An Evolutionary Algorithm for Expensive Mixed-Integer Black-Box Optimization with Explicit Constraints

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Determining the feasibility of a candidate solution to a constrained black-box optimization problem may be similarly expensive compared to the process of determining its quality, or it may be much cheaper. Constraints that allow obtaining degrees of feasibility or constraint violation without incurring significant computational costs are referred to as explicit. We present an evolutionary algorithm for solving mixed-integer black-box optimization problems where objective function evaluations are expensive but constraints are explicit. We do not assume relaxability of the constraints. The method wraps active-set evolution strategies, an algorithm for solving continuous black-box problems with explicit constraints, in a branching mechanism that allows enforcing integrality constraints. In computer experiments we demonstrate that the algorithm solves a set of mixed-integer problems with significantly fewer objective function evaluations than several algorithms that do not exploit the explicitness of the constraints.