Abstract
To effectively solve the reverse logistics distribution problem caused by the increasing number of scrapped parts in the automotive market, this study constructs a multitrip green vehicle routing problem model with time windows by comprehensively considering the coordination between carbon dioxide emissions and cost efficiency. A hybrid adaptive genetic algorithm is proposed to solve this problem, featuring innovative improvements in the nearest neighbor rule based on minimum cost, adaptive strategies, bin packing algorithm based on the transferofstate equation, and largescale neighborhood search. Additionally, to efficiently obtain location data for supplier factory sites in the distribution network, a coordinate extraction method based on image recognition technology is proposed. Finally, the scientific validity of this study is verified based on the actual case data, and the robust optimization ability of the algorithm is verified by numerical calculations of different examples. This research not only enriches the study of green vehicle routing problems but also provides valuable insights for the industry to achieve cost reduction, efficiency enhancement, and sustainable development in reverse logistics.
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Introduction
Driven by scientific and technological innovations and economic development, the world automobile market has been expanding rapidly in recent years, and the number of automobiles in the market has been rising gradually^{1}. In addition, consumers' increasing demands for quality and innovative performance of automobiles have prompted automobile manufacturers to introduce more diversified model categories to meet the everchanging market demands. This trend has forced the choice of materials, production processes, and quality control in the automobile manufacturing process to become increasingly demanding. Many of the reasons mentioned above ultimately lead to a significant increase in the number of faulty parts produced by users during the warranty period and the number of defective products produced by automotive companies during the manufacturing process, which are collectively referred to as automotive scrap parts in this paper. The automotive industry is a typical resourceintensive industry, and more than 90% of the steel and nonferrous metals on the parts are recyclable, which can bring considerable economic benefits^{2}. Therefore, the recycling and remanufacturing of scrap parts materials have positive impacts on the return of funds to the automotive industry system and the implementation of the government's sustainable development strategy, and has become a research hotspot in the field of remanufacturing in various countries^{3,4}. At the same time, the reverse logistics recycling process of scrap parts has also become an issue of great concern in the field of environmental resource protection and green logistics^{5}.
For the world's largest automobile producer like China, the recycling of scrap parts for remanufacturing recovery is particularly urgent^{6}. According to China’s National Bureau of Statistics (NBS), as of the beginning of 2023, China’s civilian ownership of automobiles amounted to 319 million, ranking first in the world. In recent years, the scrapping rate of automobiles is about 3.5%, from which it can be approximated that the scale of China's automobile scrapping parts is gradually expanding, as shown in Fig. 1. The Chinese government has also launched a number of policies around 2020 to regulate the recycling mechanism of scrap parts and strengthen the guidance of the industry's sustainable development practices. At present, China's major automobile companies and their parts suppliers have strengthened their efforts to handle scrap parts to accelerate the return of capital and respond to the call for a sustainable development strategy.
To achieve technological spillover, reduce costs, and improve competitiveness, the automobile industry usually adopts the development mode of industrial clustering, which means that many automobile parts suppliers have set up manufacturing factories around the locations of automobile manufacturing enterprises. Therefore, the reverse logistics terminal for scrap parts usually has a corresponding logistics center to undertake the task of receiving scrap parts from vehicle manufacturing plants and automobile service stations around the world, and delivering them to the suppliers, as shown in Fig. 2. The importance of logistics terminal distribution is becoming more and more prominent. However, as the number and diversity of scrap parts continue to increase, logistics centers are facing greater operational pressure, and many problems are gradually being exposed. Among them, the most common problems include the waste of resources by adopting a pointtopoint mode for terminal distribution, the difficulty of coordinating the high inventory level, and the lack of scientific and reasonable planning for vehicle scheduling relying on the experience of drivers.
In previous studies, experts and scholars on automotive reverse logistics have focused on scrap parts recycling policy^{7,8}, reverse logistics network design and planning^{9,10}, and reverse logistics network efficiency evaluation^{11,12}. For the reverse logistics terminal of automobile remanufacturing, especially in the logistics terminal distribution for parts suppliers in industrial cluster areas, there are fewer researches in the past, and there is a lack of relevant theories and case studies. Therefore, the purpose of this paper is to establish a new model of terminal distribution of automotive scrap logistics that can be adapted to the context of sustainable development. To effectively realize the coordination between environmental cleanliness and enterprise costeffectiveness, ease the inventory pressure of the automotive scrap logistics center, and promote the efficient operation of the distribution network. At the same time, we analyze the effectiveness of this study in actual operation to create a benchmark case and provide a case reference for the transformation and upgrading of the industry. The main contributions of the study are as follows:

(1)
In terms of model construction, this paper intervenes to analyze the terminal distribution mode of automobile scrap parts reverse logistics through practical cases. Under the background of sustainable development strategy, carbon emission, overall logistics costs, and delayed delivery rate are introduced as the optimization objectives, and the multitrip green vehicle routing problem model with time windows (MTGVRPTW) is constructed.

(2)
In terms of algorithm design, this paper combines the nearest neighbor rule based on minimum cost, adaptive strategy, bin packing algorithm based on transferofstate equation, largescale neighborhood search algorithm and genetic algorithm to design a hybrid adaptive genetic algorithm to solve the MTGVRPTW problem. At the same time, the adaptive genetic algorithm, genetic algorithm, and hierarchical particle swarm algorithm are used to conduct comparative experimental analysis to verify the validity and advancement of the algorithm.

(3)
In terms of factories location data collection, this paper proposes a coordinate extraction method based on image recognition technology that is feasible within a specific range, replacing the traditional method of converting latitude and longitude coordinates to plane rectangular coordinates, improving the efficiency of data collection.

