A method and system for solving medical waste transportation schemes based on a two-level optimization model.

Abstract

This invention belongs to the field of smart logistics technology, specifically relating to a method and system for solving medical waste transportation problems based on a two-level optimization model. The method includes the following steps: Step 1, constructing a two-level optimization model for solving the medical waste transportation problem. The two-level optimization model includes the following three stages: First stage, determining the optimal location of the transfer center; Second stage, planning the collection route from the collection center to the transfer center; Third stage, optimizing the transportation route from the transfer center to the processing center; Step 2, using the Gurobi optimizer to solve the problems in the first and second stages; and using an adaptive neighborhood search algorithm to solve the problem in the third stage. The model of this invention comprehensively considers site selection costs and infection risks, effectively addressing the complexity of the algorithm and real-world constraints. Therefore, this invention has excellent application prospects in solving medical waste transportation problems.

Description

Technical Field

[0001] This invention belongs to the field of intelligent logistics technology, specifically relating to a solution method and system for medical waste transportation schemes based on a two-layer optimization model. Background Technology

[0002] With urbanization, population growth, and the impact of the pandemic, medical waste has increased dramatically, making its collection and treatment one of the most pressing needs and challenges in public services. Medical Waste Management (MWM) aims to provide efficient, economical, and environmentally friendly solutions for waste disposal. It typically includes three key steps: collection and separation, transportation to a treatment site, and final treatment.

[0003] The transportation phase, commonly known as Medical Waste Transportation (MWT), can be viewed as a path problem. Most existing research treats waste management as a single-level path problem: vehicles depart from a treatment center, collect waste from medical facilities, and return to the treatment center. However, a more promising strategy is to establish temporary transfer centers at medical facilities, forming a two-level route structure: waste is first transported from the medical facility to the transfer centers, and then from these centers to the treatment center. By optimizing the path in two levels, the distance of the MWT can be shortened, thereby reducing transportation costs and risks. The two-level path optimization of medical waste can be viewed as a Location-Path Problem (LRP). LRP belongs to the NP-hard combinatorial optimization problem, combining facility location and path decisions. Many problems from various industries can be classified as LRP, including green logistics, disaster relief distribution, battery replacement optimization, and so on. In recent years, LRP has evolved to consider not only basic location and route optimization but also various real-world constraints, such as time windows, vehicle capacity, and vehicle type.

[0004] Most LRP studies on MWT (Medical Waste Management) focus primarily on economic objectives, with limited attention to risk control. Medical waste typically contains hazardous pathogens, posing a higher risk than general waste. Accidents during collection can severely endanger the health and safety of nearby residents, especially vulnerable groups such as the elderly and children. Therefore, considering the risks of medical waste collection is crucial. Some studies have implemented time window constraints to achieve timely waste transfer and reduce risks during collection. For example, Zhang et al. solved the multi-cycle medical waste collection vehicle routing problem considering time windows by establishing a MILP (Missing Principle of Dynamics) optimization model and applied it to a real-world case in Beijing. Similarly, Gao et al. proposed a comprehensive optimization framework to address the urban medical waste collection problem. They established a MILP model considering time windows and applied particle swarm optimization to solve problems of different scales. Eren and Tuzkaya used hospital safety scores as one of their objective functions. They developed a TSP-based model to solve the MWT problem in Istanbul and employed fuzzy objective programming to solve the multi-objective model.

[0005] Recently, researchers have begun to focus on infection control in the MWT process. Taslimi et al. addressed the problem of cyclical load-dependent CVRP, minimizing transportation and occupational risks. They introduced a decomposition-based heuristic algorithm and used a real-world case study from Dolj, Romania, to evaluate its performance. Shen et al. proposed a bi-level optimization model to minimize site selection costs, transportation costs, time window penalties, and transportation risks. Wang et al. incorporated infection risk and multiple disposal centers into the MWT process, using a susceptible infection model (SI model) to assess the final infected population after an incident. In 2018, Rabbani et al. proposed a MILP model for hazardous waste management based on LRP, reducing total cost and total transportation risk by considering heterogeneous vehicles. The same team added workload balancing constraints in 2021 to improve their initial research.

[0006] Although some existing research exists on the MWT problem, current techniques employ a single-level path structure, resulting in long transportation distances and low vehicle utilization, leading to low transportation efficiency. Furthermore, they lack consideration for the safety of facility locations (e.g., vulnerable groups near transfer centers), focusing solely on mitigating risks during transportation. Additionally, existing techniques primarily concentrate on developing multi-objective optimization algorithms, with limited exploration of real-world data scales; the amount of data from actual cases is no more than a few dozen, leading to an overestimation of the efficiency of technical solutions for handling massive amounts of real-world data. Currently, there is no existing technology that can simultaneously address these issues; therefore, developing new methods for solving the MWT problem is an important task in this field. Summary of the Invention

[0007] To address the problems of existing technologies, this invention provides a method and system for solving medical waste transportation schemes based on a two-layer optimization model.

[0008] A method for solving medical waste transportation schemes based on a two-level optimization model includes the following steps:

[0009] Step 1: Construct a two-level optimization model for solving the medical waste transportation problem. The two-level optimization model includes the following three stages:

[0010] The first phase involves determining the optimal location for the transit center.

[0011] The second phase involves planning the collection route from the collection center to the transfer center.

[0012] The third phase involves optimizing the transportation routes from the transshipment center to the processing center.

[0013] Step 2: Use the Gurobi optimizer to solve the problems in the first and second stages; use the adaptive neighborhood search algorithm to solve the problem in the third stage.

[0014] Preferably, the two-layer optimization model includes the following variables:

[0015] Safety score, used to assess safety based on location data of vulnerable population gathering points;

[0016] Infection risk is used to analyze and calculate the effective spread area of ​​the infection source along the path and the estimated number of exposed people along the path using the VanUldens box model.

[0017] A time window is used to limit the transportation time of medical waste, and the transportation time is set differently depending on whether the medical waste is infectious medical waste or ordinary medical waste.

[0018] Preferably, solving the problems in the first and second stages includes four objective functions, which are respectively considered as follows:

[0019] 1) Consider minimizing costs, including the construction costs of the transfer center and the total transportation costs from the transfer center to the collection center;

[0020] 2) Consider the geographical security of the transfer center construction, as well as the transportation distance from the transfer center to the collection center;

[0021] 3) Consider the distance between the transfer center and the processing center;

[0022] 4) Consider the total travel time between the transit center and the collection center.

[0023] Preferably, the two-layer optimization model includes the following constraints:

[0024] Each collection center is served by only one transfer center;

[0025] The total amount of medical waste generated by all collection centers served by a transfer center shall not exceed the processing capacity of that transfer center.

[0026] Any collection center will not be connected to other collection centers;

[0027] The number of transit centers is within a preset range;

[0028] Each collection center is visited at least once, and each transit center serves at least one collection center;

[0029] No subroutines appear;

[0030] The vehicle's load does not exceed its capacity;

[0031] The total distance from the transfer center to all collection centers it serves does not exceed the driving range of the vehicle.

[0032] Preferably, the problem in the third stage includes two objective functions, which are used to minimize the total time cost and minimize the risk of infection, respectively.

[0033] Preferably, the route model includes the following constraints:

[0034] The load on each vehicle shall not exceed its capacity;

[0035] Each collection center was visited and left once;

[0036] Each vehicle departs from the processing center;

[0037] Use time variables to eliminate sub-loops and ensure that the vehicle's route does not form a closed loop;

[0038] Define the relationship between the time a vehicle leaves a collection center and the time it departs from a subsequent collection center to ensure temporal continuity;

[0039] Ensure that the vehicles arrive at the transfer center no earlier than the transfer center's preparation time.

[0040] Preferably, in the two-level optimization model, in the upper level, a hierarchical method is used to determine the priority of the objectives; the solver first optimizes the objective with the highest priority, and then optimizes the next objective; in the lower level, a specific weight is assigned to each objective, transforming the multi-objective problem into a single-objective problem.

[0041] Preferably, the adaptive neighborhood search algorithm integrates the Pareto dominance sorting method within its framework; the adaptive neighborhood search algorithm employs the following removal and insertion operations: removal based on similar features, random removal, random sequence removal, worst-case risk-cost removal, regret repair, risk-cost greedy repair, and random repair.

[0042] The present invention also provides a system for implementing the above-mentioned solution method for medical waste transportation schemes based on a two-level optimization model, comprising:

[0043] The model building module is configured to build a two-level optimization model for solving the medical waste transportation problem, the two-level optimization model comprising the following three stages:

[0044] The first phase involves determining the optimal location for the transit center.

[0045] The second phase involves planning the collection route from the collection center to the transfer center.

[0046] The third phase involves optimizing the transportation routes from the transshipment center to the processing center.

[0047] The medical waste transportation solution module is configured to use the Gurobi optimizer to solve the problems in the first and second stages, and to use an adaptive neighborhood search algorithm to solve the problem in the third stage.

[0048] The present invention also provides a computer-readable storage medium storing: a computer program for implementing the above-described method for solving medical waste transportation schemes based on a two-layer optimization model, or a computer program for implementing the above-described system.

[0049] This invention employs a two-tier optimization model, first transporting medical waste from collection centers (CPs) to transfer centers (TCs), and then to treatment centers (DCs). The two-tier optimization model is then solved to obtain an optimized medical waste transportation scheme. The method of this invention has the following beneficial technical effects:

[0050] First, the adoption of a two-layer optimization model significantly improves the efficiency of medical waste transportation while reducing safety risks;

[0051] Second, the two-layer optimization model of this invention takes into account factors such as construction cost, transportation cost and infection risk, effectively solving the problems of algorithm complexity and complex real-world constraints.

[0052] Third, the optimized medical waste transportation scheme of this invention can enhance infection control throughout the entire medical waste management process (by quantifying the site safety of transfer centers) and ensure effective management of health risks during transportation.

[0053] Fourth, this invention uses real data from Chengdu and randomly generated instances for simulation to verify the model and demonstrate its effectiveness in solving large-scale problems and balancing multiple optimization objectives, including cost efficiency, transportation efficiency, and infection risk management.

[0054] In summary, the technical solution of this invention has excellent application prospects.

[0055] Obviously, based on the above description of the present invention, and according to common technical knowledge and conventional methods in the field, various other modifications, substitutions or alterations can be made without departing from the basic technical concept of the present invention.

[0056] The following detailed embodiments further illustrate the above-described content of the present invention. However, this should not be construed as limiting the scope of the present invention to the following examples. All technologies implemented based on the above-described content of the present invention fall within the scope of the present invention. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating Embodiment 1 of the present invention.

[0058] Figure 2 This is the preferred time window limiting method in Embodiment 1 of the present invention.

[0059] Figure 3 This refers to the performance difference in solving different comparison algorithms when focusing on the total distance in Embodiment 1 of the present invention.

[0060] Figure 4 This refers to the performance difference of different comparison algorithms in Embodiment 1 of the present invention when focusing on economic cost. Detailed Implementation

[0061] In the following examples and experimental cases, reagents and raw materials not specifically described are all commercially available products.

[0062] Example 1: A method and system for solving medical waste transportation schemes based on a two-level optimization model

[0063] The system in this embodiment includes:

[0064] The model building module is configured to build a two-level optimization model for solving the medical waste transportation problem, the two-level optimization model comprising the following three stages:

[0065] The first phase involves determining the optimal location for the transit center.

[0066] The second phase involves planning the collection route from the collection center to the transfer center.

[0067] The third phase involves optimizing the transportation routes from the transshipment center to the processing center.

[0068] The medical waste transportation solution module is configured to use the Gurobi optimizer to solve the problems in the first and second stages, and to use an adaptive neighborhood search algorithm to solve the problem in the third stage.

[0069] The specific process for solving medical waste transportation schemes using this system includes:

[0070] Step 1: Construct a two-level optimization model to solve the medical waste transportation problem, which involves first transporting medical waste from collection centers (CPs) to transfer centers (TCs), and then to treatment centers (DCs). The two-level optimization model includes the following three stages:

[0071] The first phase involves determining the optimal location for the transit center.

