一种新的求解动态连续优化的分层粒子群算法

为了高效求解动态连续优化问题,提出一种分层粒子群优化算法。该算法将动态函数定义域分成Q个子空间,每个空间用一个粒子群作为第一层进行独立搜索,Q个子空间的最优粒子再组成一个全局粒子群进行全局搜索,以达到全局牵引的作用,同时提出探测环境和响应环境的策略。利用经典的动态函数对算法进行测试,结果表明所提出算法能够迅速适应环境变化和跟踪最优解的变化,效果令人满意。     

Synchronous parallelization of Particle Swarm Optimization with digital pheromones

In this paper, Particle Swarm Optimization (PSO) using digital pheromones to coordinate swarms within n-dimensional design spaces in a parallel computing environment is presented. Digital pheromones are models simulating real pheromones emitted by insects for communication to indicate suitable food or nesting location. Particle swarms search the design space with digital pheromones aiding communication within the swarm during an iteration to improve search efficiency. Previous work by the authors demonstrated the capability of digital pheromones within PSO for searching the global optimum with improved accuracy, efficiency and reliability in a single processor computing environment. When multiple swarms explore and exploit the design space in a parallel computing environment, the solution characteristics can be further improved. This premise is investigated through deploying swarms on multiple processors in a distributed memory parallel computing environment. The primary hurdle for the developed algorithm was bandwidth latency due to synchronization across processors, causing the solution duration due to each swarm to be only as fast as the slowest participating processor. However, it has been observed that the speedup and parallel efficiency improved substantially as the dimensionality of the problems increased. The development of the method along with results from six test problems is presented.     

Asynchronous parallelization of particle swarm optimization through digital pheromone sharing

In this paper, a model for sharing digital pheromones between multiple particle swarms to search n-dimensional design spaces in an asynchronous parallel computing environment is presented. Particle swarm optimization (PSO) is an evolutionary technique used to effectively search multi-modal design spaces. With the aid of digital pheromones, members in a swarm can better communicate with each other to improve search performance. Previous work by the authors demonstrated the capability of digital pheromones within PSO for searching the global optimum in both single and coarse grain synchronous parallel computing environments. In the coarse grain approach, multiple swarms are simultaneously deployed across various processors and synchronization is carried out only when all swarms achieved convergence, in an effort to reduce processor-to-processor communication and network latencies. However, it is theorized that with an appropriate parallelization scheme, the benefits of digital pheromones and communication between swarms can outweigh the network bandwidth latencies resulting in improved search efficiency and accuracy. To explore this idea, a swarm is deployed in the design space across different processors. Through an additional processor, each part of the swarm can communicate with the others. While digital pheromones aid communication within a swarm, the developed parallelization model facilitates communication between multiple swarms resulting in improved search accuracy and efficiency. The development of this method and results from solving several multi-modal test problems are presented.     

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 hierarchical particle swarm optimizer with latin sampling based memetic algorithm for numerical optimization

Memetic algorithms, one type of algorithms inspired by nature, have been successfully applied to solve numerous optimization problems in diverse fields. In this paper, we propose a new memetic computing model, using a hierarchical particle swarm optimizer (HPSO) and latin hypercube sampling (LHS) method. In the bottom layer of hierarchical PSO, several swarms evolve in parallel to avoid being trapped in local optima. The learning strategy for each swarm is the well-known comprehensive learning method with a newly designed mutation operator. After the evolution process accomplished in bottom layer, one particle for each swarm is selected as candidate to construct the swarm in the top layer, which evolves by the same strategy employed in the bottom layer. The local search strategy based on LHS is imposed on particles in the top layer every specified number of generations. The new memetic computing model is extensively evaluated on a suite of 16 numerical optimization functions as well as the cylindricity error evaluation problem. Experimental results show that the proposed algorithm compares favorably with conventional PSO and several variants.     

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.     

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.     

分层粒子群优化算法

针对粒子群优化算法存在进化后期局部搜索能力不强、收敛速度变慢的问题,提出一种分层粒子群优化算法。利用标准粒子群优化算法在整个搜索空间内进行全局搜索,由全局搜索获得的较优个体产生局部搜索区域,在局部区域内进行进一步搜索。为避免陷入局部最优,采用动态调整局部搜索区域的策略,保持算法的全局收敛性。通过典型测试函数计算表明,该算法的收敛速度和局部搜索能力有明显改善。     

PSO-Based Multiobjective Optimization With Dynamic Population Size and Adaptive Local Archives

Recently, various multiobjective particle swarm optimization (MOPSO) algorithms have been developed to efficiently and effectively solve multiobjective optimization problems. However, the existing MOPSO designs generally adopt a notion to “estimate” a fixed population size sufficiently to explore the search space without incurring excessive computational complexity. To address the issue, this paper proposes the integration of a dynamic population strategy within the multiple-swarm MOPSO. The proposed algorithm is named dynamic population multiple-swarm MOPSO. An additional feature, adaptive local archives, is designed to improve the diversity within each swarm. Performance metrics and benchmark test functions are used to examine the performance of the proposed algorithm compared with that of five selected MOPSOs and two selected multiobjective evolutionary algorithms. In addition, the computational cost of the proposed algorithm is quantified and compared with that of the selected MOPSOs. The proposed algorithm shows competitive results with improved diversity and convergence and demands less computational cost.      

