Quality-uncertain integrated optimization method for recycling and disassembling of waste power battery

Abstract

The application provides a quality-uncertain waste power battery recycling and disassembling integrated optimization method, which firstly takes minimization of total operation cost as an objective function, considers coupling constraints, recyclable packaging related constraints, vehicle related constraints, demand satisfaction constraints, inventory related constraints, disassembling line related constraints and decision variable value range constraints, and constructs a stochastic programming model of waste power battery recycling-disassembling integrated optimization; a sample average approximation method is used to convert the stochastic model into an equivalent deterministic model, and a linearization treatment is performed on nonlinear terms to enhance the solving performance; finally, a two-stage heuristic algorithm is used to solve the proposed mathematical model, and the required optimal scenario number can be selected according to the actual problem. The application realizes the integrated optimization of the recycling and disassembling two-stage problems of waste power batteries in the quality-uncertain environment, and provides a scientific solution for the complex optimization problems in the waste power battery recycling field.

Description

Technical Field

[0001] This invention relates to the field of waste power battery recycling, specifically to an integrated optimization method for recycling and dismantling waste power batteries with uncertain quality. Background Technology

[0002] With the transformation of the global energy structure and increasing pressure on environmental protection, the new energy vehicle industry has developed rapidly, becoming an important component of strategic emerging industries in various countries. As a core component of new energy vehicles, the lifespan of power batteries is typically 5 to 8 years. In recent years, as early-used power batteries gradually enter their retirement phase, my country is facing a massive "retirement wave." Statistics show that in 2024, the total amount of retired waste power batteries in China reached 400,000 tons, with the recycling market exceeding 48 billion yuan, and is projected to exceed 100 billion yuan by 2030. Therefore, how to efficiently, economically, and environmentally recycle and utilize waste power batteries has become a key issue in promoting the sustainable development of the new energy vehicle industry.

[0003] Currently, the lifecycle management of spent power batteries mainly includes two paths: secondary utilization and recycling. Typically, batteries with a remaining State of Health (SOH) between 40% and 80% can be reassembled for secondary utilization scenarios such as energy storage, while batteries with an SOH below 40% enter the dismantling and smelting stage to recover valuable metals. Whether for secondary utilization or recycling, dismantling centers are crucial hubs connecting the recycling and utilization ends. Especially for secondary utilization, it is necessary to meticulously dismantle the recycled battery packs into modules and then sort them according to their quality levels. Therefore, the dismantling process is not only about physical separation but also a key step in value identification and tiered sorting, directly affecting the selection of subsequent utilization paths and economic viability.

[0004] However, the current waste power battery recycling and dismantling system faces multiple challenges in actual operation:

[0005] First, the quality exhibits significant uncertainty: due to differences in the usage history, environmental conditions, and charge / discharge frequency of power batteries, the state of harmonics (SOH) of recycled batteries displays a significant random distribution. This quality variation directly determines the usable scenarios of the disassembled modules. For example, modules with an SOH of 70%–80% can be used in scenarios with high stability requirements, such as communication base stations; modules with an SOH between 60% and 70% are suitable for applications with relatively lower performance requirements, such as low-speed electric vehicles and streetlights; while modules with an SOH below 60% typically can only be recycled through material crushing. Existing recycling systems struggle to effectively cope with this quality fluctuation, leading to resource misallocation and value loss.

[0006] Secondly, reverse logistics costs have risen significantly: as the recycling network expands and recycling points become more dispersed, the complexity of transporting used power batteries has increased, leading to a significant rise in transportation costs. Furthermore, since used power batteries are classified as Class 9 hazardous materials, specialized protective packaging is required during transportation, further exacerbating the operational pressure on the logistics system. Moreover, there is a significant mismatch between the recycling pace and downstream module demand, often resulting in large backlogs of used batteries awaiting dismantling, or unmet demand and inventory buildup of dismantled modules, leading to high inventory holding costs and stockout penalties.

[0007] In summary, the existing waste power battery recycling and dismantling system still has significant shortcomings in dealing with quality uncertainties, controlling logistics costs, and matching supply and demand. There is an urgent need to develop an integrated method that can achieve coordinated optimization of transportation, dismantling, and inventory under uncertain environments in order to improve the overall operational efficiency and economy of the waste power battery recycling system. Summary of the Invention

[0008] Existing research often focuses on local optimization of single stages such as recycling, transportation, dismantling, or inventory management, lacking a systematic and integrated consideration of the entire process, making it difficult to achieve global optimality in uncertain environments. In particular, traditional deterministic models struggle to provide robust and reliable decision support when multiple uncertainties such as quality fluctuations and supply-demand mismatches are intertwined.

[0009] To address the shortcomings of existing power battery recycling and dismantling processes, such as fragmentation, difficulty in handling quality fluctuations, and supply-demand mismatches, this invention proposes an integrated optimization method for the recycling and dismantling of waste power batteries with uncertain quality. This method treats the entire process of reverse logistics, inventory management, and dismantling operations of waste power battery recycling enterprises as a tightly coupled operating system. By overcoming the limitations of local optimization in a single stage, an integrated optimization stochastic programming model for recycling and dismantling considering quality uncertainty is constructed. Sample averaging approximation and linearization techniques are used for model transformation, and a two-stage heuristic optimization algorithm is designed. The aim is to reduce the total operating cost of the system, providing a scientific solution to the complex decision-making problems in power battery recycling.

[0010] The technical solution of this invention is as follows:

[0011] An integrated optimization method for recycling and dismantling spent power batteries with uncertain quality includes the following steps:

[0012] Step 1: With the objective function of minimizing the total operating cost under uncertain conditions of waste power battery recycling quality, and considering coupling constraints, recyclable packaging constraints, vehicle-related constraints, demand satisfaction constraints, inventory-related constraints, dismantling line-related constraints, and decision variable value range constraints, a stochastic programming model for integrated optimization of waste power battery recycling and dismantling is constructed.

[0013] Step 2: For the stochastic programming model constructed in Step 1, the high-dimensional integral is approximated as the mean of discrete scenarios by using the sample averaging approximation method, and the nonlinear constraints are linearized to obtain a linearized ensemble optimization model.

[0014] Step 3: For the ensemble optimization model obtained in Step 2, a two-stage heuristic algorithm is used to solve it. The first stage is the batch decomposition decision stage, and the relaxed fixed heuristic method is used for optimization. The second stage uses the adaptive large neighborhood algorithm to solve the multi-period vehicle path planning problem. The two stages are interactively iteratively solved to achieve the purpose of ensemble optimization.

