Instance Scale, Numerical Properties and Design of Metaheuristics: A Study for the Facility Location Problem

Abstract

Metaheuristics are known to be strong in solving large-scale instances of computationally hard problems. However, their efficiency still needs exploration in the context of instance structure, scale and numerical properties for many of these problems. In this paper, we present an in-depth computational study of two local search metaheuristics for the classical uncapacitated facility location problem. We investigate four problem instance models, studied for the same problem size, for which the two metaheuristics exhibit intriguing and contrasting behaviours. The metaheuristics explored include a local search (LS) algorithm that chooses the best moves in the current neighbourhood, while a randomised local search (RLS) algorithm chooses the first move that does not lead to a worsening. The experimental results indicate that the right choice between these two algorithms depends heavily on the distribution of coefficients within the problem instance. This is also put further into context by finding optimal or near-optimal solutions using a mixed-integer linear programming problem solver. Since the facility location problem is a relatively simple example of a choice-and-assignment problem, similar phenomena are likely to be discovered in a number of other, possibly more complex computational problems in science and engineering.

A multi-objective optimization model for a multi-period mobile facility location problem with environmental and disruption considerations

“…The facility location problem is widely studied in many areas, as for example, remanufacturing (Mishra & Singh, 2020), telecommunication and hub location (Contreras & O'Kelly, 2019), robotics location (Moarref & Sayyaadi, 2008), ambulance location (El Itani et al, 2019a;El Itani et al, 2019b), humanitarian relief chain (Balcik & Beamon, 2008), food grain supply network (Sharma et al, 2021),…, using different techniques and tools, like exact methods (Christensen & Klose, 2020), metaheuristics (Chalupa & Nielsen, 2019), heuristics (Silva et al, 2020).…”

Two strategies of two-level facility network design for autonomous ground vehicle operations

“…Such applications include location problems in logistics systems for remanufacturing (Lu & Bostel, 2007), distribution system design (Klose & Drexl, 2005), aerial search optimisation (Kress & Royset, 2008), positioning of UAVs in mobile ad-hoc networks (Wang, Huo, & Alidaee, 2014) or k-level facility location games (Xu & Du, 2006). Sectors and areas of interest the agricultural sector (Zangeneh, Akram, Nielsen, & Keyhani, 2015), warehouse location (Michel & Van Hentenryck, 2004) or customer service centre location (Chalupa & Nielsen, 2018a).…”

A simple multi-wave algorithm for the uncapacitated facility location problem

“…Additional recent investigations of UFLP have been carried out by Albareda-Sambola et al (2017), Atta et al (2018), Galli et al (2018), Sahman et al (2017), Tsuya et al (2017). There also exist several recent studies of variants and extensions of UFLP, including Akbaripour et al (2017), Chalupa and Nielsen (2018), Han et al (2018), Jiang et al (2018), Pearce and Forbes (2018), Todosijević et al (2017), An and Svensson (2017). Also quite recently, Ortiz-Astorquiza et al (2017a, 2017b respectively provide formulations and approximation algorithms for Multilevel Uncapacitated Facility Location and a comprehensive review on multi-level facility location problems that extend several classical facility location problems.…”