In the industrial sector, transportation plays an essential role in distribution. This activity impacts climate change and global warming. One of the critical problems in distribution is the green vehicle routing problem (G-VRP). This study focuses on G-VRP for a single distribution center. The objective function is to minimize the distribution costs by considering fuel costs, carbon costs, and vehicle use costs. This research aims to develop the hybrid butterfly optimization algorithm (HBOA) to minimize the distribution costs on G-VRP. It was inspired by the butterfly optimization algorithm (BOA), which was by combining the tabu search (TS) algorithm and local search swap and flip strategies. BOA is a new metaheuristic algorithm that has been successfully applied in various engineering fields. Experiments were carried out to test the parameters of the proposed algorithm and vary the speed of vehicles. The proposed algorithm was also compared with several procedures of prior study. The experimental results proved that the HBOA could minimize the total distribution cost compared to other algorithms. Moreover, the computation time is also included in the analysis.

中文翻译：

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绿色车辆路径问题的新型混合蝴蝶优化算法

在工业部门中，运输在分销中起着至关重要的作用。这项活动影响气候变化和全球变暖。配送中的关键问题之一是绿色车辆路径问题（G-VRP）。这项研究的重点是单个配送中心的G-VRP。目标功能是通过考虑燃料成本，碳成本和车辆使用成本来最小化分销成本。这项研究旨在开发混合蝴蝶优化算法（HBOA），以最大程度地减少G-VRP的分销成本。它受蝶优化算法（BOA）的启发，该算法是将禁忌搜索（TS）算法与本地搜索交换和翻转策略结合在一起的。BOA是一种新的元启发式算法，已成功应用于各种工程领域。进行了实验以测试所提出算法的参数并改变车辆的速度。还将所提出的算法与先前研究的几种程序进行了比较。实验结果证明，与其他算法相比，HBOA可以使总发行成本最小化。此外，计算时间也包括在分析中。