REMS: A Unified Solution Representation, Problem Modeling and Metaheuristic Algorithm Design for General Combinatorial Optimization Problems

Abstract

Combinatorial optimization problems (COPs) with discrete variables and finite search spaces are critical across various 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, it is valuable to leverage general problem domain knowledge to establish a framework that formulates diverse COPs into a unified paradigm and supports the design of broadly applicable metaheuristic algorithms. A COP can typically be viewed as the process of giving resources to perform specific tasks, subject to given constraints. Motivated by this, a resource-centered modeling and solving framework (REMS) is introduced. We first extract and define resources and tasks from a COP. Subsequently, given predetermined resources, the solution structure is unified by assigning tasks to resources, from which variables, objectives, and constraints can be derived, thereby constructing the problem model. To solve the COPs, several fundamental operators are designed from the resource-task perspective 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. Specifically, 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 by the algorithms in REMS without any specific design. Furthermore, REMS is more competitive than Gurobi optimizer (GUROBI) and solving constraint integer programs (SCIP) in tackling large-scale instances and complex COPs, and outperforms OR-TOOLS on several challenging COPs.