Cooperative particle swarm optimization for multiobjective transportation planning

The paper presents a multiobjective optimization problem that considers distributing multiple kinds of products from multiple sources to multiple targets. The problem is of high complexity and is difficult to solve using classical heuristics. We propose for the problem a hierarchical cooperative optimization approach that decomposes the problem into low-dimensional subcomponents, and applies Pareto-based particle swarm optimization (PSO) method to the main problem and the subproblems alternately. In particular, our approach uses multiple sub-swarms to evolve the sub-solutions concurrently, controls the detrimental effect of variable correlation by reducing the subproblem objectives, and brings together the results of the sub-swarms to construct effective solutions of the original problem. Computational experiment demonstrates that the proposed algorithm is robust and scalable, and outperforms some state-of-the-art constrained multiobjective optimization algorithms on a set of test problems.     

Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization

We propose a novel hybrid algorithm named PSO-DE, which integrates particle swarm optimization (PSO) with differential evolution (DE) to solve constrained numerical and engineering optimization problems. Traditional PSO is easy to fall into stagnation when no particle discovers a position that is better than its previous best position for several generations. DE is incorporated into update the previous best positions of particles to force PSO jump out of stagnation, because of its strong searching ability. The hybrid algorithm speeds up the convergence and improves the algorithm’s performance. We test the presented method on 11 well-known benchmark test functions and five engineering optimization functions. Comparisons show that PSO-DE outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions.     

A two-stage quantum-behaved particle swarm optimization with skipping search rule and weight to solve continuous optimization problem

Quantum-behaved particle swarm optimization (QPSO) is a recently developed heuristic method by particle swarm optimization (PSO) algorithm based on quantum mechanics, which outperforms the search ability of original PSO. But as many other PSOs, it is easy to fall into the local optima for the complex optimization problems. Therefore, we propose a two-stage quantum-behaved particle swarm optimization with a skipping search rule and a mean attractor with weight. The first stage uses quantum mechanism, and the second stage uses the particle swarm evolution method. It is shown that the improved QPSO has better performance, because of discarding the worst particles and enhancing the diversity of the population. The proposed algorithm (called ‘TSQPSO’) is tested on several benchmark functions and some real-world optimization problems and then compared with the PSO, SFLA, RQPSO and WQPSO and many other heuristic algorithms. The experiment results show that our algorithm has better performance than others.     

一种基于免疫原理的多目标优化方法

借鉴生物免疫原理中抗体多样性产生及保持的机理，建立了一种多目标优化方法．该方法定义了多目标选择熵和浓度调节选择概率的概念，采用了抗体克隆选择策略和高度变异策略．最后采用四种典型的多目标优化函数，将本方法同几种常用的多目标遗传算法进行了比较研究，证明了所建立的基于免疫原理的多目标优化方法能有效解决多目标优化问题且具有一定的优越性．     

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.     

多Agent 主从粒子群分布式计算框架

面向大规模复杂优化问题,提出了一个基于并行粒子群优化的分布式Agent计算框架.框架中使用一个主群(master swarm)来演化问题的完整解,并使用一组从群(slave swarm)来并行优化一组子问题的解,主群和从群通过交替执行来提高问题的求解效率.采用异步组结构,主群/从群中的各类Agent共享一个解群,并通过相互协作,对解群进行构造、改进、修补、分解和合并等演化操作.该框架可用于求解复杂的约束多目标优化问题.通过一类典型运输问题上的实验,其结果表明,所提出的方法明显优于另外两种先进的演化算法.     

Communication latency tolerant parallel algorithm for particle swarm optimization

Particle swarm optimization (PSO) algorithm is a population-based algorithm for finding the optimal solution. Because of its simplicity in implementation and fewer adjustable parameters compared to the other global optimization algorithms, PSO is gaining attention in solving complex and large scale problems. However, PSO often requires long execution time to solve those problems. This paper proposes a parallel PSO algorithm, called delayed exchange parallelization, which improves performance of PSO on distributed environment by hiding communication latency efficiently. By overlapping communication with computation, the proposed algorithm extracts parallelism inherent in PSO. The performance of our proposed parallel PSO algorithm was evaluated using several applications. The results of evaluation showed that the proposed parallel algorithm drastically improved the performance of PSO, especially in high-latency network environment.     

