Black-box mixed-variable optimisation using a surrogate model that satisfies integer constraints

Laurens Bliek, Arthur Guijt, Sicco Verwer, Mathijs de Weerdt

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

11 Citations (Scopus)


A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for example in automatic algorithm configuration. Surrogate-based algorithms are very suitable for this type of problem, but most existing techniques are designed with only continuous or only discrete variables in mind. Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) is a surrogate-based algorithm that uses a linear combination of rectified linear units, defined in such a way that (local) optima satisfy the integer constraints. Unlike other methods, it also has a constant run-time per iteration. This method outperforms the state of the art on several synthetic benchmarks with up to 238 continuous and integer variables, and achieves competitive performance on two real-life benchmarks: XG-Boost hyperparameter tuning and Electrostatic Precipitator optimisation.

Original languageEnglish
Title of host publicationGECCO'21
Subtitle of host publicationProceedings of the 2021 Genetic and Evolutionary Computation Conference Companion
PublisherAssociation for Computing Machinery, Inc
Number of pages9
ISBN (Electronic)9781450383516
Publication statusPublished - 7 Jul 2021
Event2021 Genetic and Evolutionary Computation Conference, GECCO 2021 - Virtual/Online, Lille, France
Duration: 10 Jul 202114 Jul 2021


Conference2021 Genetic and Evolutionary Computation Conference, GECCO 2021
Abbreviated titleGECCO 2021
Internet address


  • Bayesian optimisation
  • expensive optimisation
  • mixed-variable optimisation
  • surrogate models


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