Differential Evolution without the Scale Factor and the Crossover Probability

Differential evolution has made great achievements in various fields such as computational sciences, engineering optimization, and operations management in the past decades. It is well known that the control parameter setting plays a very important role in terms of the performance improvement of differential evolution. In this paper, a differential evolution without the scale factor and the crossover probability is presented, which eliminates almost all control parameters except for the population size. The proposed algorithm looks upon each individual as a charged particle to decide on the shift of the individual in the direction of the difference based on the attraction-repulsion mechanism in Coulomb's Law. Moreover, Taguchi's parameter design method with the two-level orthogonal array is merged into the crossover operation in order to obtain better individuals in the next generation by means of better combination of factor levels. What is more, a new ratio of the signal-to-noise is proposed for the purpose of fair comparison of the numerical experiment for the tested functions which have an optimal value with 0. Numerical experiments show that the proposed algorithm outperforms the other 5 compared algorithms for the 10 benchmark functions.

Automated summary

This paper proposes a differential evolution algorithm without the scale factor and crossover probability, reducing the number of control parameters. The algorithm treats each individual as a charged particle and applies the attraction-repulsion mechanism based on Coulomb's Law. Furthermore, Taguchi's parameter design method is integrated into the crossover operation for better combination of factor levels. Numerical experiments demonstrate the superiority of this proposed algorithm over 5 other compared algorithms for 10 benchmark functions.