(4)
This paper discusses the effectiveness of the proposed method in actual operation based on practical case study, which provides substantial reference value for the solution of reverse logistics terminal distribution problems in the industry.
The other sections are organized as follows. “Literature review” section reviews literature studies on related topics. “Problem description and formulation” section describes the problems in the case and constructs a mathematical model. “Solution methodology” section describes the design process of the solving algorithm. “Computational experiments” section discusses the numerical calculations of practical cases and simulation examples.
Literature review
As the concept of sustainable development continues to spread, the optimization and design of reverse logistics systems have attracted the attention of many scholars. Facing the optimization and design problem of the reverse logistics network of waste batteries in Turkey, Kilic et al.^{13} proposed a twostage multiobjective optimization method, achieving an effective combination of economic and environmental benefits. In terms of logistics network structure design, Sun et al.^{14} focused on the ecommerce closedloop supply chain network under uncertain environment. They used a robust pointtopoint optimization method to establish a robust optimization model to reduce the negative impacts of uncertainties in forward and reverse logistics on the logistics network. Faced with the problem of reverse logistics of infectious healthcare waste in the context of the COVID19 pandemic, Yaspal et al.^{15} developed an optimization model considering costeffectiveness and risk avoidance, using datadriven digital transformation to manage disposable medical waste.
The reverse logistics distribution problem studied in this paper essentially falls into the category of the vehicle routing problem (VRP), first proposed by Dantzig and Ramser^{16}, which is an NPhard problem. After conducting a literature review on related topics, we found that there has been limited research on the vehicle routing problem in reverse logistics. Regarding the recycling and reuse of recyclable waste, Cao et al.^{17} studied the vehicle routing problem of a twoechelon collaborative reverse logistics network. Aiming to minimize total costs and considering constraints such as vehicle load, they established a heterogeneous electric vehicle routing model with time windows and designed an intelligent optimization algorithm for solving problems efficiently. For the reverse logistics system of urban sorted waste, Hong et al.^{18} studied the joint decision problem of transfer station location and vehicle route planning. Their model considered greenhouse gas emissions and distribution costs, and they proposed a fast hybrid heuristic algorithm based on column generation and adaptive large neighborhood search, which effectively solved the problem. In the reverse logistics problem of kitchen waste, Shi et al.^{19} studied the problem of the location of processing center and route planning, incorporating carbon trading policies into the model. Their scenario analysis of transportation capacity and methods concluded that the larger the capacity of electric trucks, the greater the economic and environmental benefits. Regarding the reverse logistics of construction waste, Chen et al.^{20} focused on multidepot vehicle routing problems with transport time windows of collision risk. They proposed costeffective and environmentally friendly transport plans and developed an intelligent optimization algorithm for problemsolving. In considering dynamic energy consumption for multicenter mixed fleet reverse logistics distribution, Li et al.^{21} conducted research on mixed fleet operating costs, charging station insertion strategies, and algorithm design. Their method demonstrated outstanding results in reducing total cost expenditure and improving average customer satisfaction across 15 sets of case experiments. Regarding the reverse logistics distribution of endoflife electronic products in South Korea, Kim et al.^{22} studied vehicle route planning operation modes with the objective of reducing transportation distance. They constructed a subvehicle routing problem for each regional center and designed a Tabu search algorithm for effective problemsolving.
A comprehensive review is conducted after combing through the relevant literature in the above research areas. First of all, from the perspective of research scenarios, there are fewer practical case studies on engineering applications, especially for the reverse logistics distribution of scrap parts returned to the factory for remanufacturing in automobile industry cluster areas, which have not been studied. Automobile scrap parts have high potential value, and there is an urgent need for academics to deal with this special scenario to provide the industry with a combination of theory and engineering case reference.
Secondly, regarding research models, previous studies have primarily focused on optimization objectives such as cost, carbon emissions, and customer satisfaction. However, the calculation methods for these objectives still need further study, particularly in addressing the mutual coupling issues among the objectives. In the VRP field, the design of optimization models often requires personalized analysis combined with specific application scenarios and cannot be generalized directly from different research contexts. The green distribution problem (GVRP) is particularly considered in this study, and there are a certain number of research results in the field of GVRP, which can provide a reference for the study of this paper. For example, for the green vehicle routing problem with simultaneous pickups, Olgun et al.^{23} focused on reducing fuel consumption costs and meeting demand from customers in both pickup and delivery. They proposed a hyperheuristic algorithm based on iterative local search and variable neighborhood descent heuristics to solve the problem. Regarding the green heterogeneous vehicle routing problem, Behnamian et al.^{24} specifically considered the location and time of vehicle refueling while reducing carbon dioxide emissions, and designed a data miningbased firefly algorithm to solve the problem.
In addition, in terms of distribution mode selection, previous studies have considered multicenter and mixed fleet operation modes, but the integration of multitrip distribution modes has not been adequately discussed. Assigning a singletrip delivery task to a single vehicle leads to substantial resource consumption, which is not conducive to achieving clean production. Some studies on multitrip distribution are also worth noting. For example, inspired by urban waste collection practices, Huang et al.^{25} introduced a new multitrip vehicle routing problem with time windows and proposed a branchandpricecut algorithm to solve the problem. In addressing distribution issues in the beverage logistics industry, Sethanan et al.^{26} considered multitrip and heterogeneous fleet distribution modes. They proposed an integer linear programming formulation and a hybrid differential evolution algorithm combining genetic operators and a fuzzy logic controller.
Problem description and formulation
This section discusses the RT logistics center as a typical industry case study. Firstly, we analyze the original operation mode and the exposed problems. Then we propose an improved logistics terminal distribution mode. Finally, we construct a mathematical model based on the improved mode to solve the terminal distribution problem.
Describe the case and analyze the problem
The automotive scrap parts logistics center is responsible for receiving scrap parts from automotive service stations around the country and delivering them to the suppliers. RT logistics center mainly has the following functions: collection, sorting, inventory, storage and custody, and distribution. In the original distribution model, the RT logistics center adopts a pointtopoint batch pickup model with suppliers, as shown in Fig. 3. That is, when the suppliers' materials in the logistics center reach the set inventory level, the logistics center will send a pickup notice to the supplier, and then the supplier will arrange its vehicle to pick up the materials and send them back to the factory. Through field research, we found the following problems in the logistics center under the original model:

(1)
The pointtopoint bulk pickup model leads to high inventory levels, which results in expensive inventory costs. At the same time, excessive inventory takes up a large amount of storage space, making it difficult to adapt to future growth within the rapidly expanding automotive market.

