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

David Chalupa,Peter Nielsen

doi:10.1016/j.ifacol.2019.11.535

Abstract

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.

Highlights

Many problems in science and engineering are widely regarded as computationally hard
We present a computational study of local search strategies for the classical uncapacitated facility location problem [2, 16]
As the facility location problem belongs to a class of classical assignment and cost optimisation problems, we find it reasonable that the results can be generalised to other popular real-world combinatorial optimisation problems

Summary

Introduction

Many problems in science and engineering are widely regarded as computationally hard. Within operations research, these involve a number of planning, Instance Scale, Numerical Properties and Design of Metaheuristics scheduling or production optimisation problems. These involve a number of planning, Instance Scale, Numerical Properties and Design of Metaheuristics scheduling or production optimisation problems Such problems include a variety of facility location [22] and supply chain optimisation problems [34], as well as shop scheduling problems [8], including job shop scheduling [4] and flow shop scheduling [33]. A variety of optimisation algorithms have been developed and experimentally verified over the last decades. This holds for real-world variants of these problems [11], and for a wider range of NP-hard optimisation problems such as knapsack [23], resource allocation [30] or the k-reachability problem [13]

Results

Discussion

Conclusion