Shared bicycle rebalancing method considering operator and user excitation

Abstract

The invention discloses a shared bicycle rebalancing method considering operator and user excitation. The method comprises the following steps: abstracting a shared bicycle initial distribution and multi-vehicle type rebalancing problem into a two-stage stochastic programming model and solving the two-stage stochastic programming model; describing a first-stage initial allocation optimization problem including a single vehicle total amount constraint and a budget constraint; after initial distribution is completed, in the rebalance problem of the second stage, user incentive constraints and truck dispatching related constraints are described; generating a random demand scene; an SAA algorithm is used for solving initial putting of the single vehicles, and the total expected cost is minimized; solving a user incentive task based on an upper-layer VNS algorithm; and further optimizing a shared bicycle redistribution strategy of the operator through the lower layer VNS, wherein the shared bicycle redistribution strategy comprises path planning of a scheduling motorcade and loading and unloading amount decision of each station. According to the invention, joint optimization of initial allocation and rebalance decision is realized, the resource utilization rate is improved, and the overall operation cost is effectively reduced.

Description

Technical Field

[0001] This invention belongs to the field of urban transportation engineering, and specifically relates to a shared bicycle rebalancing method that considers operator and user incentives, for the formulation and decision-making of initial deployment and rebalancing plans for shared bicycle operations. Background Technology

[0002] As a rapidly developing green mode of transportation in recent years, shared bicycles have become an important transportation choice for people's daily travel. In particular, they have become an important means of transportation for the "last mile" of many citizens' journeys, helping to alleviate urban traffic congestion and achieve a sustainable urban transportation system.

[0003] However, in actual operation, a series of problems have gradually emerged with shared bicycles, such as over-deployment, refurbishment of broken bikes, significant occupation of public resources, and increased burden on urban management due to rapid growth. These problems have resulted in high management costs and constitute new challenges for urban transportation. To address the existing problems with shared bicycles in cities, operators need to take corresponding management measures and strengthen the rational scheduling of bicycles. Operators need to pay attention to the fluctuations in bicycle inventory and demand in different areas, rationally plan the initial deployment of bicycles, and also plan truck transportation routes, arrange scheduling tasks, and formulate incentive strategies to improve overall operational efficiency.

[0004] Currently, operators often consider the site selection, allocation, and redistribution of shared bicycles in isolation, typically neglecting the relationship between initial allocation and rebalancing. Furthermore, they tend to focus on single bicycle models rather than incorporating multiple vehicle types and multi-vehicle collaboration into the scheduling process. Finally, while existing technologies consider user incentives, they often overlook the relationship between price incentives and the number of incentivized users, and lack coordinated consideration of operator and user incentives, leaving significant room for improvement.

[0005] Therefore, for the initial allocation and multi-model rebalancing of shared bicycles, it is necessary to abstract its mathematical model and design a new decision-making algorithm. Summary of the Invention

[0006] Purpose of the invention: This invention addresses the shortcomings of relatively crude decision-making in the operation of shared bicycles by proposing a shared bicycle rebalancing method that considers the incentives of operators and users. This method achieves joint optimization of initial allocation and rebalancing decisions, effectively reducing operating costs.

[0007] Technical Solution: The present invention provides a shared bicycle rebalancing method considering operator and user incentives. It abstracts the initial allocation and multi-model rebalancing problem of shared bicycles into a two-stage stochastic programming model and solves it. The decision elements of the model include the initial deployment volume in each service area, the incentive price for users during rebalancing, and the specific plan for truck scheduling. The objective function is to maximize the net revenue under stochastic demand. Specifically, it includes the following steps:

[0008] S1: Describes the initial allocation optimization problem in the first stage, including the total number of vehicles and the budget constraint;

[0009] S2: Describes the second-stage rebalancing allocation problem. After the initial allocation is completed, the second-stage rebalancing problem describes user incentive constraints and truck scheduling-related constraints, which incentivize users to complete scheduling tasks or adopt multi-vehicle truck scheduling.

