Particle Swarm Optimization - A Survey <s> Improving Exploration and Exploitation <s> 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. <s> BIB001 </s> Particle Swarm Optimization - A Survey <s> Improving Exploration and Exploitation <s> In this paper, a novel dynamic multi-swarm particle swarm optimizer (PSO) is introduced. Different from the existing multi-swarm PSOs and the local version of PSO, the swarms are dynamic and the swarms' size is small. The whole population is divided into many small swarms, these swarms are regrouped frequently by using various regrouping schedules and information is exchanged among the swarms. Experiments are conducted on a set of shifted rotated benchmark functions and results show its better performance when compared with some recent PSO variants. <s> BIB002 </s> Particle Swarm Optimization - A Survey <s> Improving Exploration and Exploitation <s> Many real-world problems are dynamic, requiring an optimization algorithm which is able to continuously track a changing optimum over time. In this paper, we explore new variants of particle swarm optimization (PSO) specifically designed to work well in dynamic environments. The main idea is to split the population of particles into a set of interacting swarms. These swarms interact locally by an exclusion parameter and globally through a new anti-convergence operator. In addition, each swarm maintains diversity either by using charged or quantum particles. This paper derives guidelines for setting the involved parameters and evaluates the multiswarm algorithms on a variety of instances of the multimodal dynamic moving peaks benchmark. Results are also compared with other PSO and evolutionary algorithm approaches from the literature, showing that the new multiswarm optimizer significantly outperforms previous approaches <s> BIB003 </s> Particle Swarm Optimization - A Survey <s> Improving Exploration and Exploitation <s> In this paper, we propose two hybrid algorithms of the particle swarm optimization and the simultaneous perturbation optimization method. The proposed algorithms can utilize local information of an objective function and global shape of the function at the same time. The first information is given by the simultaneous perturbation. The second one is from the particle swarm optimization. The proposed scheme has good properties of global search and efficient local search. However, the algorithms themselves are very simple and easy to implement. Moreover, this method only requires values of the function similar to the original particle swarm optimization and the simultaneous perturbation method. Three examples including an application for a neural network are shown. <s> BIB004 </s> Particle Swarm Optimization - A Survey <s> Improving Exploration and Exploitation <s> Particle swarm has proven to be competitive to other evolutionary algorithms in the field of optimization, and in many cases enables a faster convergence to the ideal solution. However, like any optimization algorithm it seems to have difficulties handling optimization problems of high dimension. Here we first show that dimensionality is really a problem for the classical particle swarm algorithms. We then show that increasing the swarm size can be necessary to handle problem of high dimensions but is not enough. We also show that the issue of scalability occurs more quickly on some functions. <s> BIB005 </s> Particle Swarm Optimization - A Survey <s> Improving Exploration and Exploitation <s> In this paper, the performance of dynamic multi-swarm particle swarm optimizer (DMS-PSO) on the set of benchmark functions provided for the CEC2008 Special Session on Large Scale optimization is reported. Different from the existing multi-swarm PSOs and local versions of PSO, the sub-swarms are dynamic and the sub-swarmspsila size is very small. The whole population is divided into a large number sub-swarms, these sub-swarms are regrouped frequently by using various regrouping schedules and information is exchanged among the particles in the whole swarm. The Quasi-Newton method is combined to improve its local searching ability. <s> BIB006
Although numerous early works report PSO's high efficiency in finding a near-optimal solution in small-scale problems (n ≈ 30 or less), PSO does suffer from the curse of dimensionality in large-scale problems as in other optimization methods employing parallel search BIB005 . The issue here is how to balance exploration in the vast search space and exploitation at the proximity of promising regions, using a limited number of particles. Most of the genetic operations reviewed in Sec. 3.3 contribute to exploration which enforces a divide-and-conquer strategy in some way. Division of the swarm into subswarms, or the multiswarm approach BIB003 are among such approaches. In Dynamic Multi-Swarm PSO (DMSPSO) by Liang and Suganthan BIB002 , random re-definition of small-sized (3-5 particles) neighborhood occurs, thereby forcing exchange of information among the particles. Recently, the modified DM-SPSO with exploitation by Quasi-Newton method by Zhao et al. BIB006 . achieved comparable to better results to other optimization algorithms in the large-scale optimization competition held at the CEC2008 conference. As an example of other additional exploitation features, Maeda BIB004 introduces PSO with local search using simultaneous perturbation. The method is reported to outperform PSO with constriction in convergence efficiency for several problems. As another approach of task division, Van den Bergh and Engelbrecht BIB001 introduced Cooperative PSO (CPSO) which divides the swarm to multiple subswarms assigned to searches in particular low-dimensional subspaces. The communication among the subswarms are achieved by sharing the best-achieving components upon evaluating the objective function.