Optimization of Fuzzy Reasoning by Using Genetic Algorithm with Variable Bit-Selection Probability in its Mutation Operator

Abstract

A problem on an optimization of fuzzy reasoning presents two aspects, a numerical optimization problem and an order optimization problem. The genetic algorithm (GA) is able to be applied to both these problems. In many research works, though the configuration of the fuzzy reasoning is optimized by using the GA, shapes of the membership functions are optimized by using another optimizing algorithm, such as a steepest descent method. In the background of this method, since a mutation operator of the GA always globally searches in a solution space, the GA optimizes slowly. In the case of applying the fuzzy reasoning to a field of control, the global optimum is not always required. There are many cases that some local optima give appropriate performance. To obtain such local optima, the authors have proposed a variable bit-selection probability (VBSP) in process of the mutation operator. The VBSP allows the GA to search around a good solution candidate. In this method the bit-selection probability (BSP) is partially defined for each bit position and varied according to the fitness value. However, this method requires designer's experiences and preliminary implementation in a phase of designing in some cases. To improve this difficulty, we propose to linearly vary the VBSP according to the number of the generations in this paper. By means of this new method, the GA with the VBSP becomes a general purpose algorithm that the designer's experiences and the preliminary implementation are not required.