An Evolutionary Algorithm for the Leader-Follower Facility Location Problem with Proportional Customer Behavior

The leader-follower facility location problem arises in the context of two non-cooperating companies, a leader and a follower, competing for market share from a given set of customers. In our work we assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. The customers are assumed to split their demand inversely proportional to their distance to all opened facilities. In this work we present an evolutionary algorithm with an embedded tabu search to optimize the location selection for the leader. A complete solution archive is used to detect already visited candidate solutions and convert them into not yet considered ones. This avoids unnecessary timeconsuming re-evaluations, reduces premature convergence and increases the population diversity at the same time. Results show significant advantages of our approach over an existing algorithm from the literature.