A Novel Discrete Rat Swarm Optimization Algorithm for the Quadratic Assignment Problem

Abstract

The quadratic assignment problem (QAP) is an NP-hard problem with a wide range of applications in many real-world applications. This study introduces a discrete rat swarm optimizer (DRSO)algorithm for the first time as a solution to the QAP and demonstrates its effectiveness in terms of solution quality and computational efficiency. To address the combinatorial nature of the QAP, a mapping strategy is introduced to convert real values into discrete values, and mathematical operators are redefined to make then suitable for combinatorial problems. Additionally, a solution quality improvement strategy based on local search heuristics such as 2-opt and 3-opt is proposed. Simulations with test instances from the QAPLIB test library validate the effectiveness of the DRSO algorithm, and statistical analysis using the Wilcoxon parametric test confirms its performance. Comparative analysis with other algorithms demonstrates the superior performance of DRSO in terms of solution quality, convergence speed, and deviation from the best-known values, making it a promising approach for solving the QAP.

Metaheuristic Algorithms for the Optimization of Integrated Production Scheduling and Vehicle Routing Problems in Supply Chains

“…The concept of metaheuristic was first mentioned by the renowned scientist Fred Glover in 1986 [6]. These algorithms or methods are now recognized as some of the most practical approaches to solving many complex problems, which is particularly relevant for addressing various real-world combinatorial optimization problems [7,8]. Fig.…”

“…Simulated Annealing (SA) belongs to the category of metaheuristic algorithms and mimics the natural process based on the tempering of materials, a technique commonly used in the metal tempering process in metallurgy. The SA algorithm was first proposed by the renowned scientist Kirkpatrick and his collaborators back in 1983 [7,8]. The simulation of the material tempering process involves gradually decreasing the temperature until the initial optimization conditions are met, aiming to achieve an optimal solution based on the specified objective function [6,9].…”

“…To address real-world issues in VRP solutions, several constraints are typically introduced, such as a larger number of depots, different types of vehicles (homogeneous and heterogeneous), different types of customer demands (deterministic and stochastic), infrastructure constraints (one-way streets, restricted paths), types of services (transport, delivery, and mixed services), etc. [7,8].…”

A Discrete Hybrid Grey Wolf Optimizer Algorithm to solve QuadraticAssignment Problem

“…In recent years, various algorithms, including Rat Swarm Optimization [9], Iterative Local Search [55], and others [56], have been extensively investigated to address the QAP.…”

“…Finding even an approximation solution to QAP is challenging due to the quadratic form of its objective function and its combinatorial nature. QAP has received considerable attention from the researchers in last decade [2,3,4,5,6,7,8,9,10]. Several problems which are either variant of QAP or closely related to QAP are available in the literature, such as Quadratic Bottleneck Assignment Problem, Generalized Quadratic Assignment Problem, Biquadratic Assignment Problem, and Quadratic Semi-Assignment Problem [11].…”