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.