto解集.之后对IANNC方法的收敛性进行了分析.最后应用IANNC方法对冷连轧轧制规程进行多目标优化,结果表明与基于遗传算法的NNC方法相比,IANNC方法用较少的运行时间获得了更好的冷连轧轧制规程多目标优化问题的Pareto解集.     

基于随机黑洞和逐步淘汰策略的多目标粒子群优化算法

提出一种基于随机黑洞粒子群算法(RBH-PSO) 和逐步淘汰策略的多目标粒子群优化(MRBHPSO-SE) 算法. 利用RBH-PSO 全局优化能力强和收敛速度快的优点逼近Pareto 最优解; 为了避免拥挤距离排序策略的缺陷, 提出逐步淘汰策略, 并将其应用到下一代粒子的选择策略中. 同时, 动态选择领导粒子, 运用动态惯性权重系数和变异操作 来增强种群全局寻优能力, 以及避免早熟收敛. 利用具有不同特点的测试函数进行验证, 结果表明, 与同类算法相比, 该算法具有较高的精度并兼顾优化解的多样性.

     

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.     

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.      

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.     

一种改进的多目标约束优化差分进化算法

提出一种新的多目标优化差分进化算法用于求解约束优化问题.该算法利用佳点集方法初始化个体以维持种群的多样性.将约束优化问题转化为两个目标的多目标优化问题.基于Pareto支配关系,将种群分为Pareto子集和Non-Pareto子集,结合差分进化算法两种不同变异策略的特点,对Non-Pareto子集和Pareto子集分别采用DE/best/1变异策略和DE/rand/1变异策略.数值实验结果表明该算法具有较好的寻优效果.     

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.     

一种改进的鲁棒多目标优化方法

针对在解决某些复杂多目标优化问题过程中,所得到的Pareto最优解易受设计参数或环境参数扰动的影响,引入了鲁棒的概念并提出一种改进的鲁棒多目标优化方法,它利用了经典的基于适应度函数期望和方差方法各自的优势,有效地将两种方法结合在一起。为了实现该方法,给出一种基于粒子群优化算法的多目标优化算法。仿真实例结果表明,所给出的方法能够得到更为鲁棒的Pareto最优解。     

多目标人工蜂群算法在服务组合优化中的应用

应用广泛的聚集函数法可将多目标问题转换为单目标问题,但函数设计困难,通用性不强,且优化结果不能直观反映各目标的优化情况。提出了一个基于Pareto占优的多目标人工蜂群算法,改进了邻域搜索策略,给出一个对比实验。实验结果表明,改进算法在个体多样性与对Pareto最优边界的趋近程度方面均有优势。     

A fuzzy particle swarm optimization algorithm for computer communication network topology design

Particle swarm optimization (PSO) is a powerful optimization technique that has been applied to solve a number of complex optimization problems. One such optimization problem is topology design of distributed local area networks (DLANs). The problem is defined as a multi-objective optimization problem requiring simultaneous optimization of monetary cost, average network delay, hop count between communicating nodes, and reliability under a set of constraints. This paper presents a multi-objective particle swarm optimization algorithm to efficiently solve the DLAN topology design problem. Fuzzy logic is incorporated in the PSO algorithm to handle the multi-objective nature of the problem. Specifically, a recently proposed fuzzy aggregation operator, namely the unified And-Or operator (Khan and Engelbrecht in Inf. Sci. 177: 2692–2711, 2007), is used to aggregate the objectives. The proposed fuzzy PSO (FPSO) algorithm is empirically evaluated through a preliminary sensitivity analysis of the PSO parameters. FPSO is also compared with fuzzy simulated annealing and fuzzy ant colony optimization algorithms. Results suggest that the fuzzy PSO is a suitable algorithm for solving the DLAN topology design problem.     

膜系统下的一种多目标优化算法

提出一种基于膜优化理论的多目标优化算法,该算法受膜计算的启发,结合膜结构、多重集和反应规则来求解多目标优化问题。为了增强算法的适应能力,采用了遗传算法中的交叉与变异机制,同时在膜中引入外部档案集,并采用非支配排序和拥挤距离方法对外部档案集进行更新操作来提高搜索解的多样性。仿真实验采用标准的KUR和ZDT系列多目标问题对所提出的算法进行测试,通过该算法得出的非支配解集能够较好地逼近真实的Pareto前沿,说明所提算法在求解多目标优化问题上具有可行性和有效性。     

A novel combination of Particle Swarm Optimization and Genetic Algorithm for Pareto optimal design of a five-degree of freedom vehicle vibration model

In this paper, at first, a novel combination of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) is introduced. This hybrid algorithm uses the operators such as mutation, traditional or classical crossover, multiple-crossover, and PSO formula. The selection of these operators in each iteration for each particle or chromosome is based on a fuzzy probability. The performance of the proposed hybrid algorithm for solving both single and multi-objective optimization problems is challenged by using of some well-known benchmark problems. Obtained numerical results are compared with those of other optimization algorithms. At the end, the proposed multi-objective hybrid algorithm is used for the Pareto optimal design of a five-degree of freedom vehicle vibration model. The comparison of the obtained results with it in the literature demonstrates the superiority of this work.