Combinatorial optimization problems (COPs) with discrete variables and finite search space are critical across numerous fields, and solving them in metaheuristic algorithms is popular. However, addressing a specific COP typically requires developing a tailored and handcrafted algorithm. Even minor adjustments, such as constraint changes, may necessitate algorithm redevelopment. Therefore, establishing a framework for formulating diverse COPs into a unified paradigm and designing reusable metaheuristic algorithms is valuable. A COP can be typically viewed as the process of giving resources to perform specific tasks, subjecting to given constraints. Motivated by this, a resource-centered modeling and solving framework (REMS) is introduced for the first time. We first extract and define resources and tasks from a COP. Subsequently, given predetermined resources, the solution structure is unified as assigning tasks to resources, from which variables, objectives, and constraints can be derived and a problem model is constructed. To solve the modeled COPs, several fundamental operators are designed based on the unified solution structure, including the initial solution, neighborhood structure, destruction and repair, crossover, and ranking. These operators enable the development of various metaheuristic algorithms. Specially, 4 single-point-based algorithms and 1 population-based algorithm are configured herein. Experiments on 10 COPs, covering routing, location, loading, assignment, scheduling, and graph coloring problems, show that REMS can model these COPs within the unified paradigm and effectively solve them with the designed metaheuristic algorithms. Furthermore, REMS is more competitive than GUROBI and SCIP in tackling large-scale instances and complex COPs, and outperforms OR-TOOLS on several challenging COPs.

翻译：组合优化问题（COPs）具有离散变量和有限搜索空间，在众多领域中至关重要，采用元启发式算法求解此类问题已十分普遍。然而，解决一个特定的组合优化问题通常需要开发定制化的、手工设计的算法。即使是微小的调整（例如约束条件的改变），也可能需要重新设计算法。因此，建立一个能够将多样化的组合优化问题形式化为统一范式，并设计可复用的元启发式算法的框架具有重要价值。通常可以将一个组合优化问题视为在给定约束条件下，分配资源以执行特定任务的过程。受此启发，本文首次提出了一种以资源为中心的建模与求解框架（REMS）。我们首先从组合优化问题中提取并定义资源和任务。随后，在给定预设资源的前提下，将解结构统一为将任务分配给资源，并由此推导出变量、目标函数和约束条件，从而构建问题模型。为了求解建模后的组合优化问题，我们基于统一的解结构设计了若干基础算子，包括初始解生成、邻域结构、破坏与修复、交叉以及排序。这些算子使得开发多种元启发式算法成为可能。特别地，本文配置了4种基于单点的算法和1种基于种群的算法。在涵盖路径规划、设施选址、装载、分配、调度和图着色等10类组合优化问题上的实验表明，REMS能够将这些组合优化问题在统一范式下建模，并利用所设计的元启发式算法有效求解。此外，在处理大规模实例和复杂组合优化问题时，REMS比GUROBI和SCIP更具竞争力，并且在多个具有挑战性的组合优化问题上表现优于OR-TOOLS。