## 3 Materials and Methods
### Proposed Adaptive Large Neighborhood Search
#### 3.2.1 Initial Solution
It was found that metaheuristic algorithms are frequently used in EVRP studies (58.5%), and the ALNS algorithm is used in more than 30%. The ALNS algorithm was found to be overused for the problem, and a hybrid ALNS algorithm was developed. New purpose-specific operator designs for the minimum total tardiness objective function were designed and contributed to the literature. Figure 8: Number of tardy deliveries in problems with 40 (**a**) and 60 (**b**) customers according to the number of vehicles. Figure 9: Trade-off between fleet size and total tardiness (in seconds) for 60-customer instances. The functionality of ALNS is extended with the LS-based VNS algorithm. In order to prove the effectiveness of the proposed ALNS for the minimum total tardiness objective function, the problems were first solved with CPLEX, and the results were compared. With the proposed ALNS, large-size problems can be solved in a reasonable time, such as 70-80 s. The results of two scenarios, customer-satisfaction-oriented and cost-oriented solutions, were compared. The relationship between meeting the customer time windows and the number of vehicles was analyzed, and trade-offs were presented to guide decision-makers. In future studies, charging costs will be taken into account by taking into account issues such as the condition of the charging station and waiting time for charging. The impact of using different charging strategies on cost and customer satisfaction will be analyzed. In this context, showing trade-offs will contribute to the literature and decision-makers. Conceptualization: Y.U., I.S. and S.B.K. ; methodology: Y.U., I.S. and S.B.K. ; writing--original draft: Y.U., I.S. and S.B.K. ; writing--review and editing: Y.U., I.S., S.B.K. and A.Y. ; funding acquisition: A.Y. All authors have read and agreed to the published version of the manuscript. This study is supported by the OPEVA project, which has received funding within the Chips Joint Undertaking (Chips JU) from the European Union's Horizon Europe Programme and the National Authorities (France, Belgium, Czechia, Italy, Portugal, Turkey, Switzerland), under grant agreement 101097267. The views and opinions expressed are, however, those of the author(s) only, and do not necessarily reflect those of the European Union or the Chips JU. Neither the European Union nor the granting authority can be held responsible for them. This work is supported by the Scientific and Technical Research Council of Turkey (TUBITAK), Contract No. 222N269, project title: \"OPtimization of Electric Vehicle Autonomy (OPEVA)\". Not applicable. The dataset used in this study is publicly available on Mendeley Data at the following link: [[https://data.mendeley.com/datasets/Yvjzvxh72d/1](https://data.mendeley.com/datasets/Yvjzvxh72d/1)]([https://data.mendeley.com/datasets/Yvjzvxh72d/1](https://data.mendeley.com/datasets/Yvjzvxh72d/1)). Details regarding the dataset and its structure are also presented in the following publication: [[https://doi.org/10.3390/app15031068](https://doi.org/10.3390/app15031068)]([https://doi.org/10.3390/app15031068](https://doi.org/10.3390/app15031068)), accessed on 12 April 2025. The authors declare no conflicts of interest. ## References

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