ILP-BO: Integer Linear Programming-Based Black-Box Optimization

2026-09-27

AI Summary

This study addresses the inability of traditional black-box optimization to guarantee global optimality of candidate solutions by proposing an Integer Linear Programming (ILP)-based black-box optimization framework. The proposed method reformulates discrete-domain kernel surrogate models as ILP problems, innovatively introducing binary auxiliary variables to exactly represent nonlinear kernel functions for objective linearization. Furthermore, it incorporates a Hamming distance margin mechanism to balance exploration and exploitation. Experimental results on synthetic and discrete benchmark problems demonstrate that this approach achieves performance comparable to mainstream Bayesian optimization algorithms while delivering transparent discrete optimization with provable global optimality certificates.

Abstract

Black-box Optimization (BO) is a powerful framework for optimizing expensive objective functions or unknown functions with a limited number of evaluations. A central step of standard BO such as Bayesian optimization is the optimization of a surrogate-based acquisition criterion, which is commonly performed using nonlinear optimization or heuristic search. Therefore, conventional black-box optimization generally does not guarantee global optimality in candidate selection. In this study, we propose Integer Linear Programming-based Black-box Optimization (ILP-BO), a quasi-Bayesian optimization framework that transforms kernel-based surrogate optimization over discrete domains into an Integer Linear Programming (ILP) problem. The key idea is to represent nonlinear kernel functions exactly on finite discrete distance levels by introducing binary one-hot auxiliary variables. This transformation converts the nonlinear surrogate into a linear objective with linear constraints and binary variables. To incorporate exploration while preserving the linear structure, we further introduce a Hamming-distance margin that excludes neighborhoods around previously observed points. We derive the proposed formulation for several standard kernels and obtain an analytical upper bound on the Hamming-distance threshold based on the measure in the binary search space. The resulting candidate-selection problem can be solved by integer programming solvers with certificates of optimality. Thus, our methodology has the potential to serve as a highly transparent black-box optimization framework. Experiments on synthetic and discrete optimization benchmarks show that ILP-BO achieves competitive optimization performance compared with practical Bayesian optimization methods.

Problem

• Black-box Optimization
• Bayesian Optimization
• Global Optimality
• Candidate Selection
• Surrogate Optimization

Innovation

• Black-box Optimization
• Integer Linear Programming
• Bayesian Optimization
• Surrogate Model
• Hamming Distance