Surrogate assisted-hybrid differential evolution algorithm using diversity control

Evolutionary algorithms (EAs) being a major optimization framework, typically require a considerable number of function evaluations to locate an optimal solution for computationally intensive real-world optimization problems. In order to solve complex multimodal problems within a limited computational budget, surrogate models are integrated with EA. The overall performance of such algorithms not only depends on the construction and integration procedure of the model, but also on the efficiency of the underlying EA in overcoming premature convergence. This can be achieved through diversity control and parameter adaptation methodology in EAs. In this paper, an improved algorithm, namely Diversity Controlled Parameter adapted Differential Evolution with Local Search (DCPaDE-LS) is integrated into two dynamic surrogate models and two variants, namely Surrogate Assisted Parameter adapted Differential Evolution with Artificial Neural Networks and Response Surface Methodology (SAPDE-ANN and SAPDE-RSM) are proposed. They reduce the exact function evaluations for complex, multimodal problems. The performance of the proposed variants are compared on a set of 26 bound-constrained benchmark functions scalable with 10 and 30 dimensions, with respect to average number of function evaluations (NFE), success rate (SR) and % reduction in NFE in 30 independent trials. The SAPDE variants are compared with Self-adaptive Differential Evolution, DCPaDE-LS, Increasing Population Size Covariance Matrix Adaptation Evolution Strategy and Comprehensive Learning Particle Swarm Optimization. The SAPDE variants are able to reduce the NFE without loss in SR for all the functions. The algorithms are also validated using 12 solvable functions from CEC 2005. Of the two variants, SAPDE-ANN reports reduced NFE in more functions compared with SAPDE-RSM. Results reveal that the proposed SAPDE algorithm can be applied to real-world optimization problems.