Differential Evolution With Search Space Adaptation

Adaptive differential evolution (ADE) algorithms have demonstrated promising performance in solving complicated optimization problems. Parameter adaptation and strategy adaptation have been proposed to enhance the performance of DE to tackle different fitness landscapes at different evolutionary phases. However, at a certain phase, the adaptation methods tend to focus on adjusting parameters and strategies to better suit the current landscape, overlooking the fact that the regional characteristics of some complicated fitness landscapes may hinder the process of population optimization. To resolve this problem, this paper proposes a DE with search space adaptation (SSADE). In SSADE, an additional fitness landscape, referred to as the transformation fitness landscape, is introduced. Together with the original fitness landscape, they provide two alternative search spaces for the population. A suitable search space is derived based on performance-driven and progress-aware adaptations. In the performance-driven adaptation, a search space evaluation mechanism is proposed to measure the current performance of the original and transformation spaces through the successful feedback information, and a superior space reward mechanism is introduced to enable more individuals to search in the space with better performance. In the progress-aware adaptation, the search space is further adjusted based on the evolution progress. Simulation results demonstrate that SSA significantly improves the performance of both single-space search and hybrid-space search strategies. The superiority of SSADE is further validated through comprehensive comparisons with several state-of-the-art DE variants, evolutionary algorithms (EAs), and hybrid algorithms on benchmark problems with diverse characteristics. In particular, SSADE achieves statistically superior performance over most advanced DE variants, with especially pronounced advantages in 50- and 100-dimensional settings, where it outperforms on more than 70%–90% of the problems, highlighting its robustness and scalability.