Optimization of Multiple Vehicle Routing Problems using Approximation Algorithms

TL;DR

This paper presents a method combining k-means clustering and genetic algorithms to efficiently solve multi-vehicle routing problems by simplifying the problem and optimizing routes for each vehicle.

Contribution

It introduces a hybrid approach that converts mVRP into multiple VRPs using clustering and applies genetic algorithms for optimal routing, improving efficiency and solution quality.

Findings

Genetic algorithm outperforms other heuristics in route optimization.

Clustering simplifies mVRP into manageable subproblems.

Optimized routes reduce total travel distance.

Abstract

This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the various heuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorithms due to the extensive search and constructive nature of the algorithm.