[0015] In a further preferred embodiment, the objective function in step 1 includes transportation costs, empty packaging inventory costs, and expected operating costs. The expected operating costs include the dismantling line start-up costs under each discrete random scenario, the dismantling costs of used power batteries, the inventory holding costs of undismantled used power batteries and unused modules, and the penalty costs incurred due to unmet module demand.

[0016] A further preferred embodiment is that the sample average approximation method in step 2 is as follows: based on the probability distribution information of random variables in the stochastic programming model, a finite number of random discrete scenarios are generated by Monte Carlo sampling; the objective function and constraints containing random variables in the stochastic programming model are approximated by the arithmetic mean of the corresponding function values ​​under each scenario.

[0017] A further preferred embodiment is that the linearization process in step 2 includes: linearizing the nonlinear constraints in the approximate model by introducing a large M constraint to obtain a deterministic solvable optimization model.

[0018] A further preferred embodiment of step 3, the interactive iterative solution process of the two-stage heuristic algorithm, includes:

[0019] First, the mathematical model of the batch dismantling decision stage is solved using a solver combined with a relaxation fixation method to obtain the set of recycling center nodes visited in each cycle.

[0020] Based on the set of recycling center nodes that need to be visited in each cycle, the adaptive large neighborhood algorithm is used to solve the multi-cycle vehicle routing problem.

[0021] During the interaction process, two parameters, approximate access cost and vehicle capacity utilization rate, are introduced for information feedback. The approximate access cost is updated based on the specific vehicle path results obtained in the second stage, and the vehicle capacity utilization rate is adjusted based on the feasibility of the solution in the second stage.

[0022] Furthermore, during the interactive iteration process, two diversification mechanisms were designed based on tabu cut constraints and multi-startup diversification to prevent the algorithm from getting trapped in local optima.

[0023] A further preferred embodiment is that the approximate access cost is updated as follows: when accessing the recycling center in the current cycle, the transportation cost is updated to... ,in and These represent the recycling centers in the path. Pre-processing recycling centers and post-processing recycling centers, Indicates from the recycling center To the recycling center Transportation costs, Indicates from the recycling center To the recycling center Transportation costs, Indicates from the recycling center To the recycling center The transportation cost; when the recycling center is not visited in the current cycle, its transportation cost is updated to the minimum insertion cost among all feasible insertion locations.

[0024] A further preferred embodiment is that the vehicle capacity utilization rate is adjusted as follows: if no feasible path is found in the second stage, the vehicle capacity utilization rate is reduced; if a feasible path is found in the second stage but not all vehicles are used, the vehicle capacity utilization rate is increased, and the adjustment range is controlled by a preset step size factor.

[0025] A further preferred approach is that the relaxation and fixation method described in step 3 is as follows: the decision variables are divided into fixed intervals, decision intervals, and relaxation intervals according to the planning period. By gradually moving the window forward and fixing the solved variables, the original problem can be decomposed and solved.

[0026] In a further preferred embodiment, when the adaptive large neighborhood algorithm described in step 3 solves the multi-period vehicle path planning problem, the initial solution generation adopts a "hot start" mechanism, which uses feasible solutions from historical iterations to repair and adjust in order to generate the initial solution for the current period.

[0027] In a further preferred embodiment, the adaptive large neighborhood algorithm in step 3 employs destructive operators including high-load removal, similar-demand removal, and unbalanced removal; and repair operators including load-aware greedy insertion and delivery-priority insertion.

[0028] The high-load removal refers to randomly removing several recycling centers from the path with the highest load rate;

[0029] The similarity demand removal refers to removing several recycling centers that are similar in terms of the similarity of their recycling and distribution needs along a path;

[0030] The imbalance removal refers to removing several recycling centers that have the greatest impact on the peak load of the path, based on the imbalance of the recycling centers.

[0031] The load-aware greedy insertion refers to selecting the position that minimizes the peak load of the path after insertion; if the peak load is the same, the position with the least increase in path cost is selected.

[0032] The term "delivery priority insertion" refers to prioritizing the insertion of recycling centers with empty packaging delivery needs when repairing the path.

[0033] A further preferred embodiment, the diversification mechanism described in step 3, includes:

[0034] Taboo cut constraint: When the solution in a single iteration is not improved, the currently selected combination of recycling centers is added as a taboo cut to prevent the generation of the exact same solution in subsequent iterations;

[0035] Multi-start diversification: When the algorithm fails to improve the quality of the solution after multiple iterations, a random perturbation is applied to the approximate access cost of all recycling centers, all taboo cuts are removed, and the iteration process is restarted.

[0036] Beneficial effects:

[0037] The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality proposed in this invention has the following effects:

[0038] (1) This invention integrates and optimizes the recycling, transportation, dismantling, and storage of waste power batteries by introducing stochastic programming and ensemble optimization techniques. This breaks through the limitations of traditional single-stage local optimization and effectively solves the practical dilemma of traditional waste power battery recycling models being unable to cope with quality uncertainty and supply-demand imbalance. This invention can significantly improve the decision robustness of the system under extreme fluctuations. By quantitatively modeling quality uncertainty, it effectively reduces the failure rate of traditional deterministic decisions under stochastic fluctuations. By optimizing resource allocation, it solves the problem of bounded rationality decision-making from a non-global perspective, providing a more economically feasible and comprehensive solution for the power battery recycling industry.

[0039] (2) This invention transforms the stochastic programming model, which is difficult to solve directly, into a deterministic mixed integer linear programming model by means of sample average approximation and linearization techniques, thereby reducing the difficulty of solving the model and improving its practicality and operability.

[0040] (3) This invention designs a two-stage heuristic algorithm that makes full use of the problem's structural features and achieves efficient solutions to large-scale complex problems through the organic combination of relaxation fixation methods and adaptive large neighborhood search. The interactive mechanism and diversified strategies introduced in the algorithm effectively avoid local optima. The solution quality and computation speed are both superior to those of traditional commercial solvers that solve directly, and can provide fast and reliable decision support for the operation of actual recycling and dismantling systems.

