Multi-surrogate-based Differential Evolution with multi-start exploration (MDEME) for computationally expensive optimization

In this paper, we present a new global optimization algorithm MDEME for black-box problems with computationally expensive objectives. Considering that Differential Evolution (DE) is an efficient global optimization algorithm but has difficulty in expensive optimization problems, we combine DE with three surrogate models Kriging, Radial Basis Function (RBF), and Quadratic Polynomial Response (QRS) to realize surrogate-based optimization. Although the three surrogates have different approximate effects that may generate diverse updating points, the surrogate-based DE may still get stuck in local optimal regions. In order to enhance its exploration capability, a multi-start optimization algorithm with a new selecting strategy is proposed. The multi-start optimization algorithm can capture and select several promising points from Kriging and RBF that always generate multiple local optimal solutions per optimization cycle. In the whole optimization process, DE and the proposed multi-start optimization are alternately carried out on the three surrogate models that are dynamically updated. Once no more satisfactory points can be obtained from Kriging and RBF, the multi-start optimization will explore the sparsely sampled area using the estimated mean square error of Kriging. After the comparison with 5 global optimization algorithms on 17 representative cases, MDEME shows its high efficiency, strong stability and good parallelism capability in dealing with expensive optimization problems. Finally, MDEME is used for the shape optimization of a blended-wing-body underwater glider, and the design performance gets significantly improved.