A MULTISWARM COMPETITIVE PARTICLE SWARM ALGORITHM FOR OPTIMIZATION CONTROL OF AN ETHYLENE CRACKING FURNACE

A fuzzy C-means (FCM) multiswarm competitive particle swarm optimization (FCMCPSO) algorithm is proposed, in which FCM clustering is used to divide swarms adaptively into different clusters. The large-scale swarms are according to the standard particle swarm optimization (PSO) algorithm, whereas the small-scale swarms search randomly in the neighborhood of the optimal solution to increase the probability of jumping out of the local optimization point. Within every cluster, the adaptive value gained by competitive learning is respectively found and arranged in order. Swarms of small adaptive value were integrated with the neighboring swarms of large adaptive value to search the optimal solution competitively by the swarms. The algorithm's validity was tested by benchmark functions and compared with other PSO algorithms. Furthermore, an integrated FCMCPSO-radial basis function neural network was studied for nonlinear system modeling and intelligent optimization control of cracking depth of an ethylene cracking furnace application in a chemical process.     

均匀粒子群算法

由于粒子群算法(PSO)本质上的随机性,其搜索质量和速度也呈随机性.这使得普通的粒子群算法难以满足某些需要快速优化的工程需要.利用均匀设计方法产生PSO算法的初始种群（或关键代次种群）,可以使种群中的粒子在搜索空间分布更均匀,更好地保持分散性.算法中给出了4种种群的生成方案,通过测试和对比分析表明:基于值域分割的均匀设计种群生成法能使算法的搜索效果最好;算法可以在不丧失搜索精度和效率的前提下,提高搜索效率和搜索精度的稳定性,有效减少粒子聚集和早熟的发生.     

多策略粒子群优化算法

为了克服粒子群优化算法易早熟、局部搜索能力弱的问题,提出了一种改进的粒子群优化算法--多策略粒子群优化算法。在群体寻优过程中,各粒子根据搜索到的最优位置的变动情况,从几种备选的策略中抉择出当代的最优搜索策略。其中,最优粒子有最速下降策略、矫正下降策略和随机移动策略可以选择,非最优粒子有聚集策略和扩散策略可以选择。四个典型测试函数的数值实验结果表明,新提出的算法比标准粒子群优化算法具有更强和更稳定的全局搜索能力。     

Handling multiple objectives with particle swarm optimization

This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems.     

An enhanced simulation-based design method coupled with meta-heuristic search algorithm for accurate reliability-based design optimization

The enhanced weighted simulation-based design method in conjunction with particle swarm optimization (PSO) is developed as a pseudo double-loop algorithm for accurate reliability-based design optimization (RBDO). According to this hybrid method, generated samples of weighed simulation method (WSM) are considered as initial population of the PSO. The proposed population is then employed to evaluate the safety level of each PSO swarm (design candidates) during movement. Using this strategy, there is no required to conduct new sampling for reliability assessment of design candidates (PSO swarms). Employing PSO as the search engine of RBDO and WSM as the reliability analyzer provide more accurate results with few samples and also increase the application range of traditional WSM. Besides, a shift strategy is also introduced to increase the capability of the WSM to investigate general RBDO problems including both deterministic and random design variables. Several examples are investigated to demonstrate the accuracy and robustness of the method. Results demonstrate the computational efficiency and superiority of the proposed method for practical engineering problems with highly nonlinear and implicit probabilistic constrains.     

Cultural-based particle swarm for dynamic optimisation problems

Many practical optimisation problems are with the existence of uncertainties, among which a significant number belong to the dynamic optimisation problem (DOP) category in which the fitness function changes through time. In this study, we propose the cultural-based particle swarm optimisation (PSO) to solve DOP problems. A cultural framework is adopted incorporating the required information from the PSO into five sections of the belief space, namely situational, temporal, domain, normative and spatial knowledge. The stored information will be adopted to detect the changes in the environment and assists response to the change through a diversity-based repulsion among particles and migration among swarms in the population space, and also helps in selecting the leading particles in three different levels, personal, swarm and global levels. Comparison of the proposed heuristics over several difficult dynamic benchmark problems demonstrates the better or equal performance with respect to most of other selected state-of-the-art dynamic PSO heuristics.     

