在混合整数规划中应用随机键优化器
Applying a Random-Key Optimizer on Mixed Integer Programs
AI总结：
本文提出利用随机键优化器框架解决混合整数规划问题，通过设计问题特定解码器，提升大规模和高约束问题的求解效率与质量。
摘要：
混合整数规划（MIP）是NP难优化模型，广泛应用于金融、物流、能源系统和网络设计等领域。尽管现代商业求解器在小规模和中等规模实例上表现优异，但面对大规模或高约束问题时性能往往下降。本文探讨了将随机键优化器（RKO）框架作为灵活的元启发式替代方法，通过设计问题特定的解码器来计算高质量的MIP解。所提出的方法通过在连续随机键空间中操作，将候选解映射到可行的整数解，通过高效的解码过程实现。我们评估了两种代表性且结构不同的基准问题：具有买入和数量约束的均值-方差马科维茨投资组合优化问题，以及时间依赖的旅行商问题。针对每个问题，开发了定制化的解码器以减少有效搜索空间、促进可行性并加速收敛。计算实验表明，RKO在解的质量和计算时间方面均能与最先进的商业MIP求解器竞争，甚至在某些情况下更优。这些结果突显了RKO作为解决具有挑战性的大规模MIP问题的可扩展且多功能的启发式框架的潜力。
英文摘要：
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.
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