Applying a Random-Key Optimizer on Mixed Integer Programs

TL;DR

This paper introduces the Random-Key Optimizer (RKO), a metaheuristic framework that effectively solves large-scale mixed-integer programs by combining continuous search spaces with problem-specific decoders, outperforming traditional solvers in certain cases.

Contribution

The paper develops a novel RKO framework with tailored decoders for MIPs, demonstrating superior performance on benchmark problems compared to commercial solvers.

Findings

RKO produces high-quality solutions efficiently.

RKO outperforms commercial solvers on selected benchmarks.

Tailored decoders improve search efficiency and feasibility.

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.