(2)
The limited scale of the supplier's selfpickup model leads to high transportation costs and low logistics efficiency, resulting in high logistics costs and high levels of carbon emissions for the entire distribution network.

(3)
Since multiple suppliers are involved, it is difficult to coordinate the vehicle models and pickup times of each supplier, this can easily lead to confusion in the management of the logistics center, interfering with the normal operation status of the outbound storage link.
Designing improved distribution mode
Under the original distribution model, a direct way to reduce inventory levels was to increase the frequency of supplier pickups. However, the rational decisionmakers of the suppliers, are not willing to bear more logistics and transport costs while their interests remain unchanged. Therefore, this paper decides to improve the logistics system from the perspective of changing the pointtopoint transport mode to reduce the logistics inventory level and the overall logistics costs of the whole supply chain. It will also help to reduce the carbon emissions in the logistics process and support the implementation of green sustainable development policies.
The Milkrun model is a pointtogroup efficient delivery method, which many scholars^{27,28} have applied in production research. Studies have shown that the adoption of this model can reduce transport and inventory costs by increasing the loading rate of transport vehicles, thus achieving a reduction in the total costs of logistics. In view of its characteristics of “multifrequency, small batch, and fixed time window”, it can be a better solution to the problems existing in the RT logistics center under the original model. Therefore, this paper decides to establish a kind of circular distribution network based on Milkrun with the logistics center as the leader, as shown in Fig. 4, and then combines it into the MTGVRPTW for indepth study.
Model assumptions and symbol description
Model assumptions
In the actual transportation and distribution process, the vehicle will be affected by a variety of uncontrollable factors, so this paper makes the following assumptions about the mathematical model: (1) Sufficient capacity to take on the distribution needs of suppliers. (2) The transport process is not affected by weather, traffic control, travel peaks, etc., and always maintains the set average speed at an even pace. (3) After each trip delivery departs from the logistics center, it serves the customers in turn according to the optimization results and returns to the logistics center upon completing the delivery task. (4) Each distribution trip can serve multiple suppliers, but each supplier set cannot be delivered by multiple distribution trips. (5) Distribution vehicles are subject to the double limitation of carrying capacity and loading space, which cannot exceed the constraints limitations, and the loading space is expressed in the form of the number of loading units that can be loaded. (6) The vehicle stays at each site for the same time.
Symbol description
The symbols used in the MTGVRPTW model constructed in this paper and their related descriptions are shown in Tables 1 and 2.

(1)
Sets

(2)
Parameters

(3)
Decision variables
$$x_{ijk}^{m} = \left\{ {\begin{array}{*{20}l} {1,} \hfill & {{\text{A}}\;{\mathrm{direct}}\;{\mathrm{path}}\;{\mathrm{exists}}\;{\mathrm{between}}\;{\mathrm{arc}}\;{(}i{, }j{)}\;{\mathrm{and}}\;{\mathrm{belongs}}\;{\mathrm{to}}\;{\mathrm{the}}\;{\mathrm{trip}}\;k\;{\mathrm{of}}\;{\mathrm{vehicle}}\;m} \hfill \\ {0,} \hfill & {{\mathrm{otherwise}}} \hfill \\ \end{array} } \right.$$$$y_{km} = \left\{ {\begin{array}{*{20}l} {1,} \hfill & {{\mathrm{Distribution}}\;{\mathrm{task}}\;{\mathrm{for}}\;{\mathrm{trip}}\;k\;{\mathrm{is}}\;{\mathrm{carried}}\;{\mathrm{by}}\;{\mathrm{vehicle}}\;m} \hfill \\ {0,} \hfill & {{\mathrm{otherwise}}} \hfill \\ \end{array} } \right.$$$$r_{m} = \left\{ {\begin{array}{*{20}l} {1,} \hfill & {{\mathrm{The}}\;{\mathrm{vehicle}}\;m\;{\mathrm{of}}\;{\mathrm{the}}\;{\mathrm{set}}\;{\mathrm{of}}\;{\mathrm{vehicles}}\;{\mathrm{is}}\;{\mathrm{in}}\;{\mathrm{service}}} \hfill \\ {0,} \hfill & {{\mathrm{otherwise}}} \hfill \\ \end{array} } \right.$$$$ds_{i} = \left\{ \begin{gathered} 0,\quad ET_{i} \le t_{a\_i} < LT_{i} \, \hfill \\ 1,\quad {\mathrm{otherwise}} \hfill \\ \end{gathered} \right.$$
Mathematical model
Objective functions
In the context of cleaner production and sustainable development strategies, when building the MTGVRPTW model for automotive scrap parts distribution, it is necessary to consider the impacts of various factors, including: (1) Reducing ecological impacts. (2) Achieving cost reduction and efficiency in logistics. (3) Ensuring the timely delivery of distribution services. On this basis, this study proposes three different optimization objectives.

(1)
Minimizing carbon dioxide emissions
The ecological impact of the vehicle distribution process is usually caused by the fact that driving a vehicle consumes fuel and produces carbon dioxide. Therefore, the first optimization objective in the model is set to minimize carbon dioxide emissions during the delivery process. Zhou et al. summarized most of the estimation methods on carbon emissions from automobiles^{29}, considering the difficulty of obtaining data, this paper decided to use the fuel consumption rate measure to calculate. The specific formula is shown in Eq. (1).

(2)
Minimizing overall logistics costs
In the process of logistics distribution, a variety of transportation resources need to be deployed, which will generate several costs, including internal preparation, vehicle rental, driver labor, and distance transportation. The goal of the actual operation of the enterprise is to reduce the overall logistics costs and improve the efficiency of resource utilization. Therefore, this paper sets the lowest overall logistics costs as the second optimization objective. The specific formula is shown in Eq. (2).

(i)
Preparation costs for departure
Before the departure of each trip within the enterprise involved in the shelves, moving storage, loading and other logistics arrangements, including a large number of logistics equipment, material and human resources, the unified deployment. The costs of this item is shown in Eq. (3).