[0072] The second phase involves planning the collection route from the collection center to the transfer center.

[0073] The third phase involves optimizing the transportation routes from the transshipment center to the processing center.

[0074] Step 2, as follows Figure 1 As shown, the Gurobi optimizer is used to solve the problems in the first and second stages; the adaptive neighborhood search algorithm is used to solve the problem in the third stage.

[0075] The two-level optimization model includes the following variables:

[0076] Safety score, used to assess safety based on location data of vulnerable population gathering points;

[0077] Infection risk is used to analyze and calculate the effective spread area of ​​the infection source along the path and the estimated number of exposed people along the path using the VanUldens box model.

[0078] A time window is used to limit the transportation time of medical waste, and the transportation time is set differently depending on whether the medical waste is infectious or ordinary medical waste. For example, a preferred time window limitation method is as follows: Figure 2 As shown. TC 1 transports infectious medical waste (IMW), and TC 2 transports general medical waste (GMW). left These represent the earliest collection time of TC, which depends on the completion time of the first phase of collection; ST represents the actual start time of TC collection; t right This is the latest time that collection must be completed. Due to the contagiousness of IMW, its time window is much stricter than GMW's. Therefore, TC 2 can have later ST and t. right .

[0079] The solution to the problems in the first and second stages includes four objective functions, which are considered respectively:

[0080] 1) Consider minimizing costs, including the construction costs of the transfer center and the total transportation costs from the transfer center to the collection center;

[0081] 2) Consider the geographical security of the transfer center construction, as well as the transportation distance from the transfer center to the collection center;

[0082] 3) Consider the distance between the transfer center and the processing center;

[0083] 4) Consider the total travel time between the transit center and the collection center.

[0084] Specifically, the objective function is expressed as follows:

[0085]

[0086] Where G is a graph containing all the points in the problem (transfer centers, collection centers, processing centers), and i and j represent points in the graph. Let G be the set of all vertices formed by collection centers and transfer centers. Let CP represent the construction cost of each transfer center, p represent the fixed cost per kilometer traveled by a vehicle, and z represent the cost of each transfer center. ij This indicates whether collection center i needs to transport the goods to transfer center j. Indicates whether the first-layer collection vehicle k travels from point i to point j during the collection process, y i Indicates whether to select i as the transit center, d ij Let i be the distance from i to j, and let j be the score. i v is the security score for the transit center. ij Let represent the vehicle's speed from i to j. The objective function f1(x) aims to minimize the cost. f2(x) considers the geographical security of the transfer center construction and the transportation distance from the transfer center to the collection center. f3(x) minimizes the distance from the transfer center to the processing center. f4(x) minimizes the total travel time between the transfer center and the collection center.

[0087] The first and second stages of the bi-level optimization model include the following constraints:

[0088] 1. Each collection center is served by only one transit center, as shown below:

[0089]

[0090] 2. The total amount of medical waste generated by all collection centers served by a transfer center shall not exceed the processing capacity of that transfer center, as expressed in the following way:

[0091]

[0092] 3. Any collection center cannot be connected to other collection centers, as shown below:

[0093] z ij ≤y j

[0094] 4. The number of transit centers is within a preset range, which is expressed as follows:

[0095]

[0096] 5. Each collection center is visited at least once, and each transit center serves at least one collection center, as shown below:

[0097]

[0098] 6. No sub-routes (non-optimal or unnecessary route segments) are represented as follows:

[0099]

[0100] 7. The vehicle's load does not exceed its capacity, which is expressed as:

[0101]

[0102] 8. The total distance from the transfer center to all collection centers it serves does not exceed the driving range of the vehicle, as expressed in:

[0103]

[0104] Among them, Q i The weight (kg) of medical waste generated by the collection center, z ij This indicates whether collection center i needs to be transported to transfer center j, VT represents the processing capacity of the transfer center, and C represents the value of C. e L is the maximum load capacity of the vehicle. e For the vehicle's driving range, K e S is the first layer of transport vehicle assembly. t The set of collection centers serving the transit center t, s is S t Number of collection centers included.

