Combining Lipschitz and RBF Surrogate Models for High-dimensional Computationally Expensive Problems

Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions.