Abstract

An instance of a combinatorial optimization problem (COP) is the “Capacitated Vehicle Routing Problem (CVRP)”. When the CVRP is big, locating a top-quality answer is very tough. An extensive variety of real-life scenarios, consisting of garbage series, avenue cleansing, and bus schedules may be modelled as CVRP, with the model's objective being to pinpoint a series of a fleet's routes of motors that need to provide service to customers from a centralized depot. It is believed that automobiles have identical capabilities and that the departure and return points of each automobile are equal. Since every consumer has a consistent demand, the vehicle's capacity cannot be exceeded. More specifically, CVRP seeks to reduce the overall expense necessary to serve a certain group of clients. To this goal. To address CVRP, two main approaches exact and approximate "heuristic and metaheuristic" algorithms have been presented. The precise algorithms are focused on providing a worldwide optimal solution for CVRP of small size within a suitable period, whereas the approximation algorithms are focused on identifying the near-optimal or optimal solution for large-scale CVRP. This study aims at (i) conducting a thorough analysis of the approaches that have been used to solve the CVRP model, (ii) investigating the ACO family of algorithms, and (iii) identifying the best algorithm that can improve CVRP model solutions depending on how accurate the algorithm is, in an acceptable length of time. Our findings indicate that ACO-based approaches, particularly the Ant Colony System (ACS), offer significant improvements in solving large-scale CVRP instances efficiently. Specifically, the ACS algorithm evaluated the high-quality performance of computational efficiency and solution quality, making it a promising approach for realistic packages.