[0041] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0042] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0043] Figure 1 Description of the bulk recycling issue;

[0044] Figure 2 Description of the recycling batch problem based on approximate access cost;

[0045] Figure 3 Flowchart of the relaxation fixed heuristic algorithm;

[0046] Figure 4 : ALNS iteration diagram;

[0047] Figure 5 Box plots showing the distribution of objective function values ​​under different scenarios;

[0048] Figure 6 : Graph showing the change in average runtime as a function of the number of scenarios;

[0049] Figure 7 : A two-stage heuristic algorithm framework; where bestIterCost is the optimal cost value for each restart, bestOverallCost is the globally optimal cost value, max_restarts is the maximum number of restarts, maxMainIterations is the maximum number of iterations for each restart, and curCost is the cost value of the current iteration;

[0050] Figure 8 Relaxed-fixed heuristic algorithm;

[0051] Figure 9 Pseudocode for solving the VRPSPD problem using the ALNS algorithm;

[0052] Figure 10 : Verify the model parameter settings in the example; where The integers are uniformly distributed between 0 and 10;

[0053] Figure 11 : Test results of the example. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0055] This embodiment proposes an integrated optimization method for the recycling and dismantling of waste power batteries from new energy vehicles under uncertain recycling quality conditions. The method mainly includes problem description, model construction, and model solving using a two-stage heuristic algorithm. Each part is described in detail below.

[0056] I. Description of the problem of integrated optimization of recycling, dismantling and recycling of used power batteries:

[0057] like Figure 1 As shown, within a given planning period, a dismantling center needs to collect various types of used power batteries from multiple recycling centers and formulate multi-cycle batch dismantling decisions based on the amount of used power batteries recycled and the demand for modules in each quality range. Simultaneously, it needs to select appropriate dismantling lines based on the batch dismantling volume. Since the module composition and market demand vary for different battery types, the system must develop recycling and dismantling plans for each type. Furthermore, given that used power batteries are classified as Class 9 hazardous materials, relevant regulations strictly require them to be equipped with dedicated protective packaging (such as leak-proof, insulating, and fire-resistant packaging, hereinafter collectively referred to as "packaging") during transportation. Considering the high cost and durability of such dedicated packaging, constructing a closed-loop packaging circulation system is also crucial. This means that after the batteries are dismantled and stored, the empty packaging should be promptly returned to the recycling centers to achieve resource recycling and reduce operating costs.

[0058] The optimization objective is to minimize the overall system operating costs while meeting demand, including vehicle transportation costs, inventory holding costs (including inventory costs of undisassembled batteries, unused modules, and empty packaging), dismantling line usage costs (including dismantling line startup costs and battery dismantling costs), and penalty costs for unmet demand. Transportation costs are closely related to the recycling route, while dismantling costs depend on the selection of the dismantling line and the dismantling quantity decisions.

[0059] like Figure 1As shown, within a multi-cycle planning framework, decision-makers need to comprehensively consider the following key issues: how to rationally arrange recycling and distribution routes to reduce transportation costs; how to formulate dismantling plans based on the quality of recycled batteries and the corresponding quality level of battery module demand; how to select appropriate dismantling lines to balance dismantling capacity and fixed costs; and how to manage inventory levels to avoid over-storage or shortages. These decisions are interconnected and collectively determine the overall operational efficiency of the system.

[0060] It is worth noting that the quality of spent power batteries exhibits significant uncertainty. This uncertainty primarily stems from variations in factors such as battery usage history, environmental conditions, and the number of charge-discharge cycles, leading to substantial fluctuations in their State of Balance (SOH). Therefore, this embodiment uses the uncertainty of remaining capacity to characterize the uncertainty in the recycling quality of spent power batteries. Since remaining capacity directly determines the battery's reuse potential, spent power batteries with different capacity ranges correspond to different reuse paths (such as energy storage, low-speed vehicles, or material recycling), and dismantling companies have varying demands for different types of batteries. To address this challenge, this embodiment constructs a stochastic programming model designed to solve a multi-period optimization problem under uncertain remaining capacity, providing decision support for the recycling and processing of spent power batteries. The model considers multiple possible scenarios, each corresponding to a different remaining capacity distribution, thereby ensuring the robustness of the solution.

[0061] In actual operation, since the power battery modules of new energy vehicles are usually connected in series to meet high voltage requirements, the total remaining capacity of the battery pack is determined by the module with the smallest capacity. Although the degree of degradation of each module may vary in actual use, considering the characteristics of series circuits and the limitations of actual testing conditions, this invention uses the overall remaining capacity of the battery pack as the capacity estimate of its constituent modules.

[0062] II. Constructing an integrated optimization model for the recycling and dismantling of used power batteries and applying linearization:

[0063] (a) Model Assumptions:

[0064] To more easily characterize practical problems as mathematical models, the following reasonable assumptions are made about the problem:

[0065] (1) Each cycle, the vehicle departs from the dismantling center, completes the recycling task, and must return. Each recycling center can be visited at most once per cycle.

[0066] (2) The battery supply at the recycling center is limited and does not exceed the loading capacity of a single vehicle;

[0067] (3) Unmet needs are allowed, but corresponding penalty costs will be incurred;

[0068] (4) Only one dismantling line can be used for production per cycle;

[0069] (5) Due to the barrel effect of the module series structure, the total remaining capacity of the battery pack can be approximated as the capacity estimate of its constituent modules;

[0070] (6) The system needs to process multiple types of waste power batteries, and the modules obtained from dismantling different types of batteries are not interchangeable; that is, the demand for a certain type of module can only be met by dismantling the corresponding type of waste power battery.

[0071] (7) Used power batteries must be transported in special packaging, which is expensive but recyclable;

[0072] (8) During the recycling process, the vehicles can simultaneously deliver the empty packaging generated by the dismantling center to each recycling center to support their subsequent recycling operations;

[0073] (9) The return of empty packaging is allowed to have a time lag, that is, the empty packaging held by the dismantling center does not need to be returned in the current period, but can be delivered in batches in subsequent periods.

[0074] (II) Explanation of parameter symbols:

[0075] To clearly describe the model, the following symbols are defined:

[0076] : Node set ;

[0077] Collection of recycling centers;

[0078] Disassembly center collection;

[0079] :cycle The set, ;

[0080] :scene The set, ;

[0081] Disassembly Center Disassembly Line The set, ;

[0082] Remaining capacity range The set, ;

[0083] Available vehicles The set, ;

[0084] Types of used power batteries The set, ;

[0085] Recycling Center In the cycle Provided The quantity of waste power batteries;

[0086] : The remaining capacity range of waste power batteries is as follows The module in the cycle Demand;

[0087] From node To the node Transportation costs;

[0088] Capacity of each vehicle;

[0089] Inventory capacity of the dismantling center;

[0090] Disassembly line Disassembly capability;

[0091] Disassembly line Fixed usage costs;

[0092] : The number of modules obtained after dismantling waste power batteries;

[0093] : Unit inventory holding cost of waste power batteries before dismantling;

[0094] : Unit inventory holding cost of unused battery modules after dismantling waste power batteries;

[0095] : The unit dismantling cost of waste power batteries;

[0096] Not satisfied The remaining capacity range of waste power batteries is as follows The unit penalty cost of module requirements;

[0097] Undisassembled The unit inventory capacity occupied by waste power batteries;

[0098] Unused The unit inventory capacity occupied by modules dismantled from waste power batteries;

[0099] :scene The probability of;

[0100] In the cycle scene middle, The remaining capacity range of waste power batteries is as follows: The proportion of batteries;

[0101] : Inventory holding cost per unit of packaging per unit cycle;

[0102] The maximum allowable backlog of packaging, i.e., the latest period after which empty packaging must be stored. Returned within one cycle;

[0103] Recycling Center Maximum allowed packaging backlog.

