A new self-adaptation scheme for differential evolution

The performance of Differential Evolution (DE) largely depends on the choice of trial vector generation strategy and the values of its control parameters. In the past years, quite a few DE variants have been developed to adaptively adjust the strategy and control parameters during the search process. However, these variants may not perform satisfactorily when coping with computationally expensive problems (CEPs) for which a satisfying solution needs to be obtained with very limited fitness evaluations (FEs). In this paper, we demonstrate that not only can surrogate models be used to approximate the fitness function, they can also provide a good alternative method to adapt the strategy and control parameters of DE, and thus propose a framework called DE with Surrogate-assisted Self-Adaptation (DESSA). DESSA generates multiple trial vectors using different trial vector generation strategies and parameter settings, and then employs a surrogate model to identify the potentially best trial vector to undergo real fitness evaluation. As each trial vector corresponds to a unique combination of strategy and parameter setting, the surrogate model acts like a strategy/parameter setting selector that aims to identify the most suitable strategy and parameter setting for each target vector. Since DESSA can be easily combined with different DE variants, three concrete DE variants, namely DESSA-CoDE, DESSA-SaDE, and DESSA-CoDE*, are proposed. Comprehensive empirical studies demonstrate that DESSA can lead to superior performance over the compared adaptive DE variants. More importantly, it is shown that DESSA has the potential of accommodating more search strategies, which may lead to novel DE variants with even more competitive performance.