[0010] S3: Generation A random requirement scenario Each demand scenario represents a different user need;

[0011] S4: Solve the initial allocation optimization problem in the first stage, using the SAA algorithm to solve the initial deployment of a single vehicle and minimize the total expected cost;

[0012] In the second stage, S5 uses the VNS algorithm with a two-layer structure to solve the rebalancing allocation problem; it solves the user incentive task based on the upper-layer VNS algorithm; and it optimizes the overall scheduling task allocation between users and operators through the upper-layer VNS to determine the user incentive task.

[0013] S6: Solve truck scheduling tasks based on the lower-level VNS algorithm; further optimize the operator's shared bicycle redistribution strategy through the lower-level VNS, including route planning of the dispatch fleet and loading / unloading volume decisions for each station.

[0014] Furthermore, the net revenue equals the revenue from meeting demand minus the total cost; the total cost includes initial allocation costs, penalty costs for unmet demand, overflow management costs for stations with more vehicles than capacity, fixed dispatch costs for truck scheduling, handling costs, and user incentive costs.

[0015] Furthermore, the implementation process of step S1 is as follows:

[0016] The movement of shared bicycles is represented as a directed graph. ,in It is a set of nodes, containing a central warehouse marked as 0 and a set of stations. , It is a set of directed arcs in a network; directed arcs Indicates from node Move to node The number of bicycles;

[0017] This indicates the operator's initial allocation decision and service area. The initial allocation cost is , This indicates the initial budget allocation for each bicycle. Indicates the total number of bikes that can be allocated. This represents the set of service area points, and the initial allocation cannot exceed the maximum number of shared bicycles initially allocated, subject to constraints and budget constraints.

[0018] Furthermore, the process of implementing user incentive constraints described in step S2 is as follows:

[0019] Incentivized user traffic The number of users willing to relocate their bicycles is a monotonically increasing nonlinear function of the difference between the price discount and the additional costs associated with relocating the detour routes.

[0020]

[0021] in, The original planned route was The number of users, This is the price incentive coefficient. Additional time cost coefficient; price incentive coefficient The average level parameter corresponding to the price sensitivity coefficient; considering the user's original driving route is Incentives based on price may lead to a change in starting point to a similar route. ,set up To incentivize prices, The additional time cost incurred by incentivized users due to the relocation of detour routes; The expression is as follows:

[0022]

[0023] Price incentives need to meet budget constraints. Assume that when the incentive reaches... At that point, the number of incentivized users along that route eventually becomes fixed, meaning the price is reached. Afterwards, some users still will not participate in the reposting. In addition, by Click Traffic generated by user incentives:

[0024] .

[0025] Furthermore, the implementation process of the truck scheduling-related constraints described in step S2 is as follows:

[0026] The transport trucks depart from the warehouse and eventually return to the warehouse:

[0027]

[0028]

[0029] in, Indicates the first The first type of vehicle Did the vehicle come from Click point;

[0030] Truck dispatch flow balancing:

[0031]

[0032] Sub-loop constraint elimination ensures that there are no loops in the route that do not include warehouses:

[0033]

[0034] in, It is an auxiliary variable to avoid sub-loops;

[0035] The transport truck departed empty, and all bicycles loaded onto the truck were unloaded during the entire transport process.

[0036]

[0037] in, It is the first The first type of vehicle Vehicles from the area Transported to the area The loading and unloading volume;

[0038] The transport trucks must be able to return to the warehouse empty.

[0039]

[0040] Constraint (11) indicates and The quantity relationship is as follows: the number of shared bikes loaded or unloaded at each access point cannot exceed the truck's capacity; if the truck does not access any points, the number of bikes loaded or unloaded is exactly zero.

[0041]

[0042] in, It is a capacity limitation of the transport vehicles;

[0043] Truck load constraints:

[0044]

[0045]

[0046]

[0047] Among them, is the first The first type of vehicle The car was leaving Cargo capacity at the specified time;

[0048] The station's capacity constraint must be met: the number of vehicles picked up by users and the number of vehicles dispatched by truck dispatchers must not exceed the initial number allocated to the station.

[0049]

[0050] If the number of users deploying vehicles and trucks transporting goods there exceeds the station's capacity, it will incur overflow capacity management costs.

[0051]

[0052] in, Represents a node The number of bicycles exceeding capacity;

[0053] Actual network traffic:

[0054]

[0055] in, It is the user from the node To the node Total demand From node To the node Unmet needs;

[0056] Site traffic balancing constraints:

[0057]

[0058] Variable constraints:

[0059]

[0060]

[0061] .

[0062] Furthermore, step S4 is implemented as follows:

[0063] S 4.1: Initialization Variables: Uniform allocation is used to initialize the initial inventory variables at the site. ;

[0064] S4.2: Calculate the expected adjustment cost: Set the probability of the demand scenario Calculate each station Total demand in the scenario Average scheduling cost under the current allocation Estimate expected adjustment costs:

[0065] ;

[0066] S4.3: Optimize Inventory Allocation: Evaluate the total cost under different inventory allocations using the parameters returned in each iteration; calculate the expected adjustment cost under the current inventory allocation, and adjust accordingly. To reduce total cost Choose the one with the smallest objective function. As the final allocation plan;

[0067] S4.4: Rollback Strategy: If optimization fails to find a better solution, a uniform distribution strategy is adopted, that is, the inventory is distributed equally and the remainder is distributed.

[0068] Furthermore, the implementation process of step S5 is as follows:

[0069] S5.1: Constructing the Initial Solution: In the process of constructing the initial solution, firstly, for multiple excitations, an initial solution is constructed. arrive The incremental incentive cost generated by users The task allocation is performed, and if one of the following conditions is met, more scheduling tasks are allocated to the user first: ① The penalty cost for not meeting demand is less than ;② Less than the operating cost of a truck;

[0070] S5.2: Perturbation Phase: The perturbation strategy is used to escape local optima and prevent the algorithm from getting stuck in local optima; the perturbation methods include randomly removing some users' assigned tasks, recalculating the optimal incentive price, and randomly adjusting the scheduling paths of some users;

[0071] S5.3: Variable Neighborhood Descent Local Search: During the local search process, a neighborhood structure adjustment strategy is adopted to optimize user task allocation. This involves randomly selecting a combination of stations from the solution set of the initial user incentive allocation, and then... For each selected station and its incentivized combination, the number of bicycles transported by the user is adjusted. That is, the portion of the bicycles transported by the user incentive in the initial solution is used for truck scheduling, and the remaining unbalanced demand within the system is adjusted by the transport trucks.

[0072] Furthermore, the implementation process of step S5.1 is as follows:

[0073] 1) Settings The initial value is 0;

[0074] 2) Take the smallest one Check if the cost constraints are met. If not, proceed to Step 5.1.5.

[0075] 3) Regarding the current situation , allocate original The right user Subsequently, updates were made. Site Balanced number of vehicles ,as well as Remaining quantity Recalculate ;

[0076] 4) If arc All remaining quantities If all values ​​are 0, proceed to Step 5.1.5; if all sites reach a balanced state, stop the allocation; otherwise, return to Step 5.1.2 to continue execution.

[0077] 5) For the remaining unbalanced demand in the system, truck scheduling will be used.

[0078] Furthermore, step S6 is implemented as follows:

[0079] S6.1: The initial route is constructed according to the following logic:

[0080] The route starts from the warehouse and returns to the warehouse. First, add the nearest unincluded station to the route. The first station added should be one with a surplus of bicycles, and the last station added should be one with a shortage of bicycles. If the last station added has a surplus of bicycles, try replacing it with another unsaturated, last-added station. Second, check if the truck's loading capacity and budget are feasible. If adding a station causes the truck to be overloaded, select the next nearest unvisited station. Repeat the above steps until all stations are properly arranged.

