A Surrogate-Based Optimization Method with Dynamic Adaptation for High-Dimensional Mixed-Integer Problems

This study develops a Surrogate-based Optimization algorithm with Dynamic Adaptation of perturbation search of All Dimensions (SODA-AD) to address high-dimensional mixed-integer optimization problems with a black-box objective function (HMIO-B). SODA-AD improves dynamic coordinate search (DCS) in two ways, i.e., with a new way of sampling candidate points and a new adaptive scaling method, which help to balance global and local search and address high-dimensional problems. Additionally, two variants of SODA-AD are described. One is SODA-AD with a modified infill strategy (SODA-ADM), which uses the prediction scoring criterion to replace the weighted scoring criterion when the budgeted computation resources are going to run out. The second method first employs SODA-ADM and then carries out a sequential dimensioned perturbation search for each iteration periodically to continue the local search, and this is named SODA-ADM-DP. In numerical experiments, we compare SODA-AD and its two variants with other well-known counterparts using one complex real-world engineering problem and eight 100-dimensional (100-D) benchmark problems. It is concluded that SODA-AD and its two variants outperform the other counterparts on most of the test problems and are promising for solving high-dimensional mixed-integer optimization problems with black-box objective functions or nonlinear and nonconvex objective functions.