Applying a Random-Key Optimizer on Mixed Integer Programs

2026-02-25

AI Summary

This work addresses the challenge that large-scale or highly constrained mixed-integer programming (MIP) problems are often intractable for existing commercial solvers. To overcome this limitation, the authors propose integrating the Random-Key Optimizer (RKO) framework into MIP solving. The approach conducts search in a continuous random-key space and employs a problem-specific decoder to map candidate solutions into feasible integer solutions, thereby decoupling the search process from feasibility enforcement. This separation substantially reduces the effective search space and enhances both solution feasibility and convergence speed. Experimental results on portfolio optimization and time-dependent traveling salesman problems demonstrate that RKO consistently outperforms leading commercial solvers in both solution quality and computational efficiency, exhibiting strong scalability and competitive performance.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Mixed-Integer Programs
• large-scale optimization
• NP-hard problems
• computational scalability
• highly constrained formulations

Innovation

• Random-Key Optimizer
• Mixed-Integer Programming
• Problem-specific Decoder
• Metaheuristic
• Feasibility Enforcement