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A Novel Approach to Improve the Performance of Evolutionary Methods for Nonlinear Constrained Optimization

DOI: 10.1155/2012/540861

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Abstract:

Evolutionary methods are well-known techniques for solving nonlinear constrained optimization problems. Due to the exploration power of evolution-based optimizers, population usually converges to a region around global optimum after several generations. Although this convergence can be efficiently used to reduce search space, in most of the existing optimization methods, search is still continued over original space and considerable time is wasted for searching ineffective regions. This paper proposes a simple and general approach based on search space reduction to improve the exploitation power of the existing evolutionary methods without adding any significant computational complexity. After a number of generations when enough exploration is performed, search space is reduced to a small subspace around the best individual, and then search is continued over this reduced space. If the space reduction parameters (red_gen and red_factor) are adjusted properly, reduced space will include global optimum. The proposed scheme can help the existing evolutionary methods to find better near-optimal solutions in a shorter time. To demonstrate the power of the new approach, it is applied to a set of benchmark constrained optimization problems and the results are compared with a previous work in the literature. 1. Introduction A significant part of today’s engineering problems are constrained optimization problems (COP). Although there exist efficient methods like Simplex for solving linear COP, solving nonlinear COP (NCOP) is still open for novel investigations. Different methods have been proposed for solving NCOP. Among them, natural optimization and especially population-based schemes are the most general and promising ones. These methods can be applied to all types of COP including convex and nonconvex, analytical and non-analytical, real-, integer- and mixed-valued problems. One of the most applied techniques for solving NCOP are evolutionary methods. Various techniques have been introduced for handling nonlinear constrains by evolutionary optimization (EO) methods. These approaches can be grouped in four major categories [1, 2]: (1) methods based on penalty functions that are also known as indirect constraint handling, (2) methods based on a search of feasible solutions including repairing unfeasible individuals [3, 4], superiority of feasible points [5], and behavioral memory [6], (3) methods based on preserving feasibility of solutions like preserving feasibility by designing special crossover and mutation operators [7], the GENOCOP system [8], searching

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