A hybrid differential evolution for non-smooth optimization problems

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, differ-ential evolution algorithm (DE) proved itself as good method of global optimization. On the other side, approach based on subgradient methods (SG) are good for optimiz-ing 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 (SSGDE) based on differential evo-lution and subgradient algorithm as the local search procedure is proposed. Behavior of the proposed SSGDE algorithm were 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. The proposed algorithm makes it possi-ble to obtain an improvement in the average best value of the achieved global minimum by three orders of magnitude compared to DE for the non-differentiable test function characterized by high dimensionality, a large number of local extrema, and a significant ravine. Thus, 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.