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In the field of engineering, complex problems often arise that require solutions. The implementation of specific algorithms to tackle these problems becomes an essential part of this area, and optimizing these algorithms plays a crucial role in achieving good results with the available resources. The Vehicle Routing Problem (VRP) has been a central topic in distribution and logistics for decades. New VRP models and tools are continuously developed to address the challenges of modern logistics. The Energy Minimizing Vehicle Routing Problem (EMVRP) is a VRP model where the objective is to minimize the total amount of energy consumed by a fleet of vehicles. The VRP literature has focused on solving the problem using a variety of approaches and techniques, including exact methods, heuristics, metaheuristics, and hybrid algorithms. Hybrid algorithms combine different techniques, such as heuristics and metaheuristics, to obtain more effective solutions. This work presents the implementation of four hybrid algorithms to tackle the EMVRP. These algorithms combine machine learning clustering techniques, such as K-Means and K-Medoids, with metaheuristic approaches inspired by ant colony systems. The proposed algorithms are: Free Ant + K-Means, Free Ant + K-Medoids, Restricted Ant + K-Means, and Restricted Ant + K-Medoids. The Free Ant and Restricted Ant algorithms were subjected to testing using different instances from CVRPLIB, and the obtained results are promising compared to other metaheuristic techniques described in the literature. However, these results also indicate a wide scope for experimentation and algorithm tuning.
Frías et al. (Sun,) studied this question.