[0104] (III) Definition of decision variables:

[0105] In the cycle At the end, the recycling center The number of backlogged packages awaiting return;

[0106] In the cycle scene If you choose to disassemble the wire The value is 1 if it is 1, otherwise it is 0.

[0107] In the cycle From the recycling center Recycled The quantity of waste power batteries;

[0108] In the cycle If from the recycling center Recycle The value is 1 for waste power batteries, otherwise it is 0;

[0109] In the cycle If the vehicle visits the recycling center The value is 1 if it is 1, otherwise it is 0.

[0110] In the cycle If the vehicle accesses the arc The value is 1 if it is 1, otherwise it is 0; arc Indicates from node To the node The route; as mentioned earlier, both the recycling center and the dismantling center can be represented as a node;

[0111] In the cycle Vehicle access arc The number of used power batteries loaded later;

[0112] In the cycle The vehicles were transported to the recycling center. The quantity of packaging;

[0113] In the cycle Vehicle access arc The number of recyclable packages loaded later;

[0114] In the cycle scene Below, not disassembled The remaining capacity range of the class is The inventory of used power batteries;

[0115] In the cycle scene Below, unused The remaining capacity range of the class is Inventory of modules;

[0116] In the cycle scene Below, disassembled The remaining capacity range of the class is The amount of waste power batteries;

[0117] In the cycle scene Down, The remaining capacity range of waste power batteries is as follows The shortage of modules.

[0118] (iv) Constructing a mathematical model:

[0119] 1. Objective function:

[0120] The objective function is to minimize the total operating cost, as shown in equation (2-1). The total operating cost includes: transportation costs. Empty packaging inventory cost and expected operating costs The expected operating cost is shown in equation (2-2), which is the expected value of the operating cost of the dismantling center under each discrete stochastic scenario, specifically including the dismantling line startup cost. Cost of dismantling used power batteries Inventory holding costs of undisassembled used power batteries and unused modules And the penalty costs arising from unmet module requirements. .

[0121] (2-1)

[0122] (2-2)

[0123] 2. Constraints:

[0124] The constraints include:

[0125] (1) The coupling constraint between whether to visit the recycling center and whether there is a need for recycling or delivery at the recycling center is composed of equations (2-3) to (2-5).

[0126] If in the cycle Recycling Center If you need to recycle batteries or return empty packaging, you will definitely visit the recycling center. As shown in equation (2-3), where These are the parameters in the Big M constraint; if in the period Recycling Center If there is no need to recycle batteries or return empty packaging, then the recycling center will not be visited, as shown in equation (2-4); if there is a period of time Do not access the recycle center If the battery cannot be recycled at the recycling center, then at least one type of used power battery will be recycled if the recycling center is visited, as shown in Equation (2-5).

[0127] (2-3)

[0128] (2-4)

[0129] (2-5)

[0130] (2) Recyclable packaging related constraints, consisting of equations (2-6) to (2-9).

[0131] The inventory balance constraint for overstocked packaging at the dismantling center is shown in equation (2-6), where... In the cycle At the end, the recycling center The backlog of packages awaiting return; the association constraints between the package return and recycling centers and the access recycling centers, as shown in equation (2-7); recycling centers The maximum time window constraint for the delayed return of empty packages is shown in Equation (2-8); the constraint on the maximum number of empty packages that the dismantling center can accommodate from each recycling center is shown in Equation (2-9).

[0132] (2-6)

[0133] (2-7)

[0134] (2-8)

[0135] (2-9)

[0136] (3) Vehicle-related constraints, consisting of equations (2-10) to (2-24).

[0137] The quantity constraints on the number of batteries recovered from the recycling center by the vehicle are shown in Equation (2-10); all empty packages carried by the vehicle from the dismantling center must be delivered to the recycling center, as shown in Equation (2-11), where... Indicates the period Vehicle access arc The number of recyclable packages loaded later, where node 0 represents the dismantling center from which the vehicle departs; all used power batteries recovered by the vehicle from the recycling center must be delivered to the dismantling center, as shown in equation (2-12), where Indicates the period Vehicle access arc The number of subsequently loaded used power batteries, the node here This indicates the dismantling center the vehicle has arrived at; once a vehicle visits a recycling center with empty packaging return requirements, it will return all the packaging, as shown in equation (2-13); once a vehicle visits a recycling center to recycle a certain type of used power battery, it will recycle all of that type of used power battery, as shown in equation (2-14); when the vehicle returns to the dismantling center, the number of empty packages it carries is 0, as shown in equation (2-15). Indicates the period Vehicle access arc The number of recyclable packages loaded later; the number of used power batteries loaded when the vehicle departs from the dismantling center is 0, as shown in equation (2-16), where Indicates the period Vehicle access arc The number of used power batteries loaded afterward; when a vehicle visits any recycling center, the number of used power batteries loaded and the number of empty packages must not exceed the vehicle's maximum loading capacity, as shown in equation (2-17); flow balance constraints, as shown in equation (2-18); the vehicle must not return to the starting point, leave the ending point, or go directly from the starting point to the ending point, as shown in equation (2-19), where In the cycle Vehicle access arc The logo, In the cycle Vehicle access arc The logo, In the cycle Vehicle access arc The identification of the vehicle; the number of vehicles departing from the dismantling center equals the number of vehicles returning to the dismantling center, as shown in equation (2-20); the maximum number of vehicles that can be used, as shown in equation (2-21); each recycling center can be visited at most once per cycle, as shown in equation (2-22); if any dismantling center is visited or a vehicle is dispatched for a recycling task, the start and end nodes must be visited, as shown in equations (2-23) and (2-24), where In the cycle The sign indicating departure from the vehicle dismantling center. In the cycle The sign indicating that the vehicle has returned to the dismantling center. In the cycle Vehicle access arc The logo, In the cycle Vehicle access arc The logo.