(ii)
Vehicle rental costs
Distribution vehicles required for distribution are obtained by leasing with thirdparty companies, which generates vehicle leasing costs. The final decision on the number of vehicles to be rented is related to the result of combining multiple trips. The costs of this item is shown in Eq. (4).

(iii)
Driver labor costs
Each vehicle is provided with a driver, who is employed on a temporary basis. If the actual delivery time of the vehicle m is less than the legal working hours of half a working day (4 h), a halfday contract is concluded with the driver of the vehicle; otherwise, a fullday contract is concluded. The costs of this item is shown in Eq. (5).
where CH_{m} represents the labor costs of equipping the vehicle m with a driver and is related to the travel time of each vehicle. It is shown in Eq. (6).
where the formula for the travel time of each vehicle is as described in Eq. (7).

(iv)
Vehicle transportation costs
Transportation costs will be generated when transporting goods, which include fuel costs, etc. And it is directly proportional to the distance traveled. The costs of this item is shown in Eq. (8).

(3)
Minimizing delayed delivery rates
If the delivery vehicle arrives at the destination earlier or later than the time window required by suppliers, it may disrupt the supplier's normal work situation. Therefore, we expect the delayed delivery rate to be minimized to avoid disrupting the supplier's work schedule due to unfavorable delivery. The specific formula is shown in Eq. (9).
subject to
where constraint Eq. (10) restricts the allocation of each site to only one trip. Constraint Eq. (11) limits the number of times a single vehicle can enter and exit the logistics center under multitrip distribution to the same number of times. Constraint Eq. (12) restricts the number of times a vehicle can drive in and out of the same stop to remain equal. Constraint Eq. (13) restricts that no distribution task on each trip exceeds the volume limit. Constraint Eq. (14) restricts each distribution task on each trip to not exceeding the load limits. Constraint Eq. (15) limits the number of miles traveled by each carrier vehicle to no more than the vehicle's range limit. Constraint Eq. (16) restricts only vehicles that are in service to distribution duties. Constraint Eq. (17) restricts the order in which vehicles are put into service from m to m + 1. The constraint Eqs. (18–20) defines the decision variable as 0 or 1.
Multiobjective processing
There are three objectives of different properties in the optimization model. Considering the complexity of the solution and the decision preference, this study uses the weighted sum method to integrate these objectives into a single objective function^{30}. Setting the weights of the three objectives as convex combinations, i.e.,\(\lambda_{1} ,\lambda_{2} ,\lambda_{3} \ge 0\) and \(\lambda_{1} + \lambda_{2} + \lambda_{3} = 1\). Due to the large number of members in a distribution network and the fact that distribution costs are shared by all members, decisionmaking must take into account the opinions of all members. Groupanalytic hierarchy process (GAHP) is a comprehensive evaluation method developed based on hierarchical analysis, which can effectively integrate the knowledge and experience of multiple experts for group decisionmaking^{31}. Therefore, this paper will apply GAHP to determine the weights of the three objective functions, drawing on the reviews of a team of experts consisting of representatives from logistics centers and suppliers.

(1)
Calculate the weight vector of each expert's judgment matrix
In the formulation of the weight standard, a total of 5 experts participate in the group decision, and the judgment matrix constructed by the review opinion of each expert are \(A_{1} ,A_{2} ,A_{3} ,A_{4} ,A_{5}\). The expression form of each judgment matrix is \(A_{l} = (a_{ijl} ); \, i,j = 1,2,3; \, l = 1,2, \ldots ,5\), where \(a_{ijl}\) denotes the relative importance of factor i over factor j as perceived by the expert l. Separately solve their weight vectors \(\tilde{w}_{il} \, = \,(\,\tilde{w}_{1l} ,\tilde{w}_{2l} \,,\tilde{w}_{3l} \,)^{T}\), where \(\tilde{w}_{il}\) represents the judgment weight value of the expert l for the objective function i. To ensure the consistency of the weight calculation results, a consistency check is performed, aiming for \(CR_{l} = CI_{l} /RI_{l} < 0.1\).

(2)
Calculate the group’s composite weight vector
In this paper, considering the fairness and balance, under the condition that \(\sum {\lambda_{l} = 1,\quad (\lambda_{l} > 0,\quad l = 1,2, \ldots ,5)}\), the weight of each review expert's opinion is set to be \(\lambda_{l} = 1/5 = 0.2\). Performing the weighted arithmetic mean calculation on the respective components of each weight vector, as shown in Eq. (21).
Following normalization of \(\tilde{w}_{i}\) as Eq. (22), the weight vectors for the three objectives can be derived as \(w_{i} = [0.164,0.539,0.297]^{T}\).
To address the dimensional differences among \(Z_{1}\) and \(Z_{2}\), the method of min–max normalization is employed to transform the multiobjective problem into a scalar optimization problem. Where \(\underline{{Z_{1} }} ,\underline{{Z_{2} }} ,\underline{{Z_{3} }}\) are the lower bounds of \(Z_{1} ,Z_{2} ,Z_{3}\), and \(\overline{{Z_{1} }} ,\overline{{Z_{2} }} ,\overline{{Z_{3} }}\) are the upper bounds of \(Z_{1} ,Z_{2} ,Z_{3}\). The lower and upper bounds are calculated by the box constraint. The transformed single objective optimization model is shown in Eq. (23).
Solution methodology
Vehicle routing problem (VRP) is NPhard problem, which is usually solved using heuristic algorithms^{32}. Genetic algorithm searches for optimal solutions by simulating the natural selection and genetics mechanism of Darwin's biological evolution theory, which has a strong global search ability and can achieve desirable optimization effects in solving VRP. However, because it is a stochastic search method, the local search ability is insufficient. Therefore, in this paper, a hybrid adaptive genetic algorithm (HAGA) is designed to enhance the solution quality and robustness of the solution algorithm by improving the genetic algorithm on initialization population, genetic strategy, and local search, respectively, with respect to the problem characteristics. For "the bin packing problem" generated by the multitrip distribution of vehicles, this paper proposes a bin packing algorithm based on transferofstate equation to solve the problem.
Hybrid adaptive genetic algorithm

(1)
Coding method
Encoding is the process of mapping the solution space of a problem to a genotype representation in a genetic algorithm, allowing the algorithm to manipulate and evolve individuals. To increase the speed of model solving, this paper uses integer encoding.

