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.

翻译：混合整数规划(MIPs)是NP难优化模型，广泛应用于金融、物流、能源系统及网络设计等决策场景。尽管现代商业求解器在中小规模实例上取得了显著进展并表现高效，但面对大规模或高度约束的模型时，其性能常出现退化。本文探索将随机密钥优化器(RKO)框架作为灵活元启发式替代方案，通过设计问题特定解码器来获取MIP的高质量解。该方法在连续随机密钥空间中运行，经由高效解码过程将候选解映射为可行整数解，从而将搜索过程与可行性约束分离。我们选取两个具有代表性且结构迥异的基准问题——含买入约束和基数约束的均值-方差Markowitz投资组合优化问题，以及时间依赖型旅行商问题——对该方法进行验证。针对每个模型，我们开发定制解码器以缩减有效搜索空间、促进可行性并加速收敛。计算实验表明，与先进商业MIP求解器相比，RKO在解质量和计算时间两方面均能持续产出具有竞争力的解，且在多个实例中表现更优。这些结果凸显了RKO作为可扩展且通用的启发式框架，在攻克大规模复杂MIP问题中的潜力。