Empirical evaluation of changing crossover operators to solve function optimization problems

Abstract

In this paper, the effectiveness of methodologies for changing crossover operators (CXOs) to solve function optimization problems (FOP) are empirically validated in order to solve the problems of premature convergence in genetic algorithms. CXOs are methods of finding solutions for combinatorial optimization problems through genetic algorithms (GAs) while maintaining the balance of satisfying the contrary requisites for GAs: to sustain the diversity of the population and to improve the efficiency of searching for solutions. CXOs measure the diversity of the population on each end of a generation and dynamically alternate global search methods and local search methods according to the degree of that diversity. With the above devices, CXOs can decrease the probability of falling into local optima compared to using only one kind of crossover operator in the crossover operation. In FOP, considering the continuity of functions, real-coded crossover operators such as BLX-α (Blend Crossover) and SPX (Simplex Crossover) are invented and added to general crossover operators such as Two-point Crossover operators. In our investigation, we studied CXOs that exchange Two-point crossover for BLX-α and SPX for BLX-α when the diversity of the generated children drops below the required threshold. We verified experimentally that CXOs can improve the accuracy of searched solutions beyond singly used crossover operators such as Two-point Crossover, BLX-α and SPX. Two well-known multimodal functions are also investigated in this report—Shubert's test function and the Six-hump camel back function.