An improved differential evolution algorithm using efficient adapted surrogate model for numerical optimization

Abstract

Contemporary real-world optimization benchmarks are subject to many constraints and are often high-dimensional problems. Typically, such problems are expensive in terms of computational time and cost. Conventional constraint-based solvers that are used to tackle such problems require a considerable high budget of function evaluations. Such budget is not affordable in practice. In most cases, this number is considered the termination criterion in which the optimization process is stopped and then the best solution is marked. The algorithm might not converge even after consuming the pre-defined number of function evaluations, and hence it does not guarantee an optimal solution is found. Motivated by this consideration, this paper introduces an effective surrogate model to assist the differential evolution algorithm to generate competitive solutions during the search process. The proposed surrogate model uses a new adaptation scheme to adapt the theta parameter in the well-known Kriging model. This variable determines the correlation between the parameters of the optimization problem being solved. For that reason, an accurate surrogate model is crucial to have a noticeable enhancement during the search. The statistical information exploited from a covariance matrix is used to build the correlation matrix to adapt the theta variable instead of using a fixed value during the search. Hence, the surrogate model evolves over the generations to better model the basin of the search, as the population evolves. The model is implemented in the popular L-SHADE algorithm. Two benchmark sets: bound-constrained problems and real-world optimization problems are used to validate the performance of the proposed algorithm, namely iDEaSm. Also, two engineering design problems are solved: welded beam and pressure vessel. The performance of the proposed work is compared with other state-of-the-art algorithms and the simulation results indicate that the new technique can improve the performance to generate better statistical significance solutions.