MaxSumMin Model and Incremental Optimization for the Obnoxious Facility Location Problem

Public facilities are crucial to humans. However, some facilities are antagonistic to the public or environment. In many cases, these so-called obnoxious facilities had better be located far from each other and communities. Obnoxious facility location problems have been less frequently investigated, particularly those for the interactions between such facilities and their clients. Moreover, the current models that are used to address this problem involve numerous 0–1 variables, rendering them difficult to solve. This study demonstrated that most 0–1 variables can be eliminated from the model to enhance model efficiency. Additionally, the equivalence between the new and original models was proved. However, although the experimental results confirmed the efficiency of the proposed model, large problems still require a considerable computation time. A genetic algorithm and an incremental optimization algorithm are thus presented to further improve efficiency