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

TL;DR

This study analyzes how the structure and numerical properties of instances influence the performance of local search metaheuristics on the facility location problem, revealing that algorithm choice depends on coefficient distributions.

Contribution

It provides an in-depth computational comparison of local search and randomized local search metaheuristics, highlighting the impact of instance properties on their effectiveness.

Findings

Metaheuristics' performance varies with instance coefficient distribution.

Local search outperforms randomized local search in certain instance types.

Optimal solutions are benchmarked using mixed-integer linear programming.

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.