Performance Analysis of Meta-heuristic Algorithms for a Quadratic Assignment Problem

TL;DR

This paper compares various meta-heuristic algorithms, including local and global search strategies, for solving the NP-hard quadratic assignment problem, providing insights into their performance and convergence.

Contribution

It offers a comparative analysis of multiple meta-heuristics and introduces a new method to measure strong convergence conditions for these algorithms.

Findings

PSO, GWO, and 2-Opt outperform others in certain scenarios

Hybrid GA-PSO shows improved solution quality

Convergence conditions vary significantly among algorithms

Abstract

A quadratic assignment problem (QAP) is a combinatorial optimization problem that belongs to the class of NP-hard ones. So, it is difficult to solve in the polynomial time even for small instances. Research on the QAP has thus focused on obtaining a method to overcome this problem. Heuristics and meta-heuristics algorithm are prevalent solution methods for this problem. This paper is one of comparative studies to apply different metaheuristic algorithms for solving the QAP. One of the most popular approaches for categorizing meta-heuristic algorithms is based on a search strategy, including (1) local search improvement meta-heuristics and (2) global search-based meta-heuristics. The matter that distinguishes this paper from the other is the comparative performance of local and global search (both EA and SI), in which meta-heuristics that consist of genetic algorithm (GA), particle swarm optimization (PSO), hybrid GA-PSO, grey wolf optimization (GWO), harmony search algorithm (HAS) and simulated annealing (SA). Also, one improvement heuristic algorithm (ie, 2-Opt) is used to compare with others. The PSO, GWO and 2-Opt algorithms are improved to achieve the better comparison toward the other algorithms for evaluation. In order to analysis the comparative advantage of these algorithms, eight different factors are presented. By taking into account all these factors, the test is implemented in six test problems of the QAP Library (QAPLIB) from different sizes. Another contribution of this paper is to measure a strong convergence condition for each algorithm in a new way.