Medical waste transportation scheme solving method and system based on double-layer optimization model

Abstract

The invention belongs to the technical field of intelligent logistics, and particularly relates to a medical waste transportation scheme solving method and system based on a double-layer optimization model. The method comprises the following steps that 1, a double-layer optimization model used for solving the medical waste transportation problem is constructed, and the double-layer optimization model comprises the following three stages that in the first stage, the optimal position of a transfer center is determined; in the second stage, a collection route from the collection center to the transfer center is planned; in the third stage, the transportation route from the transfer center to the processing center is optimized; 2, solving the problems of the first stage and the second stage by adopting a Gurobi optimizer; and solving the problem of the third stage by adopting a self-adaptive neighborhood search algorithm. According to the model, the site selection cost and the infection risk are comprehensively considered, and the complexity of the algorithm and the limiting conditions of the real world are effectively dealt with. Therefore, the method has a good application prospect in solving the medical waste transportation problem.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent logistics, and specifically relates to a method and system for solving a medical waste transportation plan based on a double-layer optimization model. Background Art

[0002] With urbanization, population growth and the impact of the epidemic, medical waste has increased significantly, and its collection and treatment has become the most urgent need and challenge in public services in today's society. Medical waste management (MWM) aims to provide efficient, economical and environmentally friendly solutions for waste treatment. It usually includes three key steps: collection and separation, transportation to the treatment site, and final treatment.

[0003] The transportation phase, often referred to as medical waste transportation (MWT), can be formulated as a routing problem. Most existing studies consider waste disposal as a single-level routing problem: vehicles depart from the treatment center, collect waste from medical institutions, and return to the treatment center. However, another more promising strategy is to establish temporary transfer centers at medical institutions, forming a two-level routing structure: waste is first transported from medical institutions to transfer centers, and then from these centers to treatment centers. By optimizing the paths in a two-level manner, the distance of MWT can be shortened, thereby reducing transportation costs and risks. The two-level routing optimization of medical waste can be regarded as a location-route problem (LRP). LRP is an NP-hard combinatorial optimization problem that combines the decisions of facility location and routing. Many problems from various industries can be classified as LRP, including green logistics, post-disaster relief distribution, battery replacement optimization, and so on. In recent years, LRP has been developed to consider not only the basic optimization of location and routing, but also various real-life constraints such as time windows, vehicle capacity, and vehicle types.

[0004] Most LRP studies on MWT focus only on economic objectives, with limited attention to risk control. Medical waste usually contains dangerous pathogens and has higher risks than general waste. Once an accident occurs during the collection process, it will seriously endanger the health and safety of nearby residents, especially vulnerable groups such as the elderly and children. Therefore, it is important to consider the risks of medical waste collection. Some studies have achieved timely transfer of waste through time window constraints to reduce the risks in the collection process. For example, Zhang et al. solved the multi-period medical waste recycling vehicle routing problem considering time windows by establishing an MILP optimization model and applied it to a real case in Beijing. Similarly, Gao et al. proposed an integrated optimization framework to solve the urban medical waste recycling problem. They established an MILP model considering time windows and applied the particle swarm optimization algorithm 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 adopted a fuzzy goal programming method to solve the multi-objective model.

[0005] Only recently have researchers begun to focus on infection control during the MWT process. Taslimi et al. addressed the problem of periodic load-dependent CVRP to minimize transportation and occupational risks. They introduced a decomposition-based heuristic algorithm and used a real case study in Dolj, Romania to evaluate the algorithm performance. Shen et al. proposed a two-level optimization model to minimize site selection cost, transportation cost, time window penalty, and transportation risk. Wang et al. incorporated infection risk and multiple disposal centers into the MWT process and used the susceptible-infected model (SI model) to evaluate the final infected population after an accident. Rabbani et al. proposed an LRP-based MILP model for hazardous waste management in 2018, which reduced the 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 there are some existing studies on the MWT problem, the existing technology uses a single-level path structure, with long transportation distances and low vehicle utilization, resulting in low transportation efficiency; and lacks consideration of the safety of facility locations (for example, vulnerable groups near transfer centers), and only focuses on reducing the risks of the transportation process; in addition, the existing technology mainly focuses on the mining of multi-objective optimization algorithms, and the exploration of the scale of real-world data is limited. The amount of data from actual cases does not exceed dozens, resulting in an overestimation of the efficiency of technical solutions for the huge amount of real data. There is currently a lack of existing technology that can solve these problems at the same time. Therefore, developing new methods for solving MWT problems is an important topic in this field. Summary of the invention

[0007] In view of the problems of the prior art, the present invention provides a method and system for solving a medical waste transportation plan based on a double-layer optimization model.