[0105] The third stage (route model) includes two objective functions, f5(x) and f6(x), which are used to minimize the total time cost and minimize the contagion risk, respectively. The objective functions are as follows:

[0106]

[0107] Where, p fThis represents the fixed cost per kilometer traveled by a fuel-powered vehicle. Indicates whether the second-level transport vehicle k travels from point i to point j during the transport process, IP ij K represents the number of people directly affected when an accident occurs at road segment (i,j). f For the second layer of transport vehicles, V td This represents a set of transit centers and processing centers.

[0108] The constraint functions included in the third stage are as follows:

[0109] 1. Each transit center is visited and departed once, represented as follows:

[0110]

[0111] 2. The load on each vehicle shall not exceed its capacity, as expressed as:

[0112]

[0113] 3. Each vehicle departing from the processing center is represented as follows:

[0114]

[0115] 4. Define the relationship between the time a vehicle leaves a transfer center and the time it departs from a subsequent transfer center to ensure temporal continuity, expressed as:

[0116]

[0117] 5. A time window constraint is defined, which is expressed as follows:

[0118]

[0119] Where k is the serial number of the second-level transport vehicle, K f For the second layer of transport vehicles, Let G be the set of all vertices formed by transit centers. Indicates whether the second-level transport vehicle k travels from point i to point j during the transport process, C f Where n is the maximum load weight of the vehicle, and h is the sequence number of the collection point. This indicates whether the second-level transport vehicle k travels from point i to point n+1 during the transport process. This indicates whether the second-level transport vehicle k travels from point i to point h during the transport process. This indicates whether the second-level transport vehicle k travels from point h to point j during the transport process. Indicate whether the second-level transport vehicle k travels from the processing center to point j during the transport process. Let t be the time when vehicle k arrives at point i and begins service.ij Let a be the travel time of the vehicle from point i to point j. i The earliest available service time for the collection center.

[0120] To enable the nonlinear equations in the constraints to be solved using linear programming, linearization techniques are used to transform the equations into linear equations, and a suitable M is introduced to control whether the constraint conditions are triggered.

[0121] In the bi-level optimization model, a hierarchical method is used to determine the priority of objectives in the upper level; the solver first optimizes the objective with the highest priority, and then optimizes the next objective; in the lower level, a specific weight is assigned to each objective, transforming the multi-objective problem into a single-objective problem.

[0122] The expression for the lower-level single-objective function is:

[0123]

[0124] Where a1 and a2 are the weights for different objectives, p f For the vehicle's operating costs, As decision variables, The speed of travel between two points, serv j For service time, IP ij The population density between the two points.

[0125] In step 2, the Gurobi optimizer is used to solve the problem at the upper level (solving the first and second stage problems). To demonstrate the effectiveness of the proposed method, this invention uses the widely used K-means clustering algorithm as the benchmark method for determining the location of the transshipment center and compares the results with those obtained by the precise algorithm.

[0126] When solving the third stage problem at the lower level, the Adaptive Neighborhood Search Algorithm (ALNS) integrates the Pareto dominance sorting method within its framework. The ALNS employs the following removal and insertion operations: Shaw removal, Random Removal, Random Sequence Removal, Risk-Cost Worst Removal, Regret Repair, Risk-Cost Greedy Repair, and Random Repair.

[0127] The relevance measurement formula for Shaw removal is as follows:

[0128] R ij =A·d ij +B·|a i -a j |+C·|e i -e j |+D·|Q i -Q j |+E·|l ik -l jk |

[0129] TC i and TC j represent transit center i and transit center j, respectively. ij a represents the distance between TC i and TC j. i Indicates the earliest start time of TC i, e i Q represents the latest end time of TC i. i Indicates the amount of medical waste in TC i, l ik This indicates the weight of infectious medical waste carried after visiting TC i, a j Indicates the earliest start time of TC j, e j Q represents the latest end time of TC j. j Indicates the amount of medical waste in TC j, l jk This represents the weight of infectious medical waste carried after visiting TC j. A, B, C, D, and E are constants representing the importance coefficients for each evaluation criterion.

[0130] The adaptive neighborhood search algorithm improves the results using a local exploration method after each iteration. The algorithm iterates through each route, reverses the order of the locations along the way, and then calculates the infection risk of the reversed path that fits the time window. If a path with a lower infection risk is found, the result is updated.