[0138] (2-10)

[0139] (2-11)

[0140] (2-12)

[0141] (2-13)

[0142]

[0143] (2-15)

[0144] (2-16)

[0145] (2-17)

[0146] (2-18)

[0147] (2-19)

[0148] (2-20)

[0149] (2-21)

[0150] (2-22)

[0151] (2-23)

[0152] (2-24)

[0153] (4) The requirement satisfies the constraint, which is composed of equation (2-25).

[0154] The number of modules obtained from the dismantling of used power batteries in the current cycle Inventory of the corresponding module in the previous period And the current shortage of modules The sum of these amounts must not be less than the current demand for this module in the current cycle. As shown in equation (2-25).

[0155] (2-25)

[0156] (5) Inventory-related constraints, consisting of equations (2-26) to (2-28).

[0157] Inventory balance of used power batteries: the remaining capacity of this type of battery at the end of the current period. = equal to the ending inventory of the previous period Sum of the recovery amount in this cycle Subtract the dismantling volume for this period As shown in equation (2-26);

[0158] Inventory balance of unused battery modules: Module inventory at the end of the current period Equal to the ending inventory of the previous period The number of modules generated during this cycle of dismantling The sum, minus the actual number of modules used in this period. As shown in equation (2-27);

[0159] Inventory capacity limit: Under each cycle and scenario, the sum of the inventory occupancy of used power batteries and unused battery modules shall not exceed the total inventory capacity, as shown in equation (2-28).

[0160] (2-26)

[0161] (2-27)

[0162] (2-28)

[0163] (6) The relevant constraints of the disassembly line are composed of equations (2-29) to (2-30).

[0164] Under each scenario in each cycle, the upper limit constraint of the dismantling capacity of the dismantling line is shown in Equation (2-29); under each scenario in each cycle, only one dismantling line can be selected for dismantling work, as shown in Equation (2-30).

[0165] (2-29)

[0166] (2-30)

[0167] (7) The range of decision variables is constrained by equations (2-31) to (2-34).

[0168] (2-31)

[0169] (2-32)

[0170] (2-33)

[0171] (2-34)

[0172] (V) Model Transformation and Linearization:

[0173] In the above model, the objective function (2-1) is the expected value of operating costs under all possible scenarios. Essentially, it is a high-dimensional integral, highly complex, and difficult to solve directly. This embodiment employs a sample average approximation method. Based on the probability distribution information of random variables in the stochastic programming model, a finite number of random discrete scenarios are generated through Monte Carlo sampling. The uncertainty is approximated using this finite set of discrete scenarios, transforming the expected term into a weighted average of the finite set of scenarios. Thus, the original objective function is transformed into the following deterministic optimization problem:

[0174] (2-35)

[0175] Formula (2-35) represents the situation set The objective function is discretized and solved under a finite set of discrete scenarios, with each scenario having equal probability. Weights are assigned to approximate the original random expectation.

[0176] The right-hand side of formula (2-7) is in the form of the product of two decision variables. Since it is a nonlinear term, it is split into two linear constraints (2-36) and (2-37) to facilitate a better solution to the model.

[0177] (2-36)

[0178] (2-37)

[0179] Through the linearization of nonlinear terms and the application of scenario approximation methods described above, the mathematical model of the embodiment is ultimately transformed into a mixed-integer linear programming problem that is easy to solve. Specifically, the optimization objective function is defined by formula (2-35), which comprehensively considers various costs under multiple cycles; the constraints of the model are jointly expressed by formulas (2-3)-(2-6), (2-8)-(2-34), (2-36), and (2-37).

[0180] III. Design a two-stage heuristic algorithm to solve the ensemble optimization model:

[0181] Due to the large model size, directly using a solver is inefficient and may even fail to find a feasible solution within a reasonable time. Therefore, this embodiment designs a two-stage heuristic algorithm, the overall framework of which is as follows: Figure 3 As shown, the specific process is as follows.

[0182] (I) Two-stage heuristic algorithm process framework:

[0183] The first stage focuses on batch dismantling decisions under multi-cycle and multi-scenario conditions, employing a relaxed fixed heuristic algorithm for optimization to determine the access set for each recycling center. The second stage models a Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD), where pickup and delivery demands are coupled and must satisfy load constraints. To address these characteristics, an Adaptive Large Neighborhood Search (ALNS) algorithm is used, along with a dedicated optimization mechanism: a "warm-start" mechanism is incorporated into the initial solution generation, and corresponding repair-destruction operators and diversification mechanisms are designed based on problem characteristics to accelerate algorithm convergence. Through dynamic interaction and information feedback mechanisms between the two stages, the two-stage heuristic algorithm effectively overcomes the challenge of solution space explosion and efficiently finds near-optimal solutions. The overall algorithm framework is as follows: Figure 7 As shown.

[0184] (II) Batch Dismantling Decision-Making Phase (Phase 1):

[0185] In this phase, the specific recycling sequence decision in vehicle routing planning for each cycle is not considered. Instead, the focus is on key decision variables such as the recycling quantity of various types of used power batteries, dismantling line selection, inventory levels, and the set of recycling center visits under multiple cycles and scenarios. To better characterize the problem and achieve co-modeling with the problem in the second phase, batch decision sub-problems are decomposed from the original problem, and variables and constraints related to vehicle routing and vehicle capacity in the original model are removed.

[0186] Introducing two new parameters and , Indicates period Recycling Center The approximate access cost is used to estimate the recycling center. The transportation cost is initialized to ,like Figure 2 As shown, where Indicates the process from dismantling center to recycling center. Transportation costs, Indicates from the recycling center Transportation costs to the dismantling center; Used to estimate the period The vehicle capacity utilization rate, with a value range of [0,1], is initialized to 1. The batch dismantling decision-making model does not specify the order of decision paths or the vehicle's loading capacity, but rather introduces an approximate access cost. To estimate the transportation cost in the original model, using parameters The total load capacity of the vehicle is adjusted, as shown in the following model:

[0187] The objective function is:

[0188] (3-1)

[0189] The constraints are:

[0190] Equations (2-3)-(2-6), (2-8), (2-9), (2-25)-(2-30), (2-36), (2-37)

[0191] as well as

[0192] (3-2)

[0193] (3-3)

[0194] (3-4)

[0195] (3-5)

[0196] (3-6)

[0197] Constraint (3-2) limits the number of used power batteries recycled per cycle to no more than the total capacity limit of all vehicles. Constraints (3-3) and (3-4) are derived from constraints (2-23) and (2-24), indicating that if a vehicle visits the recycling center, it will first visit the dismantling center and eventually return to the dismantling center.

