Population-based algorithm for discrete facility location with ranking of candidate locations

Facility location problems are mathematical optimization problems that involve finding the best locations for facilities (e.g., factories, warehouses, stores) to serve customers within a given geographic area. The goal is typically to minimize costs, maximize efficiency, or optimize other objectives. Facility location problems can vary in several ways, including customer behavior rules, the type of search space, and constraints on locations for new facilities being located. These variations directly impact the complexity of the problem and the appropriate solution methods that can be used to tackle the problem. This research is focused on the discrete competitive facility location problem for an entering firm, which is a crucial scenario for new firms entering the existing market. The goal is to strategically locate new facilities to maximize their profit, while considering existing competitors. A new random search heuristic algorithm to approximate the optimal solution for discrete competitive facility location problems for firm expansion has been developed. The algorithm extends its precursor that ranks potential locations for the new facilities depending on their usefulness and uselessness in creating new solutions in the past. The new algorithm uses a population to handle and reuse the best solutions found so far and new strategies for ranking potential locations, considering features of the solutions in the population. The designed algorithm has been investigated by solving competitive facility location problems actual for an entering firms using real geographical data.