Evaluation of Surrogate Assisted Differential Evolution Algorithm for Single-Objective Numerical Optimization

Hard optimization problems are solved successfully using nature inspired metaheuristics. However, in many cases of practical optimization problems, also called black-box problems, the evaluation of the objective function is main cause of high demand of computational resources. In the solution of these problems, objective function landscape is modeled mathematically, called a surrogate model which consist of replacing the objective function by an equivalent mathematical model, to reduce the computational evaluation time of the fitness function. The differential evolution (DE) algorithm is implemented with 4 strategies called rand/1, rand/2, best/2 and rand to best/1 to optimize the benchmark functions listed CEC2017 competition with dimensions D=10 and D=30. CEC2017 benchmark set is composed of 30 different functions with different degree of complexities. Locations of optimal solutions for these functions is supposed to be unknown and that’s why they are called black box functions. A surrogate model called the quadratic response surface model (QRSM) is used with Latin hyper square sampling strategy to replace objective function evaluations of benchmark functions. QRMS is used with DE for the solution of CEC2017 benchmark problems for the purpose of evaluating the performance of the surrogate assisted DE algorithm in terms of solution quality and runtime complexity. Experimental results obtained from the 4 different DE and DE+QRSM strategies illustrated that the rand/1 DE strategy was generally the best strategy in speed and accuracy for both dimensions D=10 and D=30. Also, the results generated by DE and DE+QRSM are compared with each other. As illustrated in tables of experimental evaluations, DE is found more accurate in majority of benchmark functions but it is slower generally. Also, a comparative study is done with other published algorithms such as L-SHADE, JSO, DISH, L-SHADE-LBR, JSO-LBR and DISH-LBR. Results obtained by these competitors are compared to only the best DE strategy, which is rand/1, employed within DE and DE+QRSM. The rand/1 strategy implemented within DE function was quit robust and performed better than other algorithms in many cases for D=10, but when implemented within DE+QRSM it becomes the worst one. For D=30 the rand/1 strategy loosed of its performance and was classified before the last position. Its rank is around of 80% when implemented within DE but it stays in last position with DE+QRSM algorithm.