Wave Function Collapse Set Covering and the Hill Climbing Algorithm: A New, Fast Heuristic and Metaheuristic Pairing for the Minimum Set Cover Problem

Abstract: In this paper, we present a new heuristic that focuses on the optimization problem for the Minimum Set Cover Problem. Our new heuristic involves using Wave Function Collapse and is called Wave Function Collapse Set Covering (WFC-SC). This algorithm goes through observation, propagation, and collapsing, which will be explained more later on in this paper. We optimize this algorithm to quickly find optimal coverings that are close to the minimum needed. To further optimize this algorithm, we pair it with the Hill Climbing metaheuristic to help WFC-SC find a better solution than its "local optimum." We benchmark our algorithm using the well known OR library from Brunel University against other proficient algorithms. We find that our algorithm has a better balance between both optimality and time.