Efficient Search Method Using Adaptive Discretization of Design Variables on Real-Coded Genetic Algorithms

Abstract

In this paper, we propose a new adaptive discretization method of design variables on real-coded genetic algorithms(RCGAs) for improving convergence performance while maintaining diversity.The convergence can be accelerated by setting the appropriate number of discrete classes in RCGAs. However, it is difficult to decide it in advance in most of the practical optimization problems.In addition, the diversity may be lost if the number of discrete classes is too small.In order to overcome these difficulties, we use a simple index which is based on the standard deviation to adaptively determine the number of discrete classes in each design variable.Since the proposed method merely rounds the value of the design variable after applying genetic operators such as crossover and mutation, it can be applied to various RCGAs.Here, we use NSGA-II as an RCGA and investigate the performance efficiency of convergence and diversity by using nineteen benchmark problems, including engineering problems.The convergence and diversity performance are evaluated using GD and IGD, respectively.The results of the numerical experiments show that the proposed method can obtain good convergence while maintaining diversity.