[0198] The aforementioned decomposition model still exhibits high complexity and remains difficult to solve. To address this issue, this embodiment employs a relaxation-and-fix heuristic algorithm to optimize the solution. By decomposing the original problem into a series of smaller subproblems and progressively fixing the decision variables, computation time can be significantly reduced while maintaining solution quality. For this problem, the relaxation-and-fix heuristic algorithm is based on the planning period... The decision variables are divided into three intervals: the fixed interval (FI), where the values ​​of the decision variables are fixed; the decision interval (DI), where the decision variables retain their original continuous or binary / integer properties; and the relaxed interval (RI), where all integer variables are relaxed to continuous variables. The parameters required for this heuristic algorithm include the step size and the window size, denoted as follows: and And satisfy Among them, window size The decision interval DI represents the number of periods contained within it, while the moving step size... This indicates the number of cycles the DI starting position has moved forward compared to the previous iteration. The flowchart for this heuristic is shown below. Figure 3 See pseudocode Figure 8 This ultimately yields the set of recycling center nodes accessed in each cycle.

[0199] (III) Multi-period vehicle routing planning stage (second stage):

[0200] The second stage addresses the routing problem for vehicles simultaneously picking up and delivering goods, based on the set of recycling centers visited in each cycle determined in the first stage. Since multi-cycle routing problems are highly coupled, this embodiment employs the Adaptive Large Neighborhood Search (ALNS) algorithm for solving the problem.

[0201] 1. Initial solution generation:

[0202] To improve the convergence efficiency and solution quality of ALNS, this embodiment designs an initial solution generation strategy based on a "warm-start" mechanism. Specifically, in the first iteration, since no historical path information is available, the initial solution is constructed using the classic nearest neighbor algorithm. Starting from the second iteration, feasible solutions obtained from the path planning problems of each cycle in the previous iteration are used as prior information. By performing feasibility checks and necessary repairs on the prior information (such as filling in missing nodes and correcting capacity constraints), a high-quality initial solution that satisfies the constraints of the current problem is generated. This strategy effectively avoids the randomness and inefficiency of building solutions from scratch, significantly accelerates the local search process of ALNS, and provides a good foundation for the rapid convergence of the overall algorithm. See the ALNS iteration diagram below. Figure 4 .

[0203] 2. Destruction and Repair Operators:

[0204] This embodiment designs dedicated destruction and repair operators based on the characteristics of the VRPSPD problem, namely: high load removal, similar demand removal, unbalanced removal, load-aware greedy insertion, and delivery-priority insertion.

[0205] (1) High load removal. Find the load rate from all paths. The highest path. Then, randomly select from the paths. The removal is performed on each recycling center. This operator no longer destroys solely based on path length, but considers the weakest link in the path, forcing subsequent repair operators to find new, healthier path combinations for the removed customers. In formula (3-7), For path Peak load capacity, It is a vehicle Maximum loading capacity.

[0206] (3-7)

[0207] (2) Removal of similar needs. Randomly select a recycling center along a path. Traverse all remaining recycling centers along this path. Calculation recycling center With the remaining recycling centers in this path similarity Remove several similar recycling centers. By removing recycling centers with similar demand and delivery patterns, it helps to replace them with different combinations during the remediation phase. In formula (3-8), This means taking the square root. and These represent the locations at the recycling center. and recycling center The quantity of recycled used power batteries, and These represent the locations at the recycling center. and recycling center The number of recycled packaging items returned.

[0208] (3-8)

[0209] (3) Imbalanced removal. Traverse all recycling centers along all paths and calculate the imbalance degree of each recycling center. Remove those with high imbalance There are several recycling centers. By removing the "extreme" recycling centers that have the most significant impact on peak load in the path, the repair operator can reassess the optimal location of these recycling centers in the path. Indicates at the recycling center The quantity of recycled used power batteries, Indicates at the recycling center The number of recycled packaging packages returned. To prevent the denominator from being 0, a small value is set.

[0210] (3-9)

[0211] (4) Load-aware greedy insertion. Standard greedy insertion only considers distance cost, but path feasibility in the VRPSPD problem is highly dependent on real-time load. Therefore, this operator selects insertion that increases the peak load of the path. The strategy prioritizes the insertion point with the lowest possible cost. If two insertion points have the same peak load, the point with the lowest increase in path cost is selected. This strategy effectively controls vehicle load fluctuations while ensuring path feasibility, and is suitable for dynamic capacity constraint scenarios in the VRPSPD problem.

[0212] (5) Delivery priority insertion. When repairing the path, the recycling centers are divided into two groups: recycling centers with delivery needs and recycling centers with only pickup needs. The recycling centers with delivery needs are selected first to reduce the peak load in the path and improve the quality and feasibility of ALNS solution.

[0213] 3. Operator selection and weight update rules:

[0214] In each iteration of solving a single-cycle path planning problem, ALNS requires selecting a disruption operator to disrupt the existing path and then selecting an insertion operator to repair the disrupted path. This embodiment uses a roulette wheel rule for operator selection, meaning each operator... Give a certain weight The probability of this operator being selected is The operator weights are dynamically adjusted during the iteration process based on their historical optimization performance. The better the operator performs during the iteration, the higher its score, and the greater the likelihood that the operator will be selected in subsequent iterations. In this embodiment, the operator weights are updated every 20 iterations, as shown in equation (3-10), where... and These are the operators before and after the update. The weight, It is a response factor used to adjust the weighting of historical experience and current performance on the overall score. Operator The cumulative score within the current period, Operator The number of times it was selected during this weight update process.

[0215] (3-10)

[0216] Each time the operator is used, it will be awarded a certain score based on the quality of the solution generated. In this example: ① if the generated new solution becomes the global optimal solution, the score is 1.2; ② if the generated new solution is better than the current solution and is accepted (but not the global optimal solution), the score is 1.0; ③ if the generated new solution is worse than the current solution but is accepted by the simulated annealing criterion, the score is 0.8; ④ if the generated new solution is invalid or not accepted, the score for the new solution is 0.5.

[0217] 4. Criteria for accepting new solutions:

[0218] In this embodiment, ALNS uses the Metropolis acceptance criterion. When a new solution is obtained through the destruction and repair operators, if the objective function value of the new solution is less than that of the current solution, it is directly accepted as the current solution. If the objective function value of the new solution is not better than that of the current solution, it is accepted as the current solution with a certain probability. Current solution acceptance probability. The calculation formula is as follows:

[0219] (3-11)

[0220] In the above formula, and New solutions and the current solution The objective function value is the vehicle path cost, since this part solves the path planning problem using ALNS; T is the annealing temperature, initialized to T0=1000, and the temperature is determined by the formula... Update in each iteration. The updated annealing temperature. This is the current annealing temperature. As the attenuation factor, this invention sets its value to 0.99.

