%0 Journal Article
%T Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization
%A M. Fernanda P. Costa
%A Ana Maria A. C. Rocha
%A Rog¨¦rio B. Francisco
%A Edite M. G. P. Fernandes
%J Advances in Operations Research
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/215182
%X Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid ¡°erf¡± function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid ¡°erf¡± function with ¡°movements in continuous space¡± is the best, in terms of both computational requirements and accuracy. 1. Introduction This paper aims to analyze the merit, in terms of performance, of a heuristic-based firefly algorithm (HBFA) for computing the optimal and binary solution of bound constrained nonlinear optimization problems. The problem to be addressed has the form where is a continuous function. Due to the compactness of , we also have , , where and are the vectors of the lower and upper bounds, respectively. We do not assume that is differentiable and convex. Instead of searching for any local (nonglobal) solution we want the globally best binary point. Direct search methods might be suitable since we do not assume differentiability. However, they are only local optimization procedures and therefore there is no guarantee that a global solution is reached. For global optimization, stochastic methods are generally used and aim to explore the search space and converge to a global solution. Metaheuristics are higher-level procedures or heuristics that are designed to search for good solutions, known as near-optimal solutions, with less computational effort and time than more classical algorithms. They are usually nondeterministic and their behaviors do not depend on problem¡¯s properties. Population-based metaheuristics have been used
%U http://www.hindawi.com/journals/aor/2014/215182/