Solving multiobjective problems using cat swarm optimization

This paper proposes a new multiobjective evolutionary algorithm (MOEA) by extending the existing cat swarm optimization (CSO). It finds the nondominated solutions along the search process using the concept of Pareto dominance and uses an external archive for storing them. The performance of our proposed approach is demonstrated using standard test functions. A quantitative assessment of the proposed approach and the sensitivity test of different parameters is carried out using several performance metrics. The simulation results reveal that the proposed approach can be a better candidate for solving multiobjective problems (MOPs).     

Particle Swarm Optimization with Chaos-based Initialization for Numerical Optimization

Particle swarm optimization (PSO) is a population based swarm intelligence algorithm that has been deeply studied and widely applied to a variety of problems. However, it is easily trapped into the local optima and premature convergence appears when solving complex multimodal problems. To address these issues, we present a new particle swarm optimization by introducing chaotic maps (Tent and Logistic) and Gaussian mutation mechanism as well as a local re-initialization strategy into the standard PSO algorithm. On one hand, the chaotic map is utilized to generate uniformly distributed particles to improve the quality of the initial population. On the other hand, Gaussian mutation as well as the local re-initialization strategy based on the maximal focus distance is exploited to help the algorithm escape from the local optima and make the particles proceed with searching in other regions of the solution space. In addition, an auxiliary velocity-position update strategy is exclusively used for the global best particle, which can effectively guarantee the convergence of the proposed particle swarm optimization. Extensive experiments on eight well-known benchmark functions with different dimensions demonstrate that the proposed PSO is superior or highly competitive to several state-of-the-art PSO variants in dealing with complex multimodal problems.     

多策略协同进化粒子群优化算法

为了提高粒子群优化(PSO)算法的优化性能, 提出了一种多策略协同进化PSO(MSCPSO)算法。该方法引入了多策略进化模式和多子群协同进化机制, 将整个种群划分为多个子群, 每个子群中的粒子按照不同的进化策略产生新的粒子。子群周期性地更新共享信息, 以加快算法的收敛速度。通过六个基准函数实验, 仿真结果表明, 新算法在计算精度和收敛速度方面均优于其他七种PSO算法。     

Multiobjective structural optimization using a microgenetic algorithm

In this paper, we present a genetic algorithm with a very small population and a reinitialization process (a microgenetic algorithm) for solving multiobjective optimization problems. Our approach uses three forms of elitism, including an external memory (or secondary population) to keep the nondominated solutions found along the evolutionary process. We validate our proposal using several engineering optimization problems taken from the specialized literature and compare our results with respect to two other algorithms (NSGA-II and PAES) using three different metrics. Our results indicate that our approach is very efficient (computationally speaking) and performs very well in problems with different degrees of complexity.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

Multiobjective optimization of trusses using genetic algorithms

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min–max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-offs and that the genetic algorithm can be used as a reliable numerical optimization tool.     

基于粒子滤波重采样与变异操作的改进粒子群算法

针对标准粒子群优化(PSO)算法在求解过程中存在求解精度低、搜索后期收敛速度慢等问题,提出一种基于粒子滤波重采样步骤与变异操作相结合的改进PSO算法——RSPSO。该算法充分利用重采样中具有较大权值的粒子被保留和复制、较小权值的粒子被舍弃的特点,并利用已有的变异操作方法克服粒子匮乏的缺点,大大增强了PSO算法中后期搜索阶段的局部搜索能力。在不同基准函数下对RSPSO算法和标准PSO算法以及文献中其他改进算法进行对比。实验结果表明, RSPSO算法的收敛速度较快,同时其搜索精度和解的稳定性均有所提高,且能够全局地解决多峰问题。     

A hybrid approach of dimension partition and velocity control to enhance performance of particle swarm optimization

Particle swarm optimization (PSO) is a population-based optimization technique and it has been used to solve many optimization problems successfully. However, more efficient strategies are still needed to control the trade-off between exploitation exploration in the search process for solving tasks with high complexity. In this work, we present a new hybrid PSO approach to overcome the search difficulties. Our approach focuses on two search strategies. One is a two-swarm cooperative strategy that controls search region and integrates full and single dimension PSO search. The other strategy is to control the velocity of the particles in an adaptive way, according to how they move in the space. To evaluate the performance and generality of our hybrid approach, extensive experiments have been conducted and the results confirm the effectiveness of the proposed approach.     

