A Simulated Annealing method to solve a generalized maximal covering location problem

The maximal covering location problem (MCLP) seeks to locate a predefined number of facilities in order to maximize the number of covered demand points. In a classical sense, MCLP has three main implicit assumptions: all or nothing coverage, individual coverage, and fixed coverage radius. By relaxing these assumptions, three classes of modelling formulations are extended: the gradual cover models, the cooperative cover models, and the variable radius models. In this paper, we develop a special form of MCLP which combines the characteristics of gradual cover models, cooperative cover models, and variable radius models. The proposed problem has many applications such as locating cell phone towers. The model is formulated as a mixed integer non-linear programming (MINLP). In addition, a simulated annealing algorithm is used to solve the resulted problem and the performance of the proposed method is evaluated with a set of randomly generated problems.