Applying a Random-Key Optimizer on Mixed Integer Programs
2026-02-25 • Neural and Evolutionary Computing
Neural and Evolutionary Computing
AI summaryⓘ
The authors study a hard type of math problem called Mixed-Integer Programs (MIPs), which are used in many fields like finance and logistics but are tough to solve when they get very big or complicated. They use a method called Random-Key Optimizer (RKO) that turns the problem into a simpler continuous form and then carefully translates those solutions back into valid answers. They tested this approach on two different problems: one about picking investments and another about planning routes. Their results show that RKO often finds solutions that are as good as or better than those from a top commercial solver, and it does so faster in some cases.
Mixed-Integer ProgrammingNP-hardRandom-Key OptimizerMetaheuristicsDecodersMean-Variance Portfolio OptimizationCardinality ConstraintsTime-Dependent Traveling Salesman ProblemOptimization SolversFeasibility
Authors
Antonio A. Chaves, Mauricio G. C. Resende, Carise E. Schmidt, J. Kyle Brubaker, Helmut G. Katzgraber
Abstract
Mixed-Integer Programs (MIPs) are NP-hard optimization models that arise in a broad range of decision-making applications, including finance, logistics, energy systems, and network design. Although modern commercial solvers have achieved remarkable progress and perform effectively on many small- and medium-sized instances, their performance often degrades when confronted with large-cale or highly constrained formulations. This paper explores the use of the Random-Key Optimizer (RKO) framework as a flexible, metaheuristic alternative for computing high-quality solutions to MIPs through the design of problem-specific decoders. The proposed approach separates the search process from feasibility enforcement by operating in a continuous random-key space while mapping candidate solutions to feasible integer solutions via efficient decoding procedures. We evaluate the methodology on two representative and structurally distinct benchmark problems: the mean-variance Markowitz portfolio optimization problem with buy-in and cardinality constraints, and the Time-Dependent Traveling Salesman Problem. For each formulation, tailored decoders are developed to reduce the effective search space, promote feasibility, and accelerate convergence. Computational experiments demonstrate that RKO consistently produces competitive, and in several cases superior, solutions compared to a state-of-the-art commercial MIP solver, both in terms of solution quality and computational time. These results highlight the potential of RKO as a scalable and versatile heuristic framework for tackling challenging large-scale MIPs.