(2)
Initialize population based on NNC rule
The classical genetic algorithm generates the initial population using a randomized method, resulting in a low degree of individual adaptation, which restricts the convergence speed of the algorithm. The nearest neighbor rule based on minimum cost (NNC) is a construction rule that produces higher quality feasible solutions, an idea first proposed by Solomon^{33}. In this paper, we use the NNC rule to optimize the initial individuals and leverage its local optimization search to generate new individuals, aiming to improve the overall quality of the initialized population and accelerate the optimization process.
Rule: Initialize population based on NNC rule  
Step 1  For a given departure time, start a distribution trip from the logistics center; 
Step 2  Select the unreached site with the smallest "distance" from the current site, and insert this site into the route of the current trip if it meets the constraints; 
Step 3  Repeat Step 2. If the relevant constraints are exceeded, a new distribution trip is added. If all sites are delivered, the calculation procedure is stopped 
The “distance” between sites is defined as a weighted sum of the travel time between the two sites, the proximity of the time windows, and the urgency of the time window at the latter site. The “proximity of the time window” is the difference between the “start of service” at the latter site and the “completion of service” at the former site. The “urgency of the time window” of a site is the difference between the “latest service time” of the site and the “start service time” of the site. The “distance” between the two sites is shown in Eq. (24).
where c_{ij} represents the "distance" between sites i and j. t_{ij} represents the travel time from site i to j. T_{ij} represents the proximity of the time window of sites i and j. E_{ij} represents the urgency of the time window of site j. δ_{1}, δ_{2}, δ_{3} represent the weighting coefficients, which satisfy δ_{1} + δ_{2} + δ_{3} = 1.

(3)
Fitness function
The fitness function is used to measure the degree of adaptation of an individual in the problem space. The larger the value of the individual’s fitness, the higher the probability of remaining for the next generation of individual reproduction. For the minimization optimization model in this paper, the fitness is designed to be inversely proportional to the objective function, as shown in Eq. (25).
where Z denotes the objective function after transformation processing, as shown in Eq. (23).

(4)
Selection operation
The selection operator is a key step used to choose individuals for the next generation. Its main purpose is to select superior individuals from the current population based on their fitness values for subsequent operations. In this paper, tournament selection was used.

(5)
Adaptive scheme
The genetic algorithm is improved by using an adaptive genetic strategy, which adaptively changes the crossover and mutation probabilities according to individual fitness values, effectively avoiding local optima^{34}. At the beginning of the genetic algorithm run, the individual differences are quite large. A higher crossover probability is chosen to increase the rate of new individual emergence, and a smaller mutation probability is chosen to speed up the convergence of results. In the later stages of the genetic algorithm, to reduce the probability of the algorithm falling into a local optimum, a smaller crossover probability should be used to protect welladapted individuals, and a larger mutation probability should be used to increase the diversity of the population. In this way, the algorithm can jump out of the local optimum in time and determine the optimal or nearoptimal solution in the shortest possible time. The following is the expression of crossover probability Eq. (26) and mutation probability Eq. (27) for the adaptive genetic operator proposed in this study.
where P_{c1} is the set minimum crossover probability. P_{c0} is the set maximum crossover probability. P_{m1} is the set minimum mutation probability. P_{m0} is the set maximum mutation probability. f_{avg} is the current population mean fitness value. f_{max} is the population maximum fitness value. f’ is the fitness value of the larger of the two individuals that crossover. f is the fitness value of the variant individual.

(6)
Cross operation
The crossover operator acts on the two paternal chromosomes to produce two new offspring individuals that contain the paternal genes but are different from the paternal chromosomes. In this paper, the OX crossover is used to speed up the operation and better preserve individual personality. The crossover operation process is shown in Fig. 5.

(7)
Mutation operation
The mutation operator acts on one parent chromosome to make individuals in the population mutate, enriching the diversity of chromosomes within the population, improving the algorithm's ability to find the best, and preventing the algorithm from maturing prematurely. The mutation operation process is shown in Fig. 6.

(8)
Local search operation
Largescale neighborhood search algorithms (LNS) have the advantage of local search ability. Therefore, this paper leverages the core concepts of LNS, i.e., destruction and repair^{35}, to design remove and reinserting operators to effectively compensate for the lack of local search ability of adaptive genetic algorithms. The remove operator refers to removing a portion of supplier sites from the current solution, while the reinserting operator refers to reinserting the removed supplier sites into the current solution. The schematic of local search is shown in Fig. 7.

(i)
Remove operator
The removal operator is designed to identify distribution sites for removal based on the correlation value R. The removal operator operates as follows: Firstly, set the number p of sites to be removed, randomly select a site i from the current solution to be removed, and store the sites to be removed in the set S. Then calculate the correlation R between the remaining sites and the selected sites, and sort the correlations, select the site with the largest correlation for removal, and add it to the set S. The process is repeated until p1 destructive sites have been selected. The calculation of R is shown in Eq. (28).
where \(D_{ij}{\prime}\) denotes the normalized distance value between sites i and j, which is calculated as in Eq. (29). \(V_{ij}\) denotes whether site i and j are on the same routing or not, and is 1 if they are on the same routing, and 0 otherwise.

