Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraints
This addresses the challenge of mixed-variable optimization in fields like engineering and computer science, offering a novel method for a known bottleneck.
The paper tackles the problem of optimizing expensive black-box functions with mixed continuous and integer variables, such as in automatic algorithm configuration, by introducing MVRSM, a surrogate-based algorithm that ensures integer constraints are satisfied at local optima. It outperforms state-of-the-art methods on synthetic benchmarks with up to 238 variables and achieves competitive performance on real-world tasks like XGBoost hyperparameter tuning and Electrostatic Precipitator optimization.
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. 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: XGBoost hyperparameter tuning and Electrostatic Precipitator optimisation.