基于粒子群与聚类的多目标优化算法

针对粒子群优化算法容易陷入局部最优的问题,提出了一种基于粒子群优化与分解聚类方法相结合的多目标优化算法。算法基于参考向量分解的方法,通过聚类优选粒子策略来更新全局最优解。首先,通过每条均匀分布的参考向量对粒子进行聚类操作,来促进粒子的多样性。从每个聚类中选择一个具有最小聚合函数适应度值的粒子,以平衡收敛性和多样性。动态更新全局最优解和个体最优解,引导种群均匀分布在帕累托前沿附近。通过仿真实验,与4种粒子群多目标优化算法进行对比。实验结果表明,提出的算法在27个选定的基准测试问题中获得了20个反世代距离(IGD)最优值。     

Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

基于速度交流的多种群多目标粒子群算法研究

为提高多目标优化算法的收敛精度和搜索性能,提出一种基于速度交流的多种群多目标粒子群算法。算法引入速度交流机制,将种群划分为多个子种群以实现速度信息共享,改善粒子单一搜索模式,提高算法的全局搜索能力。采用混沌映射优化惯性权重,提高粒子搜索遍历性和全局性,为降低算法在运行后期陷入局部最优Pareto前沿的可能性,对各个子种群执行不同的变异操作。将算法与NSGA-Ⅱ、SPEA2、AbYSS、MOPSO、SMPSO和GWASF-GA先进多目标优化算法进行对比,实验结果表明:该算法得到的解集具有更好的收敛性和分布性。     

Multi-objective feasibility enhanced particle swarm optimization

This article introduces a new method entitled multi-objective feasibility enhanced partical swarm optimization (MOFEPSO), to handle highly-constrained multi-objective optimization problems. MOFEPSO, which is based on the particle swarm optimization technique, employs repositories of non-dominated and feasible positions (or solutions) to guide feasible particle flight. Unlike its counterparts, MOFEPSO does not require any feasible solutions in the initialized swarm. Additionally, objective functions are not assessed for infeasible particles. Such particles can only fly along sensitive directions, and particles are not allowed to move to a position where any previously satisfied constraints become violated. These unique features help MOFEPSO gradually increase the overall feasibility of the swarm and to finally attain the optimal solution. In this study, multi-objective versions of a classical gear-train optimization problem are also described. For the given problems, the article comparatively evaluates the performance of MOFEPSO against several popular optimization algorithms found in the literature.     

Improved artificial bee colony algorithm for crack identification in beam using natural frequencies only

An improved artificial bee colony algorithm (I-ABC) is proposed for crack identification in beam structures. ABC is a heuristic algorithm and swarm technique with simple structure, which is easy to implement but with slow convergence rate. In the I-ABC, the differential evolution (DE) mechanism is introduced to employed bee phase, roulette selection strategy is replaced by tournament selection strategy and a new formula is used to simulate onlooker bee’s behaviour. A discrete open crack is used for vibration analysis of the cracked beam and only the changes in the first few natural frequencies are utilized to establish the objective function of the optimization problem for crack identification. A numerical simulation and an experimental work are studied to illustrate the efficiency of the proposed method. Studies show that the present techniques can produce more accurate damage identification results when compared with original ABC, DE algorithm, particle swarm optimization and genetic algorithm.     

A new optimization algorithm based on a combination of particle swarm optimization,convergence and divergence operators for single-objective and multi-objective problems

Particle swarm optimization (PSO) is a randomized and population-based optimization method that was inspired by the flocking behaviour of birds and human social interactions. In this work, multi-objective PSO is modified in two stages. In the first stage, PSO is combined with convergence and divergence operators. Here, this method is named CDPSO. In the second stage, to produce a set of Pareto optimal solutions which has good convergence, diversity and distribution, two mechanisms are used. In the first mechanism, a new leader selection method is defined, which uses the periodic iteration and the concept of the particle's neighbour number. This method is named periodic multi-objective algorithm. In the second mechanism, an adaptive elimination method is employed to limit the number of non-dominated solutions in the archive, which has influences on computational time, convergence and diversity of solution. Single-objective results show that CDPSO performs very well on the complex test functions in terms of solution accuracy and convergence speed. Furthermore, some benchmark functions are used to evaluate the performance of periodic multi-objective CDPSO. This analysis demonstrates that the proposed algorithm operates better in three metrics through comparison with three well-known elitist multi-objective evolutionary algorithms. Finally, the algorithm is used for Pareto optimal design of a two-degree of freedom vehicle vibration model. The conflicting objective functions are sprung mass acceleration and relative displacement between sprung mass and tyre. The feasibility and efficiency of periodic multi-objective CDPSO are assessed in comparison with multi-objective modified NSGAII.     

