A Hybrid Differential Evolution for Non-Smooth Optimization Problems

Abstract

Solving high dimentional, multimodal, non-smooth global optimization problems faces challenges concerning quality of solution, computational costs or even the impossibility of solving the problem. Evolutionary algorithms, in particular, differential evolution algorithm proved itself as good method of global optimization. On the other side, approach based on subgradient methods are good for optimizing non-smooth functions. Combination of these two approaches enables to improve the quality of the algorithm, using the best features of both methods. In this paper, a new hybrid evolutionary approach based on differential evolution and subgradient algorithm as the local search procedure is proposed. Behavior of the proposed SSGDE algorithm was studied in a numerical experiment on three groups of generated tests. Comparison of the new hybrid algorithm with the pure DE approach showed the advantage of the SSGDE. It has been experimentally established that the proposed method finds the global minimum in the best way for all considered dimensions of the problem with respect to the differential evolution method. The SSGDE algorithm showed the best results with a significant increase in the number of functions.