Optimization of multi-objective mixed-integer problems with a model-based evolutionary algorithm in a black-box setting

Mixed-integer optimization, which focuses on problems where discrete and continuous variables exist simultaneously, is a well-known and challenging area for search algorithms. Mixed-integer optimization problems are especially difficult in a black-box setting where no structural problem information is available a-prior. In this paper we bring the strengths of the recently-proposed Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT) to the multi-objective (MO) domain, and determine whether the promising performance of GAMBIT is maintained. We introduce various mechanisms designed specifically for MO optimization resulting in MO-GAMBIT. We compare performance - in terms of the number of evaluations used - and runtime with alternative techniques, particularly linear scalarization and a selection of alternative MO algorithms. To this end, we introduce a set of objective functions which vary in composition in terms of discrete and continuous variables, as well as in the strength of dependencies between variables. Our results show that MO-GAMBIT can substantially outperform the alternative MO algorithms, thereby providing a promising new approach for multi-objective mixed-integer optimization in a black-box setting.