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

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

[0010] In the first stage, the optimal location of the transshipment center is determined;

[0011] In the second stage, the collection routes from the collection centers to the transfer centers are planned;

[0012] In the third phase, the transportation routes from the transshipment center to the processing center are optimized;

[0013] Step 2, using the Gurobi optimizer to solve the problems of the first and second stages; using an adaptive neighborhood search algorithm to solve the problems of the third stage.

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

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

[0016] Infection risk, which is used to calculate the effective diffusion area of ​​the infection source along the path and the estimated number of exposed people along the path through the VanUldens box model analysis;

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

[0018] Preferably, the solving of the problems in the first stage and the second stage includes four objective functions, which are respectively used to consider:

[0019] 1) Consider minimizing the cost, which includes the construction cost of the transshipment center and the total transportation cost from the transshipment center to the collection center);

[0020] 2) Consider the geographical security of the transshipment center construction and the transportation distance from the transshipment center to the collection center;

[0021] 3) Consider the distance from the transfer center to the processing center;

[0022] 4) Consider the total travel time between the transfer 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 does not exceed the processing capacity of the transfer center;

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

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

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

[0029] No subroutes appear;

[0030] The vehicle is not loaded beyond its capacity;

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

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

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

[0034] Each vehicle is not loaded more than 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-cycles and ensure that the vehicle's route does not form a closed loop;

[0038] Define the link between the time a vehicle leaves one collection center and the time it departs from the subsequent collection center, ensuring temporal continuity;

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

[0040] Preferably, in the two-layer optimization model, at the upper level, a hierarchical approach is used to prioritize the objectives; the solver first optimizes the highest priority objective and then optimizes the next objective; at the lower level, a specific weight is assigned to each objective, converting the multi-objective problem into a single-objective problem.

[0041] Preferably, the Pareto dominance sorting method is integrated into the framework of the adaptive neighborhood search algorithm; the adaptive neighborhood search algorithm uses the following removal and insertion operations: similar feature-based removal, random removal, random sequence removal, risk-cost worst removal, regret repair, risk-cost greedy repair, and random repair.

[0042] The present invention also provides a system for implementing the above-mentioned method for solving the medical waste transportation scheme based on the double-layer optimization model, comprising:

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

[0044] In the first stage, the optimal location of the transshipment center is determined;

[0045] In the second stage, the collection routes from the collection centers to the transfer centers are planned;

[0046] In the third phase, the transportation routes from the transshipment center to the processing center are optimized;

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

[0048] The present invention also provides a computer-readable storage medium, on which is stored: a computer program for implementing the above-mentioned method for solving the medical waste transportation plan based on the double-layer optimization model, or a computer program for implementing the above-mentioned system.

[0049] The present invention adopts a two-layer optimization model, that is, the medical waste is first transported from the collection center (CPs) to the transfer center (TCs), and then transported to the treatment center (DCs), and the two-layer optimization model is solved to obtain an optimized medical waste transportation plan. According to the method of the present invention, the following beneficial technical effects are achieved:

[0050] First, the two-layer optimization model was adopted to significantly improve the efficiency of medical waste transportation while reducing safety risks;

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

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

[0053] Fourth, we used real data from Chengdu and randomly generated examples for simulation to validate the model, demonstrating 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 the present invention has good application prospects.

[0055] Obviously, according to the above contents of the present invention, in accordance with common technical knowledge and customary means in the art, without departing from the above basic technical ideas of the present invention, other various forms of modification, replacement or change may be made.

[0056] The above contents of the present invention are further described in detail below through specific implementation methods in the form of embodiments. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following examples. All technologies realized based on the above contents of the present invention belong to the scope of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a schematic diagram of the process of Example 1 of the present invention.

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

[0059] Figure 3 This is the difference in algorithm solving performance when focusing on the total distance among different comparison algorithms in Example 1 of the present invention.

