Black-box Combinatorial Optimization using Models with Integer-valued Minima

TL;DR

This paper introduces a surrogate modeling approach for black-box combinatorial optimization that guarantees integer-valued minima, improving performance on complex and noisy problems compared to traditional methods.

Contribution

The authors propose a novel surrogate model with basis functions designed to ensure integer-valued solutions, advancing black-box combinatorial optimization techniques.

Findings

Outperforms random search, simulated annealing, and a Bayesian optimization algorithm on a noisy TSP benchmark.

Achieves similar performance to another Bayesian optimization method.

Outperforms all compared algorithms on a large-scale convex binary problem.

Abstract

When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and one Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.