Kriging-assisted Discrete Global Optimization (KDGO) for black-box problems with costly objective and constraints

In this paper, a Kriging-assisted discrete global optimization method is presented for computationally expensive black-box problems. KDGO employs Kriging to approximate the landscape of a black-box model, and utilizes a novel infilling strategy to capture the promising discrete samples. In the infilling strategy, a multi-start knowledge mining approach is introduced, including Optimization, Projection, Sampling and Selection. Firstly, a multi-start optimization is used to capture the promising solutions in the continuous design range. Secondly, all these potential solutions are projected to a predefined matrix and a grid sampling method suitable for low and high-dimensional space is proposed to get the promising discrete samples. Thereafter, the k-nearest neighbors (KNN) search strategy and expected improvement (EI) criterion are jointly used to select the candidate samples. The algorithm keeps running to update Kriging and find the most promising samples until the satisfactory solution is obtained. KDGO is primarily developed to solve time-consuming black-box problems with various discrete cases including binary, integer, non-integer, uni/multimodal and box/inequality-constrained types. After the comparison tests on 20 representative benchmark cases, KDGO proves that it can build a reasonable balance between exploitation and exploration. Besides, compared with the existing 6 methods, KDGO has significant advantages on computational efficiency and robustness. Finally, KDGO is used for structure optimization of a blended-wing-body underwater glider, and gets the satisfactory design.