Global and Preference-based Optimization with Mixed Variables using Piecewise Affine Surrogates

• URL: http://arxiv.org/abs/2302.04686v3
• Date: Fri, 04 Oct 2024 00:32:32 GMT
• Title: Global and Preference-based Optimization with Mixed Variables using Piecewise Affine Surrogates
• Authors: Mengjia Zhu, Alberto Bemporad,
• Abstract summary: This paper proposes a novel surrogate-based global optimization algorithm to solve linearly constrained mixed-variable problems. We assume the objective function is black-box and expensive-to-evaluate, while the linear constraints are quantifiable unrelaxable a priori known. We introduce two types of exploration functions to efficiently search the feasible domain via mixed-integer linear programming solvers.
• Score: 0.6083861980670925
• License:
• Abstract: Optimization problems involving mixed variables, i.e., variables of numerical and categorical nature, can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result of a complicated simulation or experiment, it may be expensive-to-evaluate. This paper proposes a novel surrogate-based global optimization algorithm to solve linearly constrained mixed-variable problems up to medium size (around 100 variables after encoding) based on constructing a piecewise affine surrogate of the objective function over feasible samples. We assume the objective function is black-box and expensive-to-evaluate, while the linear constraints are quantifiable unrelaxable a priori known and are cheap to evaluate. We introduce two types of exploration functions to efficiently search the feasible domain via mixed-integer linear programming solvers. We also provide a preference-based version of the algorithm, which can be used when only pairwise comparisons between samples can be acquired while the underlying objective function to minimize remains unquantified. The two algorithms are tested on mixed-variable benchmark problems with and without constraints. The results show that, within a small number of acquisitions, the proposed algorithms can often achieve better or comparable results than other existing methods.

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