A new local search for continuous location problems

Abstract

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulation $

Incorporating neighborhood reduction for the solution of the planar p-median problem

“…The best results to date were obtained by [14]. For recent reviews of solution approaches to the continuous p-median problem the reader is referred to [4,6,13,14].…”

Solving the planar p-median problem by variable neighborhood and concentric searches

“…In this paper we employed the DSR heuristic ) which is based on the Reformulation Local Search proposed in Brimberg et al (2014), and the Delaunay triangulation proposed in Lee and Schachter (1980).…”

“…The second one (n = 287) is the ambulance problem from Bongartz et al (1994); the last two (n = 654 and 1060) are from the TSP library (Reinelt (1991)). The best known solutions are taken from Brimberg et al (2000); Taillard (2003); Brimberg et al (2014). These solutions were proven optimal by Krau (1997) for the n = 50 and 287 instances investigated.…”

“…The details of DSR are given in Drezner et al (2013). For recent reviews of solution approaches to the continuous p-median problem the reader is referred to Brimberg et al (2000Brimberg et al ( , 2008Brimberg et al ( , 2014; Drezner et al (2013).…”

“…One of the approaches is IALT which is a modification of Cooper's alternate algorithm (Cooper (1963(Cooper ( , 1964). Brimberg et al (2014) developed the reformulation local search (RLS) which is a new local search that iterates between the continuous problem and a discrete approximation. This is achieved by artificially adding the new found Weber points as potential sites when solving the discrete version of the p-median problem.…”