Using automatic programming to design improved variants of differential evolution

Abstract

To automatically design improvements of stochastic numerical optimization algorithms is challenging due to the high computation time required to ensure sufficiently rigorous evaluation of synthesized programs. In this paper, we develop evaluation methodology that is used with the evolutionary automatic programming system ADATE to enhance two variants of the differential evolution algorithm, namely, the original algorithm and the competitive differential evolution algorithm. When improving the original differential evolution algorithm, we find an improved mutation operator that is optimized to few function evaluations, while for the competitive differential evolution algorithm we find an improved pool of mutation strategies that outperforms the original for over 63% of the 30-dimensional CEC 2014 problems, while being worse for less than 10% of the problems, when comparing using a Wilcoxon rank-sum test. The successful improvement of both algorithms shows that the methodology we developed in this paper provides sufficient guidance for ADATE to navigate the stochastic search space when improving stochastic numerical optimization algorithms.