Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

Abstract

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

Keywords

• SCP
• Heuristics
• Metaheuristics
• Local Search
• VNS
• GRASP