[0081] For a given route, a greedy algorithm is used to determine the loading and unloading capacity of each station; the maximum number of bicycles a station can provide in a single unloading operation, or the maximum number of excess bicycles it can accommodate, is determined by... Let represent the nodes that appear sequentially in a truck's path. Then, the mathematical expression for the above algorithm is:

[0082] ;

[0083] S 6.2: Perturbation Phase: In each iteration, a perturbation operator is randomly selected, and the constraints are checked to generate a feasible solution; the following neighborhood structures are applied sequentially, and the best improvement strategy is used for searching; the feasibility of all candidate routes is checked, and for each feasible solution, a greedy algorithm is used to determine the loading and unloading quantities;

[0084] Step 6.3: Local Search in Variable Neighborhood Descent: The lower-level variable neighborhood descent stage also uses the neighborhood structure. The feasible solution generated during the search perturbation phase neighborhood until the optimal solution in that neighborhood is obtained. ;if Superior ,make , ;otherwise, ; until the maximum number of iterations is reached, output the local optimum. ; Including the original driving route Motivated as The incentive price, the The first type of vehicle Did the vehicle come from Click Point, and the The first type of vehicle Vehicles from the area Transported to the area The loading and unloading volume.

[0085] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: This invention establishes a two-stage stochastic programming model that simultaneously considers user incentives and multi-vehicle truck scheduling, achieving joint optimization of initial allocation and rebalancing decisions, effectively reducing operating costs; the solution algorithm based on SAA and two-layer VNS proposed in this invention improves the problem-solving efficiency; this invention can be extended to other shared mobility equipment scheduling scenarios, helping enterprises optimize capacity allocation and rebalancing scheduling strategies, further improving resource utilization and reducing overall operating costs. Attached Figure Description

[0086] Figure 1A schematic diagram of the 2-opt operator;

[0087] Figure 2 A schematic diagram of the Relocate operator;

[0088] Figure 3 This is a schematic diagram of the Exchange operator. Detailed Implementation

[0089] The present invention will now be described in further detail with reference to the accompanying drawings.

[0090] This invention proposes a shared bicycle rebalancing method considering operator and user incentives. First, the initial allocation and multi-model rebalancing problem of shared bicycles needs to be abstracted into a two-stage stochastic programming model. The decision elements of the model include the initial deployment volume of each service area, the incentive price for users during rebalancing, and the specific plan for truck dispatching. The objective function is to maximize the net revenue under stochastic demand. Net revenue equals the revenue from satisfying demand minus the total cost. The total cost includes initial allocation cost, penalty cost for unmet demand, overflow management cost when the number of bicycles at a station exceeds capacity, fixed dispatch cost for truck dispatching, handling cost, and user incentive cost. Specifically, the method includes the following steps:

[0091] Step 1: Describe the initial allocation optimization problem in the first stage.

[0092] The movement of shared bicycles is represented as a directed graph. ,in It is a set of nodes, containing a central warehouse marked as 0 and a set of stations. , It is a set of directed arcs in a network. (Directed arcs) Indicates from node Move to node The number of bicycles.

[0093] Describe the total number of vehicles and the budget constraint. This indicates the operator's initial allocation decision and service area. The initial allocation cost is , This indicates the initial budget allocation for each bicycle. Indicates the total number of bikes that can be allocated. This represents the set of service area points, and the initial allocation cannot exceed the maximum number of shared bicycles initially allocated, subject to constraints and budget constraints.

[0094]

[0095] .

[0096] Step 2: Describe the second-stage rebalancing assignment problem.