[0131] The technical solution of the present invention will be further illustrated by the following experiments.

[0132] Experiment Example 1: Verification of the superiority and feasibility of the method

[0133] I. Experimental Methods The following benchmark tests were conducted to verify the superiority and feasibility of the method.

[0134] This invention tested six algorithm combinations: M-IALNS, M-MIP, M-ACO, K-IALNS, K-MIP, and K-ACO. Real data from Wuhou District of Chengdu, Sichuan Province, and the entire city of Chengdu, along with randomly generated data, were used to solve the problems for comparison.

[0135] The comparison algorithm uses the same model as the two-layer optimization model in Example 1, the difference being the solution algorithm in step 2. The comparison algorithm is explained below:

[0136] (1) M-IALNS (Algorithm of Example 1): For the upper-level problem, Gurobi is used to solve it, with a time limit of 3600 seconds. The lower-level problem is solved using the adaptive neighborhood search algorithm (IALNS algorithm), with a maximum number of iterations of 2000 and an early stopping criterion of 50 iterations.

[0137] (2) M-MIP: Both upper and lower level problems are solved using Gurobi's MIP model. The time limit for solving each level is set to 3600 seconds.

[0138] (3) M-ACO: Similar to M-MIP, the upper-level problem is solved using the MIP model solved by Gurobi. The lower-level problem is handled using the ACO (Ant Colony Optimization) algorithm. In this study, the number of iterations for ACO was set to 2000.

[0139] (4) K-IALNS: The upper-level problem is handled using the restricted K-means clustering method. To mitigate the sensitivity of K-means to the initial solution, the algorithm is repeated five times, and the solution with the lowest cost is selected as the input for the next level. The lower-level problem is solved using the IALNS algorithm, with a maximum of 2000 iterations and an early stopping criterion set at 50 iterations.

[0140] (5) K-MIP: Similar to K-IALNS, the upper-level problem is solved using a restricted K-means clustering method. However, the lower-level problem is solved using Gurobi, with a time limit of 3600 seconds for each level.

[0141] (6) K-ACO: Similar to K-IALNS, the upper-level problem is solved using a restricted K-means clustering method. However, the lower-level problem is handled by the ACO algorithm.

[0142] Experimental environment:

[0143] The numerical experiments were conducted on an Ubuntu 20.04 platform using Gurobi 11.0 and Python 3.8, running on an Intel(R) Core(TM) i9-14900K 3.20GHz processor and 64GB of memory.

[0144] Data generation:

[0145] The size of the collection center determines the amount of medical waste generated. There are three collection centers with fixed medical waste volumes of (200, 80, 50), in kilograms. The construction cost and volume of each transfer center are (300, 1000), in CNY / kg. The first tier of collection vehicles uses new energy vehicles with a range and load capacity of (500, 1000), in km / kg. The second tier uses fuel-powered trucks with a load capacity of 3000, in kilograms. The transportation costs for new energy vehicles and fuel-powered trucks are 4 CNY / km and 10 CNY / km, respectively. The fixed labor cost per vehicle is 500 CNY.

[0146] II. Experimental Results

[0147] Actual data results:

[0148] To evaluate the proposed M-IALNS algorithm, we used real-world data of varying scales to assess its performance. This included a real-world example focusing on 60 collection centers in Wuhou District, and a real-world example in Chengdu focusing on 700 collection centers.

[0149] Table 1 Results from 60 Collection Centers

[0150] Target M-IALNS M-MIP K-IALNS K-MIP Total driving distance (km) 165.33 165.33 183.56 183.56 Number of transshipment centers 6 6 6 52 Safety score 0.62 0.57 0.57 14.13 Risk of infection 25.59 26.96 26.96 156.51 Total cost (CNY) 8408.68 8408.68 8499.43 8499.43 Algorithm running time (s) 0.29 0.52 0.51 0.72

[0151] We conducted a case study in Wuhou District, which includes 60 collection centers. The total weight of medical waste in the case was 5,110 kg, of which 1,080 kg was infectious medical waste (IMW) and 4,030 kg was general medical waste (GMW). The results (see Table 1) show that the M-IALNS and M-MIP algorithms provide the same solution, but M-IALNS is significantly more efficient, reducing the computation time by approximately 44% compared to M-MIP. K-IALNS and K-MIP show certain shortcomings compared to M-IALNS and M-MIP algorithms on all objectives.