(ii)
Reinserting operator
After removing a number of distribution sites using the remove operator, the removed distribution sites are then reinserted into the relevant locations on the routing using the reinserting operator, and the insertion is checked to see if the constraints are satisfied. The reinserting operator operates as follows: Firstly, find the best insertion position of each site in the set S that minimizes the increase of the objective function value in the postdestruction solution. Then calculate the target increase value of each site in S after inserting it to the best position, choose the site with the largest target increase value as the first insertion point, and repeat this operation until all sites in the set S are inserted into the destructed solution.
Bin packing algorithm based on transferofstate equation for solving multitrip distribution
In the MTGVRPTW, which considers singlevehicle multitrip delivery, the process of assigning trips to vehicles to obtain a solution is a typical "bin packing problem". The problem can be described as follows: there are a sufficient number of carrier vehicles \({\varvec{M}} = \{ 1,2 \ldots ,M^{*} \}\), and the maximum operation time of the vehicle is \(W\). The distribution routings set \({\varvec{K}} = \{ 1,2 \ldots ,K^{*} \}\) of several trips is obtained after decoding each chromosome of HAGA algorithm, and the distribution time of each trip is \(w_{k}\). The task now is to design an algorithm that optimizes the allocation of distribution trips, aiming to minimize the number of vehicles required. The bin packing problem in this paper can be denoted by Eq. (30–34):
subject to
where Eq. (30) denotes that the objective of optimization is to use the minimum number of vehicles. Constraint Eq. (31) denotes that the total time of multitrip distribution by each vehicle does not exceed the total working time of the sites. Constraint Eq. (32) indicates that all trips are carried by one and only one vehicle. Equations (32,34) defines the decision variable as 0 or 1.
In the solution of this problem, while the optimal solution can be obtained by using the exact solution method, the calculation process is more complicated. If the greedy algorithm is used, the results can be obtained faster, but the results are often not satisfactory. Therefore, this paper combines the exact solution method of dynamic programming with the greedy idea, and designs a combinatorial solution method based on transferofstate equation for solving the "bin packing problem" in the multitrip distribution problem.
Algorithm: Bin packing algorithm program based on transferofstate equation  
Step 1  Obtain the basic data \(W\) and \(w_{k}\), and initialize the number of vehicles to \(m = 1\). Identify the trips which the singletrip delivery time \(w_{k}\) exceeds \(W\), remove them from the set, and count their number as \(m_{0}\) 
Step2  Use dynamic programming to take out a number of delivery trips from the current "delivery trips set", and make them carried by mth vehicle, ensuring that the mth vehicle's operating time approaches W Dynamic planning procedures: (1) Initialize a twodimensional array, where \(dp[i][j]\) denotes the maximum value that can be obtained by placing a vehicle with a maximum time in service of j, considering the first i distribution trips (2) Initialize \(dp[0][j] = 0\),\(dp[i][0] = 0\), where \(i = \{ 1, \cdots ,K^{*} \}\),\(j = \{ 0,1, \cdots ,W\}\) (3) Use transferofstate equation to populate the dp array until all trips have been computed \(dp[i][j] = \left\{ {\begin{array}{*{20}c} {dp[i  1][j]} & {,j < w_{i} } \\ {\max \{ dp[i  1][j],dp[i  1][j  w[i]] + v[i]\} } & {,j \ge w_{i} } \\ \end{array} } \right.\) (4)\(dp[n][W]\) is the maximum value that can be obtained given the maximum time W that a vehicle can be put into service, and the reverse derivation to find out the selected distribution trips 
Step 3  Remove the delivery trips selected in Step2 from the "delivery trips set" and add a vehicle so that \(m = m + 1\) 
Step 4  If the current "delivery trips set" is not empty, then skip to Step 2. If the current "delivery trips set" is empty, then end the calculation and skip to Step 5 
Step 5  Output the total number of vehicles used \(m^{*} = m_{0} + m\), and the distribution trips assigned by each vehicle 
It is worth noting that the bin packing algorithm can effectively solve the multitrip merging problem when all delivery sites share a unified time window. However, it may not be applicable when the time windows of different sites vary. That said, most manufacturing factories operate under a uniform work schedule, and reverse logistics deliveries are generally less urgent. Therefore, this method can be wellcompatible within the industry.
The flowchart of the final solution algorithm for the problem model of this paper is shown in Fig. 8.
Computational experiments
In this section, we explore an application example scenario based on the MTGVRPTW model and the solution algorithm for the RT automotive scrap parts logistics center to assess the implementation benefits of the improved distribution model and the effectiveness of the solution algorithm. For those enterprises involved in more complex supply chains, which are located in industrial clusters with many suppliers, the distribution scale of reverse logistics terminals will be even larger. Therefore, this paper is oriented to medium and largescale cases for simulation and analysis, aiming to make the research more universally applicable to the industry and to test the robustness of the algorithm, thereby deepening the significance of the research.
Numerical analysis of application example scenarios
To more intuitively reflect the superiority of the hybrid adaptive genetic algorithm (HAGA) designed in this paper, the adaptive genetic algorithm (AGA), genetic algorithm (GA), and hierarchical particle swarm algorithm (HPSO) are introduced to conduct the comparative experiments. The solution results are compared and analyzed, in terms of convergence characteristics and solution quality, to verify the robustness and optimalityseeking ability of HAGA.
Algorithmic parameter setting
In this paper, the parameters of the algorithms are set utilizing arithmetic tests and references to previous research experience, as shown in Table 3. All the algorithms are implemented by MATLAB R2017a^{36} programming, and the experimental results are output by running the software. The computer parameters are configured as Intel Core i512500H, 2.5 GHz, 16 GB RAM. The results of each algorithm are based on 20 runs.
Data collection and processing

(1)
Extract supplier site coordinate data
In previous studies, to collect the planar coordinates of the distribution sites, most of the previous researchers used the method of collecting the latitude and longitude data of the distribution sites from maps, and then converting the latitude and longitude coordinates to the planar rectangular coordinates by using various software such as MAPGIS^{37}. In this paper, we argue that although the method above is feasible, it takes a long time to extract the coordinates when encountering largescale practical cases. Therefore, this paper proposes a fast extraction method of planar coordinates based on image recognition technology that is feasible on a small scale.
The idea of the method is that when the distribution area under study is small, the idea of mathematical differentiation can be applied to approximate the sphere as a plane. The distribution area of this paper is 28 km × 24 km. The schematic diagram of this method is shown in Fig. 9. The specific operational procedure is as follows:

(i)
Data preparation and original layer. Initial data collection is performed using the Google Maps service to capture a planimetric map of the area containing all suppliers and set it as Layer 1. The image must contain a clear scale, as it is a key element for precise distance calculations.

