## 1 Introduction  
Logistics management encompasses the entire process from the procurement of raw materials to the final delivery of products, integrating logistical planning, transportation, warehousing, inventory management, and the coordination and optimization of diverse supply chain activities [1]. The movement of goods from supply points to various destinations holds significant importance in logistics management, exerting a considerable impact on overall expenditures and the level of service provided to customers. The classical problem in logistics scheduling is referred to as the vehicle routing problem (VRP), initially formulated by [PERSON] and [PERSON] [2]. In recent years, numerous variants of the VRP have been extensively researched [3; 4; 5], especially those incorporating the concept of time windows, known as VRP with Time Window (VRPTW) variants [6]. Applying intelligent scheduling algorithms to design efficient allocation plans and organize vehicles systematically has proven effective in enhancing efficiency and reducing transportation costs [7; 8; 9]. Despite the progress in solving VRP, existing scheduling models still exhibit limitations, such as the lack of attention to achieving a balance among the interests of various stakeholders under urban conditions. In practical logistics systems, stakeholders possess diverse interests that may potentially conflict [10; 11; 12]. The traditional VRPTW suffers from inherent limitations, such as oversimplification of vehicle attributes and customer satisfaction, along with the absence of environmental considerations. These limitations result in the oversight of the influence of diverse vehicle characteristics on route planning, disregard for variations in customer tolerance for overdue waiting times, and the oversight of the environmental implications of distinct routes. To address these gaps, this paper introduces the heterogeneous green city VRPTW (HGCVRPTW), which aims to offer a more comprehensive and realistic solution that better aligns with diverse stakeholder requirements. Furthermore, an adaptive multi-objective genetic algorithm based on greedy initialization strategy (AMoGA-GIS) is proposed to solve this novel HGCVRPTW problem. Firstly, a greedy initialization strategy (GIS) is devised to generate multiple subpopulations, and each subpopulation corresponds to a specific objective. This allows the overall population to evolve from optimal single objectives, expediting population convergence. To ensure population diversity, an additional subpopulation is generated through a random approach. Secondly, the adaptive multiple mutation operators (AMMO) are designed to ensure that the algorithm has opportunities to employ suitable mutation strategies at different evolutionary stages. The AMMO adjusts the selection probability of mutation operators based on the success rate of mutation, favoring different mutation operators that are more likely to drive population evolution at the current stage, thereby accelerating population convergence. The diagram of the AMoGA-GIS is shown in Figure 1.  
The novelty of our work lies in its comprehensive approach to the VRP, incorporating heterogeneous vehicle attributes, customer satisfaction levels, and environmental impacts, which are often overlooked in traditional models. By addressing these aspects, our research fills the gaps in current VRP studies, which typically oversimplify vehicle attributes and disregard customer and environmental considerations. The primary contributions of our work are as follows:  
Figure 1: The diagram of AMoGA-GIS. 1. Introducing the novel concept of the heterogeneous green city VRPTW (HGCVRPTW), which incorporates multiple stakeholder interests and environmental considerations into the VRP framework;
2. Proposing an adaptive multi-objective genetic algorithm based on a greedy initialization strategy to solve the HGCVRPTW problem.