Differential evolution with different crossover operators for solving unconstrained global optimization algorithms

Abstract

The Evolutionary Algorithms (EAs) are the part of bio-inspired algorithms used for solving a wide variety of real-world optimization problems. Differential Evolution (DE) is one of the algorithms in the pool of EA. DE is designed particularly for real-valued parameter optimization problems. The mutation and crossover operators of DE are designed in such a way that they are apt for real-valued parameters. The native crossover operators of DE are Binomial Crossover and Exponential Crossover. This paper proposes to test the suitability of other Crossover operators in the EA community to DE. The empirical study presented in this paper includes four crossover operators – DE’s native crossover (binomial crossover), simple arithmetic crossover, single arithmetic crossover, and uniform arithmetic crossover. The DE with these crossover operators is implemented to solve four standard benchmarking functions with different features. The empirical results are compared based on the accuracy and speed of the algorithm. The primary observations found were the arithmetic crossover was good at achieving good optimal results than the binomial crossover. However, the binomial crossover was faster in reaching a threshold set for the optimal value in the experiment.