Efficient heuristics for the obnoxious planar p-median problem with variable sizes

The location of obnoxious facilities is an optimization problem with a large social impact. Specifically, the obnoxious facility location problem in the plane with variable sizes (OPPMVS) studies the location of facilities considering that the obnoxious effect is transmitted through the air and depends on the production or service of the facility. In this work, a memetic algorithm is proposed in which the generation of the initial population and the genetic operators have been specifically designed for the target problem. In this approximation of this continuous problem, competitive results have been obtained compared with the state-of-the-art. The proposal has been tested in 21 problem instances provided by the original authors, obtaining the best results in 14 of them with a total deviation of 0.07%. This performance is obtained in an average execution time of 22 s, which improves the best state-of-the-art algorithm by one order of magnitude. These results have been validated with statistical tests. Open access paper available at https://doi.org/10.1016/j.asoc.2025.113401