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（MIP）是一类NP难优化模型，广泛出现于金融、物流、能源系统和网络设计等决策应用领域。尽管现代商业求解器已取得显著进展，在中小规模算例上表现优异，但在处理大规模或强约束模型时，其性能往往下降。本文探讨如何利用随机密钥优化器（RKO）框架，通过设计问题特定的解码器，为MIP提供一种灵活的元启发式替代方案以计算高质量解。所提方法通过连续随机密钥空间进行搜索，同时借助高效解码程序将候选解映射为可行整数解，从而将搜索过程与可行性强制分离。我们在两个结构各异的代表性基准问题上评估该方法：带有投资门槛与基数约束的均值-方差马科维茨投资组合优化问题，以及时间依赖旅行商问题。针对每种模型，我们开发了定制解码器以缩减有效搜索空间、提升可行性并加速收敛。计算实验表明，与先进的商业MIP求解器相比，RKO在解质量和计算时间方面均能持续获得具有竞争力的解，并在多个案例中取得更优结果。这些发现凸显了RKO作为可扩展、通用启发式框架处理大规模复杂MIP问题的潜力。