[0060] Figure 4 This is the difference in algorithm solving performance when focusing on economic cost among different comparison algorithms in Example 1 of the present invention. DETAILED DESCRIPTION

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

[0062] Example 1 Method and system for solving medical waste transportation scheme based on double-layer optimization model

[0063] The system of this embodiment includes:

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

[0065] In the first stage, the optimal location of the transshipment center is determined;

[0066] In the second stage, the collection routes from the collection centers to the transfer centers are planned;

[0067] In the third phase, the transportation routes from the transshipment center to the processing center are optimized;

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

[0069] The method flow for solving the medical waste transportation plan through this system specifically includes:

[0070] Step 1: construct a two-level optimization model for solving the problem of medical waste transportation, that is, 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] In the first stage, the optimal location of the transshipment center is determined;

[0072] In the second stage, the collection routes from the collection centers to the transfer centers are planned;

[0073] In the third phase, the transportation routes from the transshipment center to the processing center are optimized;

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

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

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

[0077] Infection risk, which is used to calculate the effective diffusion area of ​​the infection source along the path and the estimated number of exposed people along the path through the VanUldens box model analysis;

[0078] The time window is used to limit the transportation time of medical waste, and the transportation time is set differently according to whether the medical waste is infectious medical waste or ordinary medical waste. For example, a preferred time window limitation method is as follows: Figure 2 As shown. Among them, TC 1 transports infectious medical waste (IMW) and TC 2 transports general medical waste (GMW). left They represent the earliest collection time of TC, which depends on the completion time of the first stage of collection; ST represents the actual start time of TC collection; t right The latest time that collection must be completed. Due to the infectiousness of IMW, its time window is much stricter than GMW. Therefore, TC 2 can have a later ST and t right .

[0079] The problem of solving the first and second stages includes four objective functions, which are respectively used to consider:

[0080] 1) Consider minimizing the cost, which includes the construction cost of the transshipment center and the total transportation cost from the transshipment center to the collection center);

[0081] 2) Consider the geographical security of the transshipment center construction and the transportation distance from the transshipment center to the collection center;

[0082] 3) Consider the distance from the transfer center to the processing center;

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

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

[0085]

[0086] Where G is a graph containing all the points in the problem (transshipment center, collection center, processing center), i and j represent points in the graph, is the set of vertices formed by all collection centers and transfer centers on the graph G. CP represents the construction cost of each transfer center, p represents the fixed cost per kilometer of vehicle travel, and z ij Indicates whether collection center i needs to transport to transfer center j, Indicates whether the first-level collection vehicle k goes from i to point j, y during the collection process i Indicates whether i is selected as the transshipment center, d ij is the distance from i to j, score i is the safety score of the transshipment center, v ij represents the speed of vehicle from i to j. The objective function f1(x) aims to minimize the cost. f2(x) considers the geographical security of the transshipment center construction and the transportation distance from the transshipment center to the collection center. f3(x) minimizes the distance from the transshipment center to the processing center. f4(x) minimizes the total travel time between the transshipment center and the collection center.

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

[0088] 1. Each collection center is served by only one transfer center, which is expressed as:

[0089]

[0090] 2. The total amount of medical waste generated by all collection centers served by a transfer center does not exceed the processing capacity of the transfer center, which is expressed as:

[0091]

[0092] 3. Any collection center will not be connected to other collection centers, which is expressed as:

[0093] z ij ≤y j

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

[0095]

[0096] 5. Each collection center is visited at least once, and each transfer center serves at least one collection center, which is expressed as:

[0097]

[0098] 6. No sub-routes (non-optimal or unnecessary route segments) appear, which is represented by:

[0099]

[0100] 7. The load of the vehicle 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, which is expressed as:

[0103]

[0104] Among them, Q i is the weight of medical waste generated by the collection center (kg), z ij indicates whether collection center i needs to transport to transshipment center j, VT represents the processing capacity of the transshipment center, and C e is the maximum load capacity of the vehicle, L e is the vehicle’s cruising range, K e is the first-layer transport vehicle set, S t The collection center set serving the transfer center t, s is S t The number of collection centers included.

[0105] The third stage (route model) contains two objective functions, f5(x) and f6(x), which are used to consider minimizing the total time cost and minimizing the risk of infection respectively. The objective functions included are as follows:

[0106]

[0107] Among them, p frepresents the fixed cost per kilometer of fuel vehicle travel, Indicates whether the second-level transport vehicle k travels from point i to point j during the transport process, IP ij represents the number of people directly affected when an accident occurs on road section (i, j), K f is the second-layer transport vehicle set, V td Represents a collection of transshipment centers and processing centers.

