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Abstract: In recent years, particle swarm optimization (PSO) algorithm has been used to solve global optimization problems. This algorithm is widely used as an effective optimization tool in various applications. However, traditional PSO consists of only two searching layers and thus often results in premature convergence into the local minima. Thus, multi-layer particle swarm optimization (MLPSO) is proposed in this paper to improve the performance of traditional PSO by increasing the two layers of swarms to multiple layers. The MLPSO strategy increases the diversity of searching swarms to improve its performance when solving complex problems. The experiment indicates that the novel approach improves the final results and the convergence speed. [Copyright &y& Elsevier]

Abstract: Particle Swarm Optimization (PSO) has shown an effective performance for solving variant benchmark and real-world optimization problems. However, it suffers from premature convergence because of quick losing of diversity. In order to enhance its performance, this paper proposes a hybrid PSO algorithm, called DNSPSO, which employs a diversity enhancing mechanism and neighborhood search strategies to achieve a trade-off between exploration and exploitation abilities. A comprehensive experimental study is conducted on a set of benchmark functions, including rotated multimodal and shifted high-dimensional problems. Comparison results show that DNSPSO obtains a promising performance on the majority of the test problems. [Copyright &y& Elsevier]

Abstract: Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a probabilistic metric space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of probabilistic metric spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) has been shown to yield good performance for solving various optimization problems. However, it tends to suffer from premature convergence when solving complex problems. This paper presents an enhanced PSO algorithm called GOPSO, which employs generalized opposition-based learning (GOBL) and Cauchy mutation to overcome this problem. GOBL can provide a faster convergence, and the Cauchy mutation with a long tail helps trapped particles escape from local optima. The proposed approach uses a similar scheme as opposition-based differential evolution (ODE) with opposition-based population initialization and generation jumping using GOBL. Experiments are conducted on a comprehensive set of benchmark functions, including rotated multimodal problems and shifted large-scale problems. The results show that GOPSO obtains promising performance on a majority of the test problems. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) algorithm has been developing rapidly and many results have been reported. PSO algorithm has shown some important advantages by providing high speed of convergence in specific problems, but it has a tendency to get stuck in a near optimal solution and one may find it difficult to improve solution accuracy by fine tuning. This paper presents a dynamic global and local combined particle swarm optimization (DGLCPSO) algorithm to improve the performance of original PSO, in which all particles dynamically share the best information of the local particle, global particle and group particles. It is tested with a set of eight benchmark functions with different dimensions and compared with original PSO. Experimental results indicate that the DGLCPSO algorithm improves the search performance on the benchmark functions significantly, and shows the effectiveness of the algorithm to solve optimization problems. [Copyright &y& Elsevier]