Competitive facility location problems arise in the context of two noncooperating companies, a leader and a follower, competing for market share from a given set of customers. We assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. For this bi-level optimization problem we consider six different customer behavior scenarios from the literature: binary, proportional and partially binary, each combined with essential and unessential demand. The decision making for the leader and the follower depends on these scenarios. In this work we present mixed integer linear programming models for the follower problem of each scenario and use them in combination with an evolutionary algorithm to optimize the location selection for the leader. A complete solution archive is used to detect already visited candidate solutions and convert them efficiently into similar, not yet considered ones. We present numerical results of our algorithm and compare them to so far state-of-the-art approaches from the literature. Our method shows good performance in all customer behavior scenarios and is able to outperform previous solution procedures on many occasions.

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