A multi-objective genetic algorithm for a bi-objective facility location problem with partial coverage.

*(English)*Zbl 1338.90373Summary: In this study, we present a bi-objective facility location model that considers both partial coverage and service to uncovered demands. Due to limited number of facilities to be opened, some of the demand nodes may not be within full or partial coverage distance of a facility. However, a demand node that is not within the coverage distance of a facility should get service from the nearest facility within the shortest possible time. In this model, it is assumed that demand nodes within the predefined distance of opened facilities are fully covered, and after that distance the coverage level decreases linearly. The objectives are defined as the maximization of full and partial coverage, and the minimization of the maximum distance between uncovered demand nodes and their nearest facilities. We develop a new multi-objective genetic algorithm (MOGA) called modified SPEA-II (mSPEA-II). In this method, the fitness function of SPEA-II is modified and the crowding distance of NSGA-II is used. The performance of mSPEA-II is tested on randomly generated problems of different sizes. The results are compared with the solutions of the most well-known MOGAs, NSGA-II and SPEA-II. Computational experiments show that mSPEA-II outperforms both NSGA-II and SPEA-II.

##### MSC:

90C29 | Multi-objective and goal programming |

90B80 | Discrete location and assignment |

90C59 | Approximation methods and heuristics in mathematical programming |

##### Keywords:

multi-objective genetic algorithm; facility location; maximal coverage; partial coverage; P-center
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\textit{E. Karasakal} and \textit{A. Silav}, Top 24, No. 1, 206--232 (2016; Zbl 1338.90373)

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