A parallel particle swarm optimization algorithm for multi-objective optimization problems

In this article, a new proposal of using particle swarm optimization algorithms to solve multi-objective optimization problems is presented. The algorithm is constructed based on the concept of Pareto dominance, as well as a state-of-the-art ‘parallel’ computing technique that intends to improve algorithmic effectiveness and efficiency simultaneously. The proposed parallel particle swarm multi-objective evolutionary algorithm (PPS-MOEA) is tested through a variety of standard test functions taken from the literature; its performance is compared with six noted multi-objective algorithms. The computational experience gained from the first two experiments indicates that the algorithm proposed in this article is extremely competitive when compared with other MOEAs, being able to accurately, reliably and robustly approximate the true Pareto front in almost every tested case. To justify the motivation behind the research of the parallel swarm structure, the computational results of the third experiment confirm the PPS-MOEA's merit in solving really high-dimensional multi-objective optimization problems.     

基于多目标优化策略的扭杆可靠性稳健优化设计

为提高机械零部件的安全性和稳健性,应用可靠性稳健优化设计理论和多目标决策方法,建立了适合结构可靠性稳健优化设计的多目标优化模型.为能迅速准确地对具有约束条件的多目标优化模型进行求解,提出一种利用模糊理论对约束条件进行处理的方法,然后应用灰色粒子群算法对多目标优化模型进行求解.通过对正态分布参数和任意分布参数的扭杆可靠性稳健优化设计,表明该方法行之有效.     

基于多目标粒子群协同算法的状态参数优化

针对铅锌烧结过程综合透气性、烧结终点的优化具有强非线性、计算复杂等特点,提出了一种有效的多目标粒子群协同优化算法。首先,建立了有综合透气性、烧结终点两个目标的优化模型。接着,通过改进的约束比较方法、粒子极值选取方法,以及利用不同的粒子群来分别优化相应的变量,提出了一种改进的多目标粒子群协同优化算法。最后,利用提出的多目标优化算法进行综合透气性、烧结终点的优化。仿真结果表明,所提出的多目标优化算法能较好地解决综合透气性、烧结终点的优化问题。     

磁流变智能结构的微粒群优化控制

在磁流变智能结构的减震控制中,结构的位移控制和加速度控制是其减震控制的两个重要控制目标,这就使得磁流变智能结构的减震控制成为了一多目标优化控制。为此,本文采用微粒群优化控制算法同时对磁流变智能结构的位移和加速度进行了最优控制分析,实现了磁流变智能结构多目标的优化减震控制。并对一每层各安装一个磁流变阻尼器的五层钢结构分别采用微粒群优化控制算法、ON控制算法和OFF控制算法进行了实例对比分析,结果表明：采用微粒群优化控制可显著地减小结构的位移反应,同时也可一定程度地减小结构的加速度反应。     

Multi-objective optimization of combined Brayton and inverse Brayton cycles using advanced optimization algorithms

This study explores the use of teaching-learning-based optimization (TLBO) and artificial bee colony (ABC) algorithms for determining the optimum operating conditions of combined Brayton and inverse Brayton cycles. Maximization of thermal efficiency and specific work of the system are considered as the objective functions and are treated simultaneously for multi-objective optimization. Upper cycle pressure ratio and bottom cycle expansion pressure of the system are considered as design variables for the multi-objective optimization. An application example is presented to demonstrate the effectiveness and accuracy of the proposed algorithms. The results of optimization using the proposed algorithms are validated by comparing with those obtained by using the genetic algorithm (GA) and particle swarm optimization (PSO) on the same example. Improvement in the results is obtained by the proposed algorithms. The results of effect of variation of the algorithm parameters on the convergence and fitness values of the objective functions are reported.     

The comparison of multi-objective particle swarm optimization and NSGA II algorithm: applications in centrifugal pumps

In the present study, multi-objective optimization of centrifugal pumps is performed in three steps. In the first step, efficiency (η) and the required net positive suction head (NPSHr) in a set of centrifugal pumps are numerically investigated using commercial software. Two meta-models based on the evolved group method of data handling (GMDH) type neural networks are obtained in the second step for modeling of η and NPSHr with respect to geometrical design variables. Finally, using the obtained polynomial neural networks, a multi-objective particle swarm optimization method (MOPSO) is used for Pareto-based optimization of centrifugal pumps considering two conflicting objectives, η and NPSHr. The Pareto results of the MOPSO method are also compared with those of a multi-objective genetic algorithm (NSGA II). It is shown that some interesting and important relationships as useful optimal design principles involved in the performance of centrifugal pumps can be discovered by Pareto-based multi-objective optimization of the obtained polynomial metamodels representing η and NPSHr characteristics.     

Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems

In evolutionary algorithms, elites are crucial to maintain good features in solutions. However, too many elites can make the evolutionary process stagnate and cannot enhance the performance. This article employs particle swarm optimization (PSO) and biogeography-based optimization (BBO) to propose a hybrid algorithm termed biogeography-based particle swarm optimization (BPSO) which could make a large number of elites effective in searching optima. In this algorithm, the whole population is split into several subgroups; BBO is employed to search within each subgroup and PSO for the global search. Since not all the population is used in PSO, this structure overcomes the premature convergence in the original PSO. Time complexity analysis shows that the novel algorithm does not increase the time consumption. Fourteen numerical benchmarks and four engineering problems with constraints are used to test the BPSO. To better deal with constraints, a fuzzy strategy for the number of elites is investigated. The simulation results validate the feasibility and effectiveness of the proposed algorithm.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Decomposition-based multi-objective differential evolution particle swarm optimization for the design of a tubular permanent magnet linear synchronous motor

This article proposes a decomposition-based multi-objective differential evolution particle swarm optimization (DMDEPSO) algorithm for the design of a tubular permanent magnet linear synchronous motor (TPMLSM) which takes into account multiple conflicting objectives. In the optimization process, the objectives are evaluated by an artificial neural network response surface (ANNRS), which is trained by the samples of the TPMSLM whose performances are calculated by finite element analysis (FEA). DMDEPSO which hybridizes differential evolution (DE) and particle swarm optimization (PSO) together, first decomposes the multi-objective optimization problem into a number of single-objective optimization subproblems, each of which is associated with a Pareto optimal solution, and then optimizes these subproblems simultaneously. PSO updates the position of each particle (solution) according to the best information about itself and its neighbourhood. If any particle stagnates continuously, DE relocates its position by using two different particles randomly selected from the whole swarm. Finally, based on the DMDEPSO, optimization is gradually carried out to maximize the thrust of TPMLSM and minimize the ripple, permanent magnet volume, and winding volume simultaneously. The result shows that the optimized TPMLSM meets or exceeds the performance requirements. In addition, comparisons with chosen algorithms illustrate the effectiveness of DMDEPSO to find the Pareto optimal solutions for the TPMLSM optimization problem.     

An Improved Unsupervised Image Segmentation Method Based on Multi-Objective Particle Swarm Optimization Clustering Algorithm

Most image segmentation methods based on clustering algorithms use single-objective function to implement image segmentation. To avoid the defect, this paper proposes a new image segmentation method based on a multi-objective particle swarm optimization (PSO) clustering algorithm. This unsupervised algorithm not only offers a new similarity computing approach based on electromagnetic forces, but also obtains the proper number of clusters which is determined by scale-space theory. It is experimentally demonstrated that the applicability and effectiveness of the proposed multi-objective PSO clustering algorithm.     

基于自适应粒子群遗传算法的柔性关节机器人动力学参数辨识

提出一种基于自适应粒子群遗传算法的柔性关节机器人动力学参数辨识方法。该算法采用动态自适应调整策略,提高了粒子群算法收敛速度;同时引入新型遗传算法混合交叉变异机制,避免了粒子群陷入局部最优。将自适应粒子群遗传算法与标准粒子群算法、遗传算法、人工蜂群算法进行了比较,仿真实验结果表明该算法在迭代60次左右完成参数辨识,各参数的辨识相对误差均降低到了1%以内。最后利用旋转柔性关节实验平台进行了实验验证,实验结果证明了该算法具有更好的收敛速度和寻优精度。     

基于粒子群算法的劣化桥面铺装多目标组合维护策略优化研究

发展了维护导致的间接维护成本改进模型,基于改进的桥面铺装劣化模型推导了在组合维护策略下其状态指标评估公式,建立了多目标组合维护优化模型.使用自适应粒子群优化算法,根据寿命期内维护成本现值最小化和状态指标最大化的原则,满足性能要求和预算限制约束下,优化出寿命期内成本和性能都满足要求的维护策略.以劣化水泥混凝土桥面铺装为数...