A novel differential evolution algorithm using local abstract convex underestimate strategy for global optimization

Two main challenges in differential evolution (DE) are reducing the number of function evaluations required to obtain optimal solutions and balancing the exploration and exploitation. In this paper, a local abstract convex underestimate strategy based on abstract convexity theory is proposed to address these two problems. First, the supporting hyperplanes are constructed for the neighboring individuals of the trial individual. Consequently, the underestimate value of the trial individual can be obtained by the supporting hyperplanes of its neighboring individuals. Through the guidance of the underestimate value in the select operation, the number of function evaluations can be reduced obviously. Second, some invalid regions of the domain where the global optimum cannot be found are safely excluded according to the underestimate information to improve reliability and exploration efficiency. Finally, the descent directions of supporting hyperplanes are employed for local enhancement to enhance exploitation capability. Accordingly, a novel DE algorithm using local abstract convex underestimate strategy (DELU) is proposed. Numerical experiments on 23 bound-constrained benchmark functions show that the proposed DELU is significantly better than, or at least comparable to several state-of-the art DE variants, non-DE algorithms, and surrogate-assisted evolutionary algorithms.