[0097] In the second phase, after users enter the system, they can be incentivized to complete dispatch tasks or by using multi-vehicle truck dispatching. In this phase, fulfilled dispatch tasks generate revenue, dispatching incurs operational costs, unmet needs incur penalty costs, and exceeding station capacity incurs management costs. Typically, the demand from shared bicycle users... It is uncertain or random, but in practical problems, the demand... The number of scenarios is finite. Assume the requirement scenarios... And the probability of each demand scenario occurring is .

[0098] (2.1) Describe the user incentive constraints. Incentivized user traffic. The number of users willing to relocate their bicycles is a monotonically increasing nonlinear function of the difference between the price discount and the additional costs associated with relocating the detour routes.

[0099]

[0100] The original planned route was The number of users, This is the price incentive coefficient. Additional time cost coefficient. Price incentive coefficient. The average level parameter corresponding to the price sensitivity coefficient. Considering the user's original driving route is... Incentives based on price may lead to a change in starting point to a similar route. ,set up To incentivize prices, The additional time cost incurred by incentivized users due to the relocation of detour routes. The expression is as follows:

[0101]

[0102] Price incentives need to meet budget constraints. Assume that when the incentive reaches... At that point, the number of incentivized users along that route eventually becomes fixed, meaning the price is reached. Afterwards, some users still will not participate in the reposting. In addition, by Click Traffic generated by user incentives

[0103]

[0104] (2.2) Describe the relevant constraints of truck scheduling.

[0105] The transport trucks depart from the warehouse and eventually return to the warehouse:

[0106]

[0107]

[0108] in, Indicates the first The first type of vehicle Did the vehicle come from Click point.

[0109] Truck dispatch flow balancing:

[0110]

[0111] Sub-loop constraint elimination ensures that there are no loops in the route that do not include warehouses:

[0112]

[0113] in, It is an auxiliary variable to avoid sub-loops.

[0114] The transport truck departed empty, and all bicycles loaded onto the truck were unloaded during the entire transport process.

[0115]

[0116] in, It is the first The first type of vehicle Vehicles from the area Transported to the area The loading and unloading volume.

[0117] The transport trucks must be able to return to the warehouse empty.

[0118]

[0119] Constraint (11) indicates and The quantity relationship is as follows: the number of shared bikes loaded or unloaded at each access point cannot exceed the truck's capacity; if the truck does not access any points, the number of bikes loaded or unloaded is exactly zero.

[0120]

[0121] in, It refers to the capacity limit of the transport vehicles.

[0122] Truck load constraints:

[0123]

[0124]

[0125]

[0126] in, It is the first The first type of vehicle The car was leaving Cargo capacity at the specified point.

[0127] The station's capacity constraint must be met: the number of vehicles picked up by users and the number of vehicles dispatched by truck dispatchers must not exceed the initial number allocated to the station.

[0128]

[0129] If the number of users deploying vehicles and trucks transporting goods there exceeds the station's capacity, it will incur overflow capacity management costs.

[0130]

[0131] in, Represents a node The number of bicycles exceeding capacity.

[0132] Actual network traffic:

[0133]

[0134] in, It is the user from the node To the node Total demand From node To the node Unmet needs.

[0135] Site traffic balancing constraints:

[0136]

[0137] Variable constraints:

[0138]

[0139]

[0140]

[0141] The meanings of each parameter are shown in Table 1:

[0142] Table 1 Parameter Description

[0143]

[0144] In summary, the two-stage stochastic programming model for the initial allocation and multi-model rebalancing problem of shared bicycles is as follows:

[0145]

[0146] st

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] Step 3: Generate A random requirement scenario Each demand scenario represents a different user need.

[0169] Step 4: Solve the initial allocation problem in the first stage. Use the Sample Average Approximation (SAA) algorithm to calculate the initial deployment of each vehicle and minimize the total expected cost. The specific process of the SAA algorithm is as follows:

[0170] (4.1) Initialize variables. Uniform allocation is used to initialize the initial inventory variables at the site. .

[0171] (4.2) Calculate the expected adjustment cost. Set the probability of the demand scenario. Calculate each station Total demand in the scenario Average scheduling cