A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch

Leandro dos Santos Coelho, Viviana Cocco Mariani
2009 Chaos, Solitons & Fractals  
Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the chaotic systems theory, this paper proposed a novel chaotic PSO combined with an implicit filtering (IF) local search method to solve economic dispatch problems. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed PSO introduces chaos mapping using
more » ... énon map sequences which increases its convergence rate and resulting precision. The chaotic PSO approach is used to produce good potential solutions, and the IF is used to fine-tune of final solution of PSO. The hybrid methodology is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. Simulation results are promising and show the effectiveness of the proposed approach. (Leandro dos Santos Coelho), viviana.mariani@pucpr.br (V.C. Mariani). (2009) 510-518 www.elsevier.com/locate/chaos PSO is a kind of evolutionary algorithm based on a population of potential solutions and motivated by the simulation of social behavior instead of the survival of the fittest individual. It is a population-based evolutionary algorithm. Similar to the other population-based evolutionary algorithms, PSO is initialized with a population of random solutions. Unlike the most of the evolutionary algorithms, each potential solution (individual) in PSO is also associated with a randomized velocity, and the potential solutions, called particles, are then "flown" through the problem space. Chaos, Solitons and Fractals 39 The approach of composite configuration by deterministic techniques combined with PSO algorithms is a promising alternative in optimization and must be evaluated. In this paper, an alternative hybrid method is proposed. The proposed hybrid method combines the PSO using chaotic sequences generate by Hénon map in evolution phase and the implicit filtering (IF) algorithm in the learning phase (after the stopping criterion of chaotic PSO be satisfied) to solve the EDP associated with the valve-point effect. The IF algorithm is a projected quasi-Newton method that uses finite difference gradients. The difference increment is reduced as the optimization progresses, thereby avoiding some local minima, discontinuities, or nonsmooth regions that would trap a conventional gradient-based method. The hybrid method of optimization adopted in this paper is also denominated in the literature of the hybrid algorithm, algorithm with local search, memetic algorithm or optimization based in Lamarckian evolution [11, 12] . Chaos describes the complex behavior of a nonlinear deterministic system. Optimization algorithms based on the chaos theory are search methodologies that differ from any of the existing traditional stochastic optimization techniques. Due to the non-repetition of chaos, it can carry out overall searches at higher speeds than stochastic ergodic searches that depend on probabilities. In this context, the literature contains several optimization algorithms using chaotic sequences for solving design problems, such as the presented works in [13] [14] [15] [16] [17] [18] [19] [20] [21] . The application of chaotic sequences instead of random sequences in PSO is a powerful strategy to diversify the population of particles and improve the PSO's performance in preventing premature convergence to local minima. An EDP problem with 13 unit test system using nonsmooth fuel cost function [22] is employed in this paper for demonstrate the performance of the proposed hybrid method. The results obtained with the chaotic PSO approach using Hénon map and an IF local search were analyzed and compared with those obtained in recent literature. The rest of the paper is organized as follows: Section 2 describes the EDP, while Section 3 explains the PSO, chaotic PSO and IF concepts. Section 4 presents the simulation results of the 13 unit test problem optimization and compares methods to solve the case study. Lastly, Section 5 outlines our conclusions and future research.
doi:10.1016/j.chaos.2007.01.093 fatcat:75osnb4idbbmhppkzaf7rad4iy