Approximation Schemes for Capacity Vehicle Routing Problems: A Survey

• Published in: 2023 2nd International Conference on Computational Modelling, Simulation and Optimization (ICCMSO) pp. 277 - 282
• Main Author: Chen, Yongyu
• Format: Conference Proceeding
• Language: English
• Published: IEEE 23.06.2023
• Subjects: Approximation algorithms; capacity vehicle routing problems; combinatorial optimization; Computational modeling; Extraterrestrial measurements; polynomial-time approximation scheme; Space vehicles; Surveys; Time factors; Vehicle routing
• DOI: 10.1109/ICCMSO59960.2023.00059

The Capacity Vehicle Routing Problem (CVRP) pertains to the combinatorial optimization problem of identifying the optimal route for vehicles with a capacity constraint of k to travel from the depots to customers, which minimizes the total distance traveled. The Capacitated Vehicle Routing Problem (CVRP), which is essential to modelling logistics networks, has drawn a lot of interest in the field of combinatorial optimization. It has been established that the CVRP (Capacitated Vehicle Routing Problem) with a value of k greater than or equal to three exhibits computational complexity that is classified as NP-hard. Furthermore, it has been established that the problem is APXhard. It has been previously established that the solution is not approximatable in a metric space. Furthermore, this constitutes the principal challenge among the array of issues that confront Arora's approximation algorithm. The outstanding matter concerns the presence of a (1+\epsilon) PTAS (polynomial time approximation scheme) for the capacity vehicle routing problem in Euclidean space, regardless of the vehicle's capacity. The objective of this manuscript is to furnish a thorough and all-encompassing survey of the research progressions in the domain, encompassing the evolution of the field from its inception to the most recent cutting-edge discoveries.