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

[0109] 1. Each transit center is visited and left once, which is represented by:

[0110]

[0111] 2. The load of each vehicle does not exceed its capacity, which is expressed as:

[0112]

[0113] 3. Each vehicle departs from the processing center, which is represented by:

[0114]

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

[0116]

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

[0118]

[0119] Among them, k is the serial number of the second-layer transport vehicle, K f Assemble the transport vehicles for the second level. is the set of vertices formed by all transit centers on graph G, Indicates whether the second-layer transport vehicle k travels from point i to point j during the transport process, C f is the maximum load weight of the vehicle, n and h are the serial numbers of the collection points, Indicates whether the second-layer transport vehicle k travels from point i to point n+1 during the transport process. Indicates whether the second-layer transport vehicle k goes from point i to point h during the transport process, Indicates whether the second-layer transport vehicle k goes from h to point j during the transport process, indicates whether the second-level transport vehicle k is transported from the processing center to point j during the transportation process. is the time when vehicle k arrives at point i and starts serving, tij is the travel time of the vehicle from point i to point j, a i The earliest available service time of the collection center.

[0120] In order to solve the nonlinear equations in the constraints by linear programming, the linearization technique is used to transform the equations into linear ones, and the appropriate M is introduced to control whether the constraints are triggered.

[0121] In the two-layer optimization model, at the upper level, a hierarchical approach is used to prioritize the objectives; the solver optimizes the highest priority objective first and then the next objective; at the lower level (lower layer), a specific weight is assigned to each objective, converting the multi-objective problem into a single-objective problem.

[0122] The expression of the lower single objective function is:

[0123]

[0124] Among them, a1 and a2 are the weights of different targets, p f is the vehicle’s driving cost, is the decision variable, is the driving speed between two points, serv j is the service time, IP ij is the crowd density between two points.

[0125] In step 2, at the upper level (solving the first and second stage problems), the Gurobi optimizer is used to solve. In order to prove the effectiveness of the proposed method, the widely used K-means clustering algorithm is used as a benchmark method for determining the location of the transfer center, and the results are compared with those obtained by the precise algorithm.

[0126] When solving the third stage problem at the lower level, the Pareto dominance sorting method is integrated into the framework of the adaptive neighborhood search algorithm (ALNS). The adaptive neighborhood search algorithm uses 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] Among them, the correlation measurement formula for similar feature removal (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 transshipment center i and transshipment center j, d ij represents the distance between TC i and TC j, a i represents the earliest start time of TC i, e i represents the latest end time of TC i, Q i represents the amount of medical waste in TC i, l ik represents the weight of infectious medical waste carried after visiting TC i, a j represents the earliest start time of TC j, e j represents the latest end time of TC j, Q j represents the amount of medical waste in TC j, l jk represents the weight of infectious medical waste carried after visiting TC j, A, B, C, D and E are constants, representing the important coefficient of each evaluation criterion.

[0130] The adaptive neighborhood search algorithm uses a local exploration method to improve the results after each iteration. The algorithm will traverse each route in turn, reverse the order of the locations along the route, and then calculate the infection risk of the reversed path that meets the time window. If a lower infection risk path appears, the result will be updated.

[0131] The technical solution of the present invention is further illustrated by experiments below.

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

[0133] 1. Experimental Methods,The following benchmark tests were conducted to verify the superiority and,feasibility of the method.

[0134] The present invention tests six algorithm combinations, namely, M-IALNS, M-MIP, M-ACO, K-IALNS, K-MIP and K-ACO, and uses real data from Wuhou District and the entire Chengdu City of Sichuan Province and randomly generated data to solve and compare.

[0135] The model of the comparison algorithm is the same as the two-layer optimization model of Example 1, except that the solution algorithm of step 2 is different. The comparison algorithm is described as follows:

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

[0137] (2) M-MIP: Both the 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 problem is solved using the MIP model solved by Gurobi. The lower problem is processed using the ACO (Ant Colony Optimization) algorithm. In this study, the number of iterations of ACO is set to 2000.

[0139] (4) K-IALNS: The upper level problem is solved 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 number of iterations of 2000 and an early stopping criterion set to 50 iterations.

