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

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