[0221] 5. ALNS Algorithm Flow:

[0222] Figure 9 Here is the pseudocode for solving the VRPSPD problem using the ALNS algorithm, where Indicates the number of iterations. Operator The selection weight, Operator The score, Operator The number of times it was selected during this weight update process. These represent the current optimal solution, the current iterative solution, and the new solution, respectively. Solution The corresponding objective function value.

[0223] (iv) Algorithm parameter update and interaction:

[0224] 1. Approximate access cost update:

[0225] Approximate access cost Updated using formula (3-12), when in the period Access the Recycling Center At that time, its transportation costs were updated to ,in and These represent the recycling centers in the path. Pre-processing recycling centers and post-processing recycling centers, Indicates from the recycling center To the recycling center Transportation costs, Indicates from the recycling center To the recycling center Transportation costs, Indicates from the recycling center To the recycling center Transportation costs; when in cycle Recycle Center not accessed At that time, its transportation cost is updated to its minimum insertion cost. Represents a node In the cycle Insertion position The cost of nodes In the cycle Insertion position The amount of total cost increase caused by this; For nodes The set of all possible insertion positions.

[0226] (3-12)

[0227] 2. Adjustment of vehicle capacity utilization:

[0228] Vehicle capacity utilization Adjust the step size factor using formula (3-13). If no feasible solution is found in the second phase, it indicates that too many used power batteries were recycled in the first phase, which would reduce the vehicle's capacity utilization rate. If a feasible path is found in the second phase, but not all vehicles are used, then the vehicle capacity utilization rate will be increased. .because Therefore, in the update During the process, it is necessary to ensure The value of does not exceed its feasible range.

[0229] (3-13)

[0230] (v) Diversified mechanisms:

[0231] To enhance the algorithm's global search capability and avoid getting trapped in local optima, this embodiment introduces two complementary and diversified mechanisms based on the characteristics of the problem:

[0232] Tabu cut constraint: This is a short-term memory mechanism. When the solution in a single iteration fails to improve the solution, the algorithm identifies the currently selected combination of recycling centers as a "suboptimal solution" and prevents the model from generating the exact same solution in subsequent iterations by adding a tabu cut (as shown in equation (3-14)). This forces the first-stage model to perform a more refined local exploration within the "neighborhood" of the current solution. Indicates period No. The set of recycling centers visited in each iteration.

[0233] (3-14)

[0234] Multi-start diversification: This is a global perturbation mechanism. When the algorithm fails to improve the quality of the solution in multiple consecutive iterations and gets stuck in a local optimum, this strategy approximates the cost of all recycling centers. Apply random perturbation ,Right now In this embodiment A random number with a value in the range [0.5, 1.5] is used, and then the entire two-stage iterative process is restarted. This perturbation can significantly change the decision of the first-stage model, guiding the algorithm to jump out of the current neighborhood and explore entirely new regions in the solution space. It is worth noting that before each restart, the system removes all taboo cut constraints accumulated during the previous search round, thereby avoiding unnecessary restrictions imposed by historical constraints on the new search path and ensuring that the algorithm can effectively explore a wider feasible domain.

[0235] IV. Calculation Example Verification:

[0236] The above presents a complete integrated optimization method for the recycling and dismantling of waste power batteries for new energy. To illustrate the implementation process and effectiveness of this technical solution, the following numerical examples verify the effectiveness of the proposed method.

[0237] Figure 10 The table lists the values ​​of the relevant parameters for the model. In addition to the parameters mentioned above, different module categories are set for different remaining capacity ranges. Types of used power batteries The number of recycling centers is set to Number of cycles Total number of scenarios .

[0238]

[0239]

[0240] The solution time and performance of CPLEX's direct solution of the mathematical model and the two-stage heuristic algorithm are compared to better demonstrate the correctness of the model and the efficiency of the algorithm. The results are as follows: Figure 11 As shown, in the CPLEX solver, "-" in Time indicates that the set upper limit of the solution time of 3600 seconds has been reached, LS in the CPLEX solver represents the objective function value solved by the solver, and LB is the lower bound of the theoretical optimal objective function value; This represents the objective function value of the two-stage heuristic algorithm.

[0241] As can be seen, CPLEX fails to converge within the preset time, with a residual error (Gap) as high as 52.48% to 54.76%. In contrast, the two-stage heuristic algorithm proposed in this embodiment demonstrates extremely high application value in solving large-scale problems. Data shows that the objective function value obtained by the heuristic algorithm is far superior to the solution obtained by CPLEX. The Gap1 value is between -99.94% and -107.71%, indicating that the cost of the solution found by the heuristic algorithm is only about half or even less than that found by CPLEX. In terms of computation time, the heuristic algorithm can still complete the computation within a reasonable time of approximately 200 to 350 seconds. The heuristic algorithm proposed in this embodiment shows good results in both solution time and solution quality for large-scale problems.

[0242] To determine the optimal sample size that balances solution quality and computational efficiency, in-sample stability experiments can be designed. This invention sets up scenarios of 5, 10, 20, 30, and 50 samples. For each... The model was run 20 times independently, keeping other random parameters constant, by changing the random seed of the Monte Carlo sampling, and the objective function value and computation time were recorded for each solution.

[0243] from Figure 5 It can be seen that at that time At this point, the interquartile range of the box is the largest, and the obtained objective function value fluctuates wildly within the interval of 177321.5 to 182994.2. The small sample size cannot fully cover the distribution characteristics of the random variable, and the solution is highly susceptible to extreme scenarios, resulting in poor stability. With... As the number of cells increases, the box gradually shrinks, and the variance of the objective function value gradually decreases. This is especially true when... When the value is 20, the fluctuation range of the objective function value narrows significantly. Although and It showed further convergence, but compared to from arrive However, the rate of marginal improvement has slowed significantly.

[0244] observe Figure 6It can be seen that as the number of scenarios increases, the computation time exhibits a significant superlinear growth trend. In small-scale scenarios ( The average computation time increased from 64.313 seconds to 145.129 seconds, a relatively gradual increase. However, when After exceeding 20, the slope of the curve increases significantly. From Increase to The scenario size increased by 2.5 times, but the average computation time surged from 345.314 seconds to 1582.036 seconds, an increase of nearly 5 times.

