A fuzzy adaptive Genetic Algorithms for global optimization problems

Abstract

Genetic Algorithms (GA) is a method based on natural selection in the theory of biological evolution, which has been widely applied to solve numerous optimization problems in diverse fields. However, the canonical GA is more likely to get stuck at a local optimum and thereby leads to premature convergence. To overcome such inconvenience, a fuzzy adaptive GA (FAGA) is proposed based on fuzzy clustering and adaptation policy of parameters control (probabilities of crossover and mutation, p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> respectively). Sufficiently analyzing the solution state and dynamically allocating different individuals with moderate properties, the core idea of the schema, are to maintain diversity in the population in order to cope with the deception multiple local optima. Self-adaptive adjust of p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> which is considered to be an optimal balance between exploration and exploitation. Fuzzy cluster in the approach depends on the rank of fitness, which has three categories during the whole search process; parameter control is based on the technique of negative feedback, which relieves the burden of specifying the values. The performance of the new approach is test on a set of standard benchmark functions and compares with traditional and adapted GA which has a better result.