Black-box combinatorial optimization using models with integer-valued minima

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 a 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.

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Acknowledgments

This work is part of the research programme Real-time data-driven maintenance logistics with project number 628.009.012, which is financed by the Dutch Research Council (NWO). The authors would also like to thank Arthur Guijt for helping with the python code.

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Correspondence to Laurens Bliek.

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Bliek, L., Verwer, S. & de Weerdt, M. Black-box combinatorial optimization using models with integer-valued minima. Ann Math Artif Intell (2020). https://doi.org/10.1007/s10472-020-09712-4

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Keywords

  • Surrogate models
  • Bayesian optimization
  • Black-box optimization