教与学信息交互粒子群优化算法

针对单一种群在解决高维问题中收敛速度较慢和多样性缺失的问题,提出了一种教与学信息交互粒子群优化(PSO)算法.根据进化过程将种群动态地划分为两个子种群,分别采用粒子群优化算法和教与学优化算法,同时粒子利用学习者阶段进行子种群之间信息交互,并通过评价收敛性和多样性指标让粒子的收敛能力和多样性在进化过程中得到平衡.与粒子群...     

An Effective PSO-Based Hybrid Algorithm for Multiobjective Permutation Flow Shop Scheduling

This paper proposes a hybrid algorithm based on particle swarm optimization (PSO) for a multiobjective permutation flow shop scheduling problem, which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. Not only does the proposed multiobjective algorithm (named MOPSO) apply the parallel evolution mechanism of PSO characterized by individual improvement, population cooperation, and competition to effectively perform exploration but it also utilizes several adaptive local search methods to perform exploitation. First, to make PSO suitable for solving scheduling problems, a ranked-order value (ROV) rule based on a random key technique to convert the continuous position values of particles to job permutations is presented. Second, a multiobjective local search based on the Nawaz-Enscore-Ham heuristic is applied to good solutions with a specified probability to enhance the exploitation ability. Third, to enrich the searching behavior and to avoid premature convergence, a multiobjective local search based on simulated annealing with multiple different neighborhoods is designed, and an adaptive meta-Lamarckian learning strategy is employed to decide which neighborhood will be used. Due to the fusion of multiple different searching operations, good solutions approximating the real Pareto front can be obtained. In addition, MOPSO adopts a random weighted linear sum function to aggregate multiple objectives to a single one for solution evaluation and for guiding the evolution process in the multiobjective sense. Due to the randomness of weights, searching direction can be enriched, and solutions with good diversity can be obtained. Simulation results and comparisons based on a variety of instances demonstrate the effectiveness, efficiency, and robustness of the proposed hybrid algorithm.     

LADPSO: using fuzzy logic to conduct PSO algorithm

Optimization plays a critical role in human modern life. Nowadays, optimization is used in many aspects of human modern life including engineering, medicine, agriculture and economy. Due to the growing number of optimization problems and their growing complexity, we need to improve and develop theoretical and practical optimization methods. Stochastic population based optimization algorithms like genetic algorithms and particle swarm optimization are good candidates for solving complex problems efficiently. Particle swarm optimization (PSO) is an optimization algorithm that has received much attention in recent years. PSO is a simple and computationally inexpensive algorithm inspired by the social behavior of bird flocks and fish schools. However, PSO suffers from premature convergence, especially in high dimensional multi-modal functions. In this paper, a new method for improving PSO has been introduced. The Proposed method which has been named Light Adaptive Particle Swarm Optimization is a novel method that uses a fuzzy control system to conduct the standard algorithm. The suggested method uses two adjunct operators along with the fuzzy system in order to improve the base algorithm on global optimization problems. Our approach is validated using a number of common complex uni-modal/multi-modal benchmark functions and results have been compared with the results of Standard PSO (SPSO2011) and some other methods. The simulation results demonstrate that results of the proposed approach is promising for improving the standard PSO algorithm on global optimization problems and also improving performance of the algorithm.     

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 novel particle swarm optimizer hybridized with extremal optimization

Particle swarm optimization (PSO) has received increasing interest from the optimization community due to its simplicity in implementation and its inexpensive computational overhead. However, PSO has premature convergence, especially in complex multimodal functions. Extremal optimization (EO) is a recently developed local-search heuristic method and has been successfully applied to a wide variety of hard optimization problems. To overcome the limitation of PSO, this paper proposes a novel hybrid algorithm, called hybrid PSO–EO algorithm, through introducing EO to PSO. The hybrid approach elegantly combines the exploration ability of PSO with the exploitation ability of EO. We testify the performance of the proposed approach on a suite of unimodal/multimodal benchmark functions and provide comparisons with other meta-heuristics. The proposed approach is shown to have superior performance and great capability of preventing premature convergence across it comparing favorably with the other algorithms.