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

arXiv: https://arxiv.org/abs/1911.08817 · HTML: https://mlsanity.com/paper/1911.08817/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [EXPObench: Benchmarking Surrogate-based Optimisation Algorithms on Expensive Black-box Functions](https://mlsanity.com/paper/2106.04618/) (2021)
- [Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization](https://mlsanity.com/paper/2206.01409/) (2022)
- [The First AI4TSP Competition: Learning to Solve Stochastic Routing Problems](https://mlsanity.com/paper/2201.10453/) (2022)
- [Performance Comparison of Surrogate-Assisted Evolutionary Algorithms on Computational Fluid Dynamics Problems](https://mlsanity.com/paper/2402.16455/) (2024)

## Abstract (arXiv)

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.