Analysis of Swarm Intelligence Algorithms Used for Solving Vehicle Routing Problems

• Published in: Kìbernetika ta komp'ûternì tehnologìï (Online) no. 3; pp. 37 - 52
• Main Author: Yeher, Maksym
• Format: Journal Article
• Language: English
• Published: V.M. Glushkov Institute of Cybernetics 29.09.2025
• Subjects: logistics; metaheuristic methods; swarm intelligence; vehicle routing problem
• ISSN: 2707-4501; 2707-451X; 2707-451X
• DOI: 10.34229/2707-451X.25.3.3

Introduction. The Vehicle Routing Problem (VRP), first formulated by Danzig and Ramseur in 1959, has remained one of the most popular research subjects to date. This popularity stems from numerous factors, including its wide applicability across various economic sectors. VRP belongs to the class of NP-hard problems, implying high computational complexity in finding optimal solutions, especially for large-scale variations. Over the past 25 years, approaches to its classification and solution have evolved significantly, driven by real-world requirements and constraints, as well as advancements in optimization methods and computational power. This article analyzes research findings from studies focused on VRP, confirming a substantial shift in researchers' attention towards metaheuristic approaches. It examines application of the most popular swarm intelligence algorithms and their variations, including hybrids, for solving VRP, and what makes them successful. Furthermore, the study investigates the correlation between sets of algorithm parameters. The purpose of the paper is to investigate usage of swarm intelligence algorithms for solving the Vehicle Routing Problem. Paper attempts to determine what makes them effective for solving VRPs (if such) and how this is related to their parameter set. In addition, the study explores whether there is a correlation between the parameter sets of SI algorithms considered effective for VRPs. Results. An analysis of the results of research articles on VRP was conducted, which made it possible to identify the most popular variations of VRP and rank the methods for solving them. A comprehensive analysis of the most popular SI algorithms, including their variations and hybrids, for solving VRP was conducted. Their strengths and weaknesses were analyzed, and algorithmic features that make them effective in solving VRP were identified. A correlation analysis was conducted between the optimal parameter sets of algorithms and a strong dependence of the optimal parameter sets on the specific variation of VRP being solved was revealed. Conclusions. The analysis of the literature reveals that the Capacitated Vehicle Routing Problem (CVRP) remains the most prevalent VRP variant among researchers. Another popular variant is the Vehicle Routing Problem with Time Windows (VRPTW). Overall, there is an increasing trend in the popularity of VRP variants that incorporate real-world assumptions: Open VRP (OVRP), Dynamic VRP (DVRP), and Time-Dependent VRP (TDVRP). Often, real-life parameters such as cash transportation, small parcel delivery, waste collection, or social legislation regarding drivers' working hours, prompt researchers to develop narrow mathematical models. Unfortunately, these models are typically hard-wired to a specific problem, and some are even specifically adapted to particular test instances. The most popular methods studied in the literature are metaheuristic methods, classical heuristic methods, and exact methods. Various Swarm Intelligence (SI) algorithms were analyzed. Their shared properties of exploration, exploitation, and resistance to local optima make them well-suited for the complex combinatorial nature of VRP. However, the choice of algorithm and its parameters is strongly interrelated with the specific VRP variation, emphasizing the need for integrated approaches to their selection and tuning. Despite significant progress, challenges remain in effectively solving large-scale real-world VRPs. Keywords: Vehicle Routing Problem, swarm intelligence, metaheuristic methods, logistics.