(ii)
Creation and annotation of the calculation layer. Create a new transparent layer, Layer 2, above Layer 1. In Layer 2, use a graphical marking tool (e.g., dots) to accurately annotate the scale and supplier site locations, optimizing the target capture efficiency of the image recognition algorithm. This step aims to avoid loss or noise interference in subsequent data processing.

(iii)
Image grayscale processing. Remove Layer 1. Convert the image of Layer 2 to grayscale to reduce image complexity and decrease the computational demand of the algorithm, thereby improving the accuracy of the image recognition process.

(iv)
Image recognition and data extraction. Apply image recognition technology to identify specific grayscale points in the image, which represent the pixel locations of the distribution sites. Simultaneously, the algorithm identifies the pixel coordinates at both ends of the scale and calculates the pixel distance between the two ends, providing the necessary data support for coordinate conversion.

(v)
Coordinate conversion and calibration. Based on the pixel distance provided by the scale, perform a proportional linear transformation on the pixel coordinates of the distribution sites, converting them into actual plane calculation coordinates. This step ensures the accurate conversion from the image to actual geographic locations.
To verify the accuracy and reliability of the data collection method in this paper, the collected data are compared and analyzed with the measurement data from the Baidu Maps platform. Some of the comparison results are shown in Table 4. The distance calculated by each site through the image recognition technology to extract the coordinates compared with the actual distance, the accuracy ranged from 95 to 99%, and the overall average accuracy of 98.88%. These results are within the acceptable range, proving the effectiveness of the method proposed in this paper.
The method has several advantages over traditional methods. The image recognition method significantly reduces the manual involvement in data collection. For largescale data collection scenarios, this method can complete data extraction for an entire area within minutes, whereas traditional methods may take hours or even longer to achieve the same task. The timesaving advantage of the proposed method is particularly significant when facing the coordinate collection of multichange scenarios.
In addition, in the case of natural disasters and other scenarios, emergency shelters are usually located in no fixed place, and it is more scientific and feasible to extract coordinates based on realtime remote sensing satellite images using image recognition technology in the distribution of emergency supplies.

(2)
Description of other data
The model of this paper and other data involved in the calculation of the elaboration of the description: (i) The generation of scrap parts is unpredictable, and the number of each time period varies. In order to optimize the allocation of resources, each delivery is made with a thirdparty company to reach a vehicle rental and driver temporary employment agreement, so this paper is not constrained by the number of vehicles and drivers. (ii) Considering the large number of suppliers, scrap parts belonging to the same supplier are loaded using standardized cargo units. Considering the road conditions within the city, this study focuses on leasing 6.8m vans. The vehicle specification is 6800 mm × 2450 mm × 2600 mm, with doublelayer palletizing, and a single truck with 24 cargo unit positions. The cargo unit required by each supplier for daily distribution can be calculated from the current data. (iii) Considering the realistic road conditions and other factors, the average speed of vehicle traveling was set to be 35 km/h. (iv) Preparation costs for departure is set to 50 yuan/trip. (v) In the actual distribution, the distribution site is not a straight path. To make the simulation closer to reality, we set a certain relaxation factor, which is calculated as follows: simulation distance = euclidean distance between coordinates × relaxation factor. After calculation, this paper takes the value of 1.6. (vi) Transportation cost per unit distance for distribution vehicles is 2 yuan/km. Conversion factor for carbon emissions and fuel consumption \(e_{0}\) is calculated as 0.34L of diesel fuel for 1 kg of carbon dioxide. Vehicles with a maximum load capacity \(Q_{K}\) of 8 tons. Fuel consumption per uni15t distance \(\rho_{ok}\) at no load is 0.117 L/km. Fuel consumption per unit distance \(\rho_{k}^{*}\) at full load is 0.377 L/km. (vii) The normal working time window for the logistics center and each supplier is 9:00 to 17:00, which is unified.
Practical case solving
In the new distribution mode, the number of automotive scrap parts faced at different delivery cycle intervals varies, requiring different transportation resources. In the original mode, the average shipping frequency of pointtopoint delivery is about 4–5 days. One of the purposes of this study is to reduce the operational pressure of the logistics center and reduce the inventory level, so the delivery cycle interval is set to 1–3 days, respectively. To help enterprises better reach cost reduction and efficiency, this paper analyzes the target benefits under different distribution cycle intervals. Some of the example data are shown in Table 5.
The model solution results and algorithm iteration process under different distribution cycle intervals are shown in Fig. 10 and Table 6.
Result discussion

(1)
Discussion of results using different optimization algorithms.
From Table 6, it can be seen that there are significant differences in the optimization effects of different solving algorithms. In terms of the performance of the overall objective function, HAGA > AGA > GA ≈ HPSO, and the optimized number of trips and the number of vehicles after solving the HAGA is less than those of the AGA, GA, and HPSO, regardless of the distribution cycle intervals. In terms of the performance of the objective function \(Z_{1}\), the HAGA is in the leading position, and its optimized carbon dioxide emissions are better than the AGA by an average of 7.46%, the GA by an average of 8.38%, and the HPSO by an average of 6.68% in different distribution cycle intervals. In terms of the performance of the objective function \(Z_{2}\), the HAGA is also in the leading position, and its optimized overall logistics cost is better than the AGA by an average of 3.64%, the GA by an average of 7.75%, and the HPSO by an average of 7.94% in different distribution cycle intervals. Meanwhile, in terms of convergence speed, the HAGA can enter convergence with fewer iterations, and outperforms the AGA by an average of 16.83%, the GA by an average of 20.27%, and the HPSO by an average of 20.85% in different distribution cycle intervals. Although the solution time of the HAGA is slightly longer than the other algorithms, its computation time of only a few minutes does not overburden the overall task and is within an acceptable range.
Combined with Fig. 9, HAGA initializes the population with better quality under the NNC rule, which seizes a head start for the subsequent optimality search. From the iterative curve, HAGA and AGA are better than GA and HPSO, which shows that the use of adaptive genetic strategy can help to maintain the diversity of the population and prevent the algorithm from converging to the local optimal solution too early. The superior search quality of HAGA compared to AGA shows that the global destroyrepair mechanism of the LNS algorithm can enhance the algorithm's ability of local search, and to a certain extent, prevent the algorithm from falling into local optimums. In addition, in terms of solution stability, after 20 runs, the percentage deviation of HAGA in the final objective function result is only 1.4%, while for the other algorithms is more than 15%, which sufficiently demonstrates that the solution of HAGA has stronger stability.

