A new hybrid particle swarm optimization (PSO) that incorporates a wavelet-theory-based mutation operation is proposed. It applies the wavelet theory to enhance the PSO in exploring the solution space more effectively for a better...
moreA new hybrid particle swarm optimization (PSO) that incorporates a wavelet-theory-based mutation operation is proposed. It applies the wavelet theory to enhance the PSO in exploring the solution space more effectively for a better solution. A suite of benchmark test functions and three industrial applications (solving the load flow problems, modeling the development of fluid dispensing for electronic packaging, and designing a neuralnetwork-based controller) are employed to evaluate the performance and the applicability of the proposed method. Experimental results empirically show that the proposed method significantly outperforms the existing methods in terms of convergence speed, solution quality, and solution stability. Index Terms?Load flow problem, modeling, mutation operation, neural network control, particle swarm optimization, wavelet theory. I. INTRODUCTION P ARTICLE swarm optimization (PSO) is a recently proposed population-based stochastic optimization algorithm which is inspired by the social behaviors of animals like fish schooling and bird flocking . Comparing with other population-based stochastic optimization methods, such as evolutionary algorithms, the PSO has comparable or even superior search performance for many hard optimization problems with faster and more stable convergence rates . The PSO has been used in different industrial areas, such as power systems [1], [18]?[21], parameter learning of neural networks (NNs) [16], [22], control [23], [24], prediction [25], and modeling [26], . However, observations reveal that the PSO sharply converges in the early stages of the searching process, but saturates or even terminates in the later stages. It behaves like the traditional local searching methods that trap in the local optima. As a result, it is hard to obtain any significant Manuscript improvements by examining neighboring solutions in the later stages of the search.Vaessens et al. and Reeves [14] put these searching methods into the context of local search or neighborhood search. Recently, different hybrid PSOs have been proposed to overcome the drawback of trapping in the local optima. The hybrid PSO was first proposed in 1998 , in which a standard selection mechanism is integrated with the PSO. A new hybrid gradient descent PSO (HGPSO), which is integrated with gradient information to achieve faster convergence without getting trapped in the local minima, is proposed by Noel and Jannett . However, the computational demand of the HGPSO is increased by the process of the gradient descent. Juang proposed a hybrid PSO algorithm named HGAPSO, which incorporates a genetic algorithm?s (GA?s) evolutionary operations of crossover, mutations, and reproduction. Ahmed et al. proposed a hybrid PSO named HPSOM, in which a constant mutating space is used in mutations. In the HGAPSO and the HPSOM, the solution space can be explored by performing mutation operations on particles along the search, and premature convergence is more likely to be avoided. However, the mutating space is kept unchanged all the time throughout the search, and the space for the permutation of particles in the PSO is also fixed. It can be further improved by varying the mutating space along the search. For GAs, the solution space is more likely to be explored in the early stage of the search by setting a larger mutating space, and it is more likely to be fine-tuned for a better solution in the later stage of the search by setting a smaller mutating space based on the properties of the wavelet [2]. This idea can be applied to introduce the hybrid PSO with the GA?s mutation. In this paper, a mutation with a dynamic mutating space by incorporating a wavelet function is proposed. The wavelet is a tool to model seismic signals by combining the dilations and the translations of a simple oscillatory function (the mother wavelet) of finite duration. The PSO?s mutating space is dynamically varying along the search based on the properties of the wavelet function. The resulting mutation operation aids the hybrid PSO to perform more efficiently and provides faster convergence than the PSO with constriction and inertia weight factors [9] and other hybrid PSOs [1], , [17], [28] in solving a suite of benchmark test functions. In addition, it achieves better and more stable solution quality. Application examples on solving some load flow problems [the multicontingency transient stability constrained optimal power flow (MC-TSCOPF) problem and the economic load dispatch with valve-points loading (ELD-VPL) problem], modeling the development of fluid dispensing for electronic packaging, and 1083-4419/$25.00 ? 2008 IEEE Authorized licensed use limited to: Hong Kong Polytechnic University. designing a NN-based controller (NN-BC) are employed to demonstrate that better performance can be achieved by the proposed hybrid PSO. This paper is organized as follows. Section II presents the operation of the hybrid PSO with a wavelet mutation (WM). Experimental studies and analysis are discussed in Section III. Eighteen standard benchmark test functions are given to evaluate the performance of the proposed method. Also, five