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

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

[0142] Experimental environment:

[0143] The numerical experiments are performed 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, (200, 80, 50), in kilograms. The construction cost and volume of each transfer center are (300, 1000), in (CNY, kg). The first-tier new energy collection vehicle range and load capacity are (500, 1000), in (km, kg). The second-tier fuel transport truck has a load capacity of 3000, in kilograms. The vehicle transportation costs for new energy vehicles and fuel trucks are 4CNY / km and 10CNY / km, respectively. The fixed labor cost per vehicle is 500CNY.

[0146] 2. Experimental Results

[0147] Real data results:

[0148] To evaluate the proposed M-IALNS algorithm, we use real data of different scales to assess its performance, including an example real case with 60 collection centers focusing on Wuhou District, and a real case with 700 collection centers focusing on Chengdu City.

[0149] Table 1 Results of 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 is 5,110 kg, of which 1,080 kg is infectious medical waste (IMW) and 4,030 kg is general medical waste (GMW). The results show (see Table 1) that M-IALNS and M-MIP algorithms provide the same solution, but M-IALNS is significantly more efficient, with a computational time reduction of about 44% compared to M-MIP. K-IALNS and K-MIP show some gaps in all objectives compared to M-IALNS and M-MIP algorithms.

[0152] Table 2 Results of 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 in multiple performance indicators. Compared with K-IALNS and K-MIP, M-IALNS significantly reduces the risk of infection and achieves the lowest cost. Compared with M-MIP, M-IALNS not only performs better in total distance and cost, but also reduces the risk of infection by about 29%, making it more robust in terms of public health outcomes. In addition, the running time of M-IALNS is significantly shorter than that of M-MIP, while also outperforming K-MIP. Although K-IALNS has the shortest running time, the results show that spending more time optimizing upper-level decisions can significantly improve the results. For example, the total driving distance of the K-IALNS method is about 6,558 kilometers, which is more than 50% more than the proposed M-IALNS algorithm. In addition, the proposed algorithm shows a clear advantage in selecting the location for the transfer center, with an average safety score of about 0.27 (14.13 / 52) for TCs, while that of K-IALNS is 0.18 (8.9 / 49).

[0155] Random data results:

[0156] To evaluate the robustness of the proposed M-IALNS algorithm, we tested it using a randomly generated dataset and compared its performance with two additional algorithms (M-ACO and K-ACO). In this dataset, the coordinate points of the collection center are randomly generated in the region with an X and Y range of 0 to 100, and the coordinates of the treatment center are fixed to (40,50). The amount of medical waste is divided into three levels: 200 kg, 80 kg, and 50 kg, distributed in proportions of 15%, 45%, and 40%, respectively. In the random test instance, we examined two objectives: total distance and total cost. The total distance includes the transportation distance of the upper layer and the path distance of the lower layer, and the total cost includes the construction cost of the transfer center, the vehicle fixed cost, and the transportation cost.

[0157] We calculate the performance gap between solutions based on 14 experimental examples of different sizes, which focus on two key objectives: economic cost and total distance. Figure 3 and Figure 4As shown in the figure. M-IALNS significantly outperforms other algorithms in these indicators. On average, M-IALNS reduces the economic cost by 4.45% and the transportation distance by 43.59%. More specifically, compared with the other five algorithms, M-IALNS reduces the total distance by up to 110.38% and the total cost by up to 13.77%. In addition, M-IALNS shows consistent advantages in both the upper and lower level problems. In the upper level problem, the results of the exact algorithms (M-IALNS, M-MIP, and M-ACO) are better than those of the clustering-based methods (K-IALNS, K-MIP, and K-ACO). In the lower level problem, ALNS shows better cost-effectiveness than ACO and outperforms MIP in obtaining the best solution in half of the instances. In addition, as the instance size increases, the performance gap between M-IALNS and other algorithms in total path distance becomes more significant.

[0158] Through the above comparison, it can be seen that the algorithm (M-IALNS) provided by the present invention has the best solution result compared with other algorithm combinations, and the algorithm has low algorithm consumption, high operation efficiency and high robustness.

[0159] Through the above embodiments and experimental examples, it can be seen that the present invention constructs a two-layer optimization model to solve the problem of solving the medical waste transportation plan, and comprehensively considers the site selection cost (construction and transportation cost) and the risk of infection. The model effectively copes with the complexity of the algorithm and the constraints of the real world by dealing with problems such as transportation cost, time window and accident impact. Therefore, the present invention has a good application prospect.

