Hyper-Heuristic Approach for Tuning Parameter Adaptation in Differential Evolution

Abstract

Differential evolution (DE) is one of the most promising black-box numerical optimization methods. However, DE algorithms suffer from the problem of control parameter settings. Various adaptation methods have been proposed, with success history-based adaptation being the most popular. However, hand-crafted designs are known to suffer from human perception bias. In this study, our aim is to design automatically a parameter adaptation method for DE with the use of the hyper-heuristic approach. In particular, we consider the adaptation of scaling factor F, which is the most sensitive parameter of DE algorithms. In order to propose a flexible approach, a Taylor series expansion is used to represent the dependence between the success rate of the algorithm during its run and the scaling factor value. Moreover, two Taylor series are used for the mean of the random distribution for sampling F and its standard deviation. Unlike most studies, the Student’s t distribution is applied, and the number of degrees of freedom is also tuned. As a tuning method, another DE algorithm is used. The experiments performed on a recently proposed L-NTADE algorithm and two benchmark sets, CEC 2017 and CEC 2022, show that there is a relatively simple adaptation technique with the scaling factor changing between 0.4 and 0.6, which enables us to achieve high performance in most scenarios. It is shown that the automatically designed heuristic can be efficiently approximated by two simple equations, without a loss of efficiency.

Keywords

• numerical optimization
• differential evolution
• parameter adaptation
• hyper-heuristic