[0245] This invention provides a specific case: it includes 25 recycling centers, a planning cycle of 8, a discrete scenario of 20, different module categories for different remaining capacity ranges of 4, two types of used power batteries, a maximum allowable backlog cycle for recyclable packaging of 5, and other model parameter values ​​are set in the same way. Figure 10 Consistent.

[0246] Table 1. Example of node coordinate data in the case study.

[0247]

[0248] Table 2 Examples of used power battery data available from some nodes in Cycle 1

[0249]

[0250] The final vehicle routing plans for each cycle were obtained. The total operating cost of this plan is 183,935.23. Examples of vehicle routing data for some cycles are shown in Table 3.

[0251] Table 3. Examples of partial periodic vehicle route data

[0252]

[0253] The above process verifies the correctness of the model and the effectiveness of the algorithm, and describes the process of using the method. However, the above embodiments are exemplary and not intended to limit the present invention. Those skilled in the art can change, modify, replace and transform the relevant data in the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. An integrated optimization method for recycling and dismantling waste power batteries with uncertain quality, characterized in that: Includes the following steps: Step 1: With the objective function of minimizing the total operating cost under uncertain conditions of waste power battery recycling quality, and considering coupling constraints, recyclable packaging constraints, vehicle-related constraints, demand satisfaction constraints, inventory-related constraints, dismantling line-related constraints, and decision variable value range constraints, a stochastic programming model for integrated optimization of waste power battery recycling and dismantling is constructed. Step 2: For the stochastic programming model constructed in Step 1, the high-dimensional integral is approximated as the mean of discrete scenarios by using the sample averaging approximation method, and the nonlinear constraints are linearized to obtain a linearized ensemble optimization model. Step 3: For the ensemble optimization model obtained in Step 2, a two-stage heuristic algorithm is used to solve it. The first stage is the batch decomposition decision stage, and the relaxed fixed heuristic method is used for optimization. The second stage uses the adaptive large neighborhood algorithm to solve the multi-period vehicle path planning problem. The two stages are interactively iteratively solved to achieve the purpose of ensemble optimization. The interactive iterative solution process of the two-stage heuristic algorithm includes: First, a solver combined with a relaxed fixed heuristic method is used to solve the mathematical model of the batch dismantling decision stage, and the set of recycling center nodes visited in each cycle is obtained. Based on the set of recycling center nodes to be visited in each cycle, an adaptive large neighborhood algorithm is used to solve the multi-cycle vehicle routing problem. The initial solution generation adopts a "hot start" mechanism, which uses feasible solutions from previous iterations for repair and adjustment to generate the initial solution for the current cycle. Specifically, in the first iteration, the initial solution is constructed using the nearest neighbor algorithm; starting from the second iteration, the feasible solutions obtained from the routing problems of each cycle in the previous iteration are used as prior information. By checking and repairing the prior information, an initial solution that satisfies the constraints of the current problem is generated. The adaptive large neighborhood algorithm employs destructive operators including high-load removal, similar-demand removal, and unbalanced removal; and repair operators including load-aware greedy insertion and delivery-priority insertion. The high-load removal refers to randomly removing several recycling centers from the path with the highest load rate; The similarity demand removal refers to removing several recycling centers that are similar in terms of the similarity of their recycling and distribution needs along a path; The imbalance removal refers to removing several recycling centers that have the greatest impact on the peak load of the path, based on the imbalance of the recycling centers. The load-aware greedy insertion refers to selecting the position that minimizes the peak load of the path after insertion; if the peak load is the same, the position with the least increase in path cost is selected. The term "delivery priority insertion" refers to prioritizing the insertion of recycling centers with empty packaging delivery needs when repairing the route. During the interaction process, two parameters, approximate access cost and vehicle capacity utilization rate, are introduced for information feedback. The approximate access cost is updated based on the specific vehicle path results obtained in the second stage, and the vehicle capacity utilization rate is adjusted based on the feasibility of the solution in the second stage. Furthermore, during the interactive iteration process, two diversification mechanisms were designed based on tabu cut constraints and multi-startup diversification to prevent the algorithm from getting trapped in local optima.

2. The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality as described in claim 1, characterized in that: The objective function described in step 1 includes transportation costs, empty packaging inventory costs, and expected operating costs. The expected operating costs include the dismantling line start-up costs under each discrete random scenario, the dismantling costs of used power batteries, the inventory holding costs of undismantled used power batteries and unused modules, and the penalty costs incurred due to unmet module demand.

3. The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality as described in claim 1, characterized in that: The sample average approximation method described in step 2 is as follows: Based on the probability distribution information of random variables in the stochastic programming model, a finite number of random discrete scenarios are generated through Monte Carlo sampling; the objective function and constraints containing random variables in the stochastic programming model are approximated by the arithmetic mean of the corresponding function values ​​under each scenario.

4. The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality as described in claim 1, characterized in that: The approximate access cost is updated as follows: when accessing the recycling center in the current cycle, the transportation cost is updated to... ,in and These represent the recycling centers in the path. Pre-processing recycling centers and post-processing recycling centers, Indicates from the recycling center To the recycling center Transportation costs, Indicates from the recycling center To the recycling center Transportation costs, Indicates from the recycling center To the recycling center The transportation cost; when the recycling center is not visited in the current cycle, its transportation cost is updated to the minimum insertion cost among all feasible insertion locations.

5. The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality as described in claim 1, characterized in that: The method for adjusting the vehicle capacity utilization rate is as follows: if no feasible path is found in the second stage, the vehicle capacity utilization rate will be reduced. If a feasible path is found in the second phase but not all vehicles are used, the vehicle capacity utilization rate is increased, and the adjustment range is controlled by a preset step factor.

6. The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality as described in claim 1, characterized in that: The relaxation-fixed heuristic method described in step 3 is as follows: the decision variables are divided into fixed intervals, decision intervals, and relaxation intervals according to the planning period. By gradually moving the window forward and fixing the solved variables, the original problem can be decomposed and solved.

7. The integrated optimization method for recycling and dismantling waste power batteries with uncertain quality as described in claim 1, characterized in that: The diversification mechanisms described in step 3 include: Taboo cut constraint: When the solution in a single iteration is not improved, the currently selected combination of recycling centers is added as a taboo cut to prevent the generation of the exact same solution in subsequent iterations; Multi-start diversification: When the algorithm fails to improve the quality of the solution after multiple iterations, a random perturbation is applied to the approximate access cost of all recycling centers, all taboo cuts are removed, and the iteration process is restarted.

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