[0152] Table 2 Results from 700 Collection Centers

[0153] Target M-IALNS M-MIP K-IALNS K-MIP Total driving distance (km) 4245.96 4335.54 6557.684 6655.41 Number of transshipment centers 52 52 49 49 Safety score 14.13 14.13 8.9 8.9 Risk of infection 156.51 219.03 164.7576 179.15 Total cost (CNY) 62860.6 63756.4 66350.8 67328.06 Algorithm running time (s) 3700.03 7200 208.9 3709.68

[0154] As shown in Table 2, the proposed M-IALNS algorithm significantly outperforms the other three algorithms across multiple performance metrics. Compared to K-IALNS and K-MIP, M-IALNS significantly reduces the risk of infection and achieves the lowest cost. Compared to M-MIP, M-IALNS not only performs better in terms of total distance and cost but also reduces the risk of infection by approximately 29%, making it more robust in terms of public health outcomes. Furthermore, M-IALNS has a significantly shorter running time than M-MIP and also outperforms K-MIP. Although K-IALNS has the shortest running time, the results indicate that spending more time optimizing upper-level decisions can significantly improve outcomes. For example, the total travel distance of the K-IALNS method is approximately 6,558 km, more than 50% longer than the proposed M-IALNS algorithm. In addition, the proposed algorithm shows a significant advantage in selecting transit center locations, with an average safety score of approximately 0.27 (14.13 / 52) for TCs, compared to 0.18 (8.9 / 49) for K-IALNS.

[0155] Random data results:

[0156] To evaluate the robustness of the proposed M-IALNS algorithm, we tested it on a randomly generated dataset and compared its performance with two additional algorithms (M-ACO and K-ACO). In this dataset, the coordinates of the collection center were randomly generated within an X and Y range of 0 to 100, while the coordinates of the processing center were fixed at (40, 50). The quantities of medical waste were divided into three levels: 200 kg, 80 kg, and 50 kg, distributed at proportions of 15%, 45%, and 40%, respectively. In the randomized test instance, we examined two objectives: total distance and total cost. Total distance includes the upper-level transport distance and the lower-level path distance, while total cost includes the construction cost of the transfer center, vehicle fixed costs, and transportation costs.

[0157] Based on 14 experimental instances of varying scales, we calculated the performance gap between solutions. These instances focused on two key objectives: economic cost and total distance, as shown below. Figure 3 and Figure 4As shown, M-IALNS significantly outperforms other algorithms in these metrics. On average, M-IALNS reduces economic costs by 4.45% and transportation distance by 43.59%. More specifically, compared to the other five algorithms, M-IALNS reduces total distance by up to 110.38% and total cost by up to 13.77%. Furthermore, M-IALNS demonstrates consistent superiority in both upper-level and lower-level problems. In upper-level problems, the exact algorithms (M-IALNS, M-MIP, and M-ACO) outperform clustering-based methods (K-IALNS, K-MIP, and K-ACO). In lower-level problems, ALNS demonstrates better cost-effectiveness compared to ACO and achieves the optimal solution in half of the instances, surpassing MIP. Moreover, as the instance size increases, the performance gap between M-IALNS and other algorithms in terms of total path distance becomes more significant.

[0158] As can be seen from the above comparison, the algorithm (M-IALNS) provided by this invention has the best solution results compared with other algorithm combinations, and the algorithm has low power consumption, high running efficiency and high robustness.

[0159] As can be seen from the above embodiments and experimental examples, this invention constructs a two-layer optimization model to solve the problem of medical waste transportation schemes, comprehensively considering site selection costs (construction and transportation costs) and infectious disease risks. This model effectively addresses the complexity of the algorithm and real-world constraints by handling issues such as transportation costs, time windows, and accident impacts. Therefore, this invention has excellent application prospects.