Claims

1. A method for solving medical waste transportation scheme based on a two-layer optimization model, characterized in that: The steps include: Step 1: construct a two-level optimization model for solving the problem of medical waste transportation. The two-level optimization model includes the following three stages: In the first stage, the optimal location of the transshipment center is determined; In the second stage, the collection routes from the collection centers to the transfer centers are planned; In the third phase, the transportation routes from the transshipment center to the processing center are optimized; Step 2, using the Gurobi optimizer to solve the problems of the first and second stages; using an adaptive neighborhood search algorithm to solve the problems of the third stage.

2. The method for solving a medical waste transportation scheme based on a double-layer optimization model according to claim 1, characterized in that: The two-level optimization model includes the following variables: Safety score, which is used to assess safety based on location data of vulnerable population gathering points; Infection risk, which is used to calculate the effective diffusion area of ​​the infection source along the path and the estimated number of exposed people along the path through the VanUldens box model analysis; The time window is used to limit the transportation time of medical waste, and the transportation time is set differently according to whether the medical waste is infectious medical waste or ordinary medical waste.

3. The method for solving a medical waste transportation scheme based on a double-layer optimization model according to claim 1 is characterized in that: The problem of solving the first and second stages includes four objective functions, which are respectively used to consider: 1) Consider minimizing the cost, which includes the construction cost of the transshipment center and the total transportation cost from the transshipment center to the collection center); 2) Consider the geographical security of the transshipment center construction and the transportation distance from the transshipment center to the collection center; 3) Consider the distance from the transfer center to the processing center; 4) Consider the total travel time between the transfer center and the collection center.

4. The method for solving a medical waste transportation scheme based on a double-layer optimization model according to claim 1 is 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 does not exceed the processing capacity of the transfer center; Any collection center will not be linked to other collection centers; The number of transshipment centers is within a preset range; Each collection center is visited at least once, and each transfer center serves at least one collection center; No subroutes appear; The vehicle is not loaded beyond its capacity; The total distance from the transfer center to all collection centers it serves does not exceed the vehicle's driving range.

5. The method for solving medical waste transportation scheme based on a double-layer optimization model according to claim 1, characterized in that: The problem of solving the third stage includes two objective functions, which are used to consider minimizing the total time cost and minimizing the infection risk respectively.

6. The method for solving a medical waste transportation scheme based on a double-layer optimization model according to claim 1, characterized in that: The route model includes the following constraints: Each vehicle is not loaded more than its capacity; Each collection center was visited and left once; Each vehicle departs from the processing center; Use time variables to eliminate sub-cycles and ensure that the vehicle's route does not form a closed loop; Define the link between the time a vehicle leaves one collection center and the time it departs from the subsequent collection center, ensuring temporal continuity; Ensure that the vehicle arrives at the transfer center no earlier than the transfer center's preparation time.

7. The method for solving a medical waste transportation scheme based on a double-layer optimization model according to claim 1, characterized in that: In the two-level optimization model, at the upper level, a hierarchical approach is used to prioritize the objectives; the solver optimizes the highest priority objective first and then the next objective; at the lower level, a specific weight is assigned to each objective, converting the multi-objective problem into a single-objective problem.

8. The method for solving medical waste transportation scheme based on a double-layer optimization model according to claim 1 is characterized in that: The Pareto dominance sorting method is integrated into the framework of the adaptive neighborhood search algorithm; the adaptive neighborhood search algorithm uses the following removal and insertion operations: similar feature-based removal, random removal, random sequence removal, risk-cost worst removal, regret repair, risk-cost greedy repair, and random repair.

9. A system for implementing the method for solving medical waste transportation scheme based on a double-layer optimization model as described in any one of claims 1 to 8, characterized in that: include: The model building module is configured to build a two-level optimization model for solving the medical waste transportation problem, wherein the two-level optimization model includes the following three stages: In the first stage, the optimal location of the transshipment center is determined; In the second stage, the collection routes from the collection centers to the transfer centers are planned; In the third phase, the transportation routes from the transshipment center to the processing center are optimized; The medical waste transportation solution module is configured to use the Gurobi optimizer to solve the problems of the first and second stages; and use an adaptive neighborhood search algorithm to solve the problems of the third stage.

10. A computer-readable storage medium, characterized in that: Stored thereon are: a computer program for implementing the method for solving the medical waste transportation plan based on the double-layer optimization model as described in any one of claims 1-8, or a computer program for implementing the system as described in claim 9.

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