Facility Location Optimization via Multi-Agent Robotic Systems

A facility location problem deals with locating the best place for a group of facilities, among distinct demand points, minimizing a certain locational optimization function. In this paper, distributed, asynchronous, and scalable algorithms are presented for solving a facility location problem known as continuous n-median problem (generalized Fermat-Weber problem) via multi-agent robotic systems. The algorithms are discussed both in continuous and discrete time domain, and their validity is proved. It is also shown that the solution of this facility location problem is the set of points that are the geometric medians of their corresponding Voronoi cells.