Claims

1. A method for solving medical waste transportation schemes based on a two-level optimization model, characterized in that, Includes the following steps: Step 1: Construct a two-level optimization model for solving the medical waste transportation problem. The two-level optimization model includes the following three stages: The first phase involves determining the optimal location for the transit center. The second phase involves planning the collection route from the collection center to the transfer center. The third phase involves optimizing the transportation routes from the transshipment center to the processing center. Step 2: Use the Gurobi optimizer to solve the problems in the first and second stages; use the adaptive neighborhood search algorithm to solve the problem in the third stage. The two-level optimization model includes the following variables: Safety score, used to assess safety based on location data of vulnerable population gathering points; Infection risk is used to analyze and calculate the effective spread area of ​​the infection source along the path and the estimated number of exposed people along the path using the VanUldens box model. A time window is used to limit the transportation time of medical waste, and the transportation time is set differently depending on whether the medical waste is infectious medical waste or ordinary medical waste; The problem to be solved in the third stage includes two objective functions, which are used to minimize the total time cost and minimize the risk of infection, respectively. In the bi-level optimization model, at the upper level, a hierarchical method is used to determine the priority of the objectives; the solver first optimizes the objective with the highest priority, and then optimizes the next objective; at the lower level, a specific weight is assigned to each objective, transforming the multi-objective problem into a single-objective problem. The adaptive neighborhood search algorithm integrates the Pareto dominance sorting method within its framework; the adaptive neighborhood search algorithm employs the following removal and insertion operations: removal based on similar features, random removal, random sequence removal, worst-case risk-cost removal, regret repair, risk-cost greedy repair, and random repair.

2. The method for solving medical waste transportation schemes based on a two-level optimization model according to claim 1, characterized in that: The solution to the problems in the first and second stages includes four objective functions, which are considered respectively: 1) Consider minimizing costs, including the construction cost of the transfer center and the total transportation cost from the transfer center to the collection center. 2) Consider the geographical security of the transfer center construction, as well as the transportation distance from the transfer center to the collection center; 3) Consider the distance between the transfer center and the processing center; 4) Consider the total travel time between the transit center and the collection center.

3. The method for solving medical waste transportation schemes based on a two-level optimization model according to claim 1, characterized in that: The two-level optimization model includes the following constraints: Each collection center is served by only one transfer center; The total amount of medical waste generated by all collection centers served by a transfer center shall not exceed the processing capacity of that transfer center. Any collection center will not be connected to other collection centers; The number of transit centers is within a preset range; Each collection center is visited at least once, and each transit center serves at least one collection center; No subroutines appear; The vehicle's load does not exceed its capacity; The total distance from the transfer center to all collection centers it serves does not exceed the driving range of the vehicle.

4. The method for solving medical waste transportation schemes based on a two-level optimization model according to claim 1, characterized in that: The route model includes the following constraints: The load on each vehicle shall not exceed its capacity; Each collection center was visited and left once; Each vehicle departs from the processing center; Use time variables to eliminate sub-loops and ensure that the vehicle's route does not form a closed loop; Define the relationship between the time a vehicle leaves a collection center and the time it departs from a subsequent collection center to ensure temporal continuity; Ensure that the vehicles arrive at the transfer center no earlier than the transfer center's preparation time.

5. A system for implementing the solution method for medical waste transportation schemes based on a two-level optimization model as described in any one of claims 1-4, characterized in that, include: The model building module is configured to build a two-level optimization model for solving the medical waste transportation problem, the two-level optimization model comprising the following three stages: The first phase involves determining the optimal location for the transit center. The second phase involves planning the collection route from the collection center to the transfer center. The third phase involves optimizing the transportation routes from the transshipment center to the processing center. The medical waste transportation solution module is configured to use the Gurobi optimizer to solve the problems in the first and second stages, and to use an adaptive neighborhood search algorithm to solve the problem in the third stage.

6. A computer-readable storage medium, characterized in that, It stores: a computer program for implementing the solution method of medical waste transportation scheme based on the two-layer optimization model as described in any one of claims 1-4, or a computer program for implementing the system described in claim 5.

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