Bi-sided facility location problems: an efficient algorithm for <i>k</i>-centre, <i>k</i>-median, and travelling salesman problems

This study introduces a general framework, called Bi-sided facility location, for wide range of problems in the area combined location and routing such as locating test centres designing network supermarkets. It is based on multi-objective optimisation model to enhance service quality which clients received, client-side, interconnection eligibility among centres, center-side. Well-known k-median k-centre client-side travelling salesman problem centre-side are taken into account this paper. After discussing complexity kind combination, we propose heuristic approximation algorithm find Pareto-optimal solutions problem. The an efficient local search utilising geometric objects Voronoi diagram Delaunay triangulation well algorithms computing tour. In addition comprehensive theoretical analysis proposed models algorithm, apply different instances benchmarks, compare it with NSGA-II set coverage spacing metrics. results confirm efficiency terms running time providing diverse trade-off solutions.Highlights Introducing bi-side considering clients’ utilitiesDiscussing proving NP-hardness frameworkConsidering two instances; TSP centre-sideProposing geometric-based solving problemsImplementing, testing, comparing several benchmarks