Analyzing the Scalability Performance of Crossover-First and Self-Adaptive Differential Evolution Algorithms for Complex Numerical Optimization

Abstract

Two Crossover-first Differential Evolution (XDE) algorithms as well as four self-adaptive DE algorithms are compared in this study in terms of their optimization accuracy for solving a set of 15 complex, non-linear numerical optimization functions across 4 different dimensions of 10, 30, 50 and 100 optimization variables. XDE is a crossover-first variant of the original DE algorithm where XjDE is the crossover-first variant of the self-adaptive jDE algorithm. The original DE representing a fixed parameter strategy is tested against four self-adaptive algorithms, namely the DESACR, DESACRF, SDE and jDE algorithms. Although XDE is able to outperform XjDE in all 15 test problems for the lowest dimensional benchmark test setting of 10 variables, the crossover-first approach in XjDE is able to improve its performance and obtained better results over XDE in some of the test problems for the higher-dimensional benchmark test settings of 30, 50 and 100 variables. As such, this shows that there is some merit in adopting the crossover-first approach into the self-adaptive XjDE algorithm since the CR and F parameters are automatically adjusted and optimized by the algorithm itself as compared to the fixed CR and F in XDE which has to be manually tuned by hand. The results also show that different self-adaptive parameter tuning schemes have significantly different effects on the performance of DE as the number of optimization dimensions increases.