Annealing-based particle swarm optimization to solve the redundant reliability problem with multiple component choices

In this paper, the performance of a particle swarm optimization (PSO) algorithm named Annealing-based PSO (APSO) is investigated to solve the redundant reliability problem with multiple component choices (RRP-MCC). This problem aims to choose an optimal combination of components and redundancy levels for a system with a series–parallel configuration that maximizes the overall system reliability. PSO is a population-based meta-heuristic algorithm inspired by the social behavior of the biological swarms that is designed for continuous decision spaces. As a local search engine (LSE), the proposed APSO employs the Metropolis-Hastings strategy, the key idea behind the simulated annealing (SA) algorithm. In APSO, the best position among all particles in each iteration is dynamically improved using the inner loop of the SA (i.e., equilibrium loop) while the temperature is updated in the main loop of the PSO algorithm. The well-known benchmarks are used to verify the performance of the proposed APSO. Even though APSO fails to outperform the best solution obtained in the literature, the contribution of this paper is comprised of the implementation of APSO as a hybrid meta-heuristic as well as the effect of Metropolis-Hastings strategy on the performance of the classical PSO.     

改进的r支配高维多目标粒子群优化算法

高维多目标优化问题是广泛存在于实际应用中的复杂优化问题,目前的研究方法大都限于进化算法.本文利用粒子群优化算法求解高维多目标优化问题,提出了一种基于r支配的多目标粒子群优化算法.采用r支配关系进行粒子的比较与选择,并结合粒子群优化算法收敛速度快的优势,使得算法在目标个数增加时仍保持较强的搜索能力;为了弥补由此造成的群体多样性的丢失,优化非r支配阈值的取值策略;此外,引入决策空间的拥挤距离测度,并给出新的外部存储器更新方法,从而进一步防止算法陷入局部最优.对多个基准测试函数的仿真结果表明所得解集在收敛性、多样性以及围绕参考点的分布性上均优于其他两种算法.     

A Cooperative approach to particle swarm optimization

The particle swarm optimizer (PSO) is a stochastic, population-based optimization technique that can be applied to a wide range of problems, including neural network training. This paper presents a variation on the traditional PSO algorithm, called the cooperative particle swarm optimizer, or CPSO, employing cooperative behavior to significantly improve the performance of the original algorithm. This is achieved by using multiple swarms to optimize different components of the solution vector cooperatively. Application of the new PSO algorithm on several benchmark optimization problems shows a marked improvement in performance over the traditional PSO.     

Force-imitated particle swarm optimization using the near-neighbor effect for locating multiple optima

Multimodal optimization problems pose a great challenge of locating multiple optima simultaneously in the search space to the particle swarm optimization (PSO) community. In this paper, the motion principle of particles in PSO is extended by using the near-neighbor effect in mechanical theory, which is a universal phenomenon in nature and society. In the proposed near-neighbor effect based force-imitated PSO (NN-FPSO) algorithm, each particle explores the promising regions where it resides under the composite forces produced by the “near-neighbor attractor” and “near-neighbor repeller”, which are selected from the set of memorized personal best positions and the current swarm based on the principles of “superior-and-nearer” and “inferior-and-nearer”, respectively. These two forces pull and push a particle to search for the nearby optimum. Hence, particles can simultaneously locate multiple optima quickly and precisely. Experiments are carried out to investigate the performance of NN-FPSO in comparison with a number of state-of-the-art PSO algorithms for locating multiple optima over a series of multimodal benchmark test functions. The experimental results indicate that the proposed NN-FPSO algorithm can efficiently locate multiple optima in multimodal fitness landscapes.     

独立自适应调整参数的粒子群优化算法

针对传统粒子群优化算法在求解复杂优化问题时易陷入局部最优和依赖参数的取值等问题,提出了一种独立自适应参数调整的粒子群优化算法。算法重新定义了粒子进化能力、种群进化能力以及进化率,在此基础上给出了粒子群惯性权重及学习因子的独立调整策略,更好地平衡了算法局部搜索与全局搜索的能力。为保持种群多样性,提高粒子向全局最优位置的收敛速度,在算法迭代过程中,采用粒子重构策略使种群中进化能力较弱的粒子向进化能力较强的粒子进行学习,重新构造生成新粒子。最后通过CEC2013中的10个基准测试函数与4种改进粒子群算法在不同维度下进行测试对比,实验结果验证了该算法在求解复杂函数时具有高效性,通过收敛性分析说明了算法的有效性。