(2)
Discussion of the results of the strategy using different distribution cycle intervals
The solution results for different cycle intervals are not directly comparable, so in this paper, the magnitude is transformed to be on the unit of the month. The model solution results using the HAGA are shown in Table 7 after the comparability transformation.
The general trend of the different cycle intervals of distribution in various indicators is that the smaller the cycle interval, the higher the carbon dioxide emissions during distribution, the higher the overall logistics cost, but the better the improvement in inventory levels. Considering the current situation of the RT logistics center, a 31% reduction in the inventory level can sufficiently alleviate the current operational pressure. Therefore, the decision was made to adopt a distribution plan with a 3day distribution cycle interval. In the future, according to the actual situation of the logistics center flexibly change the distribution cycle interval, in order to adapt to the needs of the development promptly. The specific distribution program is shown in Table 8.
In addition, the adoption of a circular distribution model with a 3day interval between delivery cycles has resulted in a 66.78% reduction in overall logistics cost, an 18.08% reduction in carbon dioxide emissions, and a 31% reduction in inventory levels compared to the initial pointtopoint bulk delivery model, which is a significant improvement.
Simulation analysis under medium and large scale arithmetic examples
For those enterprises with more complex supply chains, they are located in industrial clusters with a large number of suppliers, and the scale of distribution at the reverse logistics terminal will also be larger. Therefore, this paper conducts extended experiments for medium and largescale cases to make this study more universal for industry. At the same time, the robustness of the HAGA designed in this paper is examined using different example data to deepen the significance of the study.
Description of the simulation example
The randomized generation method is used to generate the medium and largescale example data with the number of distribution sites of 40, 50, 60, and 70, respectively. The coordinates of each distribution site are randomly generated from 0 to 50 km, the number of cargo units required is randomly generated from 1 to 8, and the weight of materials is randomly generated from 200 to 2000 kg. The rest of the parameter settings are consistent with those in the previous section.
Simulation example solving
The solution is solved for different size cases and the results are shown in Table 9.
Result discussion
Table 9 shows that the HAGA continues to outperform the other algorithms at all scales. It outperforms the other algorithms in terms of the total objective function \(Z\), the number of trips, and the number of vehicles transported, which is consistent with the conclusions drawn in “Result discussion” section. In terms of the objective function \(Z_{1}\), the HAGA outperforms the AGA by an average of 17.35%, the GA by an average of 25.41%, and the HPSO by an average of 20.79%. In terms of the performance of the objective function \(Z_{2}\), the HAGA outperforms the AGA by 18.29% on average, the GA by 22.59% on average, and the HPSO by 21.67% on average. In addition, as the size of the arithmetic cases increases, HAGA has a greater advantage over the rest of the algorithms, proving that it possesses strong robustness. Meanwhile, in terms of convergence speed, the HAGA is able to reach the optimization with fewer iterations. However, in terms of solution time, HAGA is at a disadvantage compared to the other algorithms.
Conclusion
Focusing on the strategy of sustainable development, this paper studies the problem of green distribution of automobile scrap reverse logistics for industrial cluster areas. The main conclusions are as follows:

(1)
Under the comprehensive consideration of reducing the inventory level and realizing the cost reduction and efficiency improvement of logistics, a circular distribution mode based on Milkrun is proposed to replace the initial pointtopoint batch distribution mode. To achieve the coordination between sustainable development strategy and enterprise costeffectiveness, this paper introduces multiple optimization objectives of minimizing carbon dioxide emissions, overall logistics cost, and delayed delivery, constructs the MTGVRPTW model, and verifies the usability of the model.

(2)
Given the characteristics of this research problem, a hybrid adaptive genetic algorithm that combines the nearest neighbor rule based on minimum cost, adaptive strategy, binpacking algorithm based on the transferofstate equation, largescale neighborhood search algorithm and genetic algorithm, and the design process of the algorithm is described in detail. The robustness and stability of the HAGA algorithm are verified by the numerical calculation.

(3)
To efficiently obtain the location data of supplier factory sites in the distribution network, a coordinate extraction method based on image recognition technology is proposed. Validation results indicate that this method achieves an overall average accuracy of 98.88% in coordinate extraction, characterized by high efficiency and accuracy.

(4)
A case study was conducted on the RT logistics center to analyze its operational performance under different distribution strategies. The results indicate that shortening the distribution cycle interval significantly reduces inventory levels but also increases logistics costs and carbon dioxide emissions. The analysis concluded that adopting a threeday cycle distribution model better meets the current development needs of the RT logistics center. Compared to the initial pointtopoint batch distribution model, overall logistics cost decreased by 66.78%, carbon dioxide emissions reduced by 18.08%, and inventory levels dropped by 31%, demonstrating significant improvements. In addition, by introducing mediumtolargescale simulation examples, the significant advantages of the HAGA algorithm over other algorithms in terms of robustness and optimization ability are verified. It also shows that the research results have good application universality in similar industries.
Data availability
Some of the data used in this study are presented in the manuscript, and the remaining data are available upon reasonable request from the corresponding author. The complete data are not directly disclosed because they may compromise the privacy of the study participants.
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Acknowledgements
This work was supported in part by the Natural Science Foundation of Heilongjiang Province, Grant No. LH2023G001.
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H.W.: Conceptualization, Data curation, Formal analysis, Methodology, Resources, Software, Validation, Project administration, Investigation, Writing—original draft. H.H.: Funding acquisition, Supervision, Writing—review and editing. M.W.: Visualization. All authors reviewed the manuscript.
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Wang, H., Hao, H. & Wang, M. Optimization research on multitrip distribution of reverse logistics terminal for automobile scrap parts under the background of sustainable development strategy. Sci Rep 14, 17305 (2024). https://doi.org/10.1038/s41598024681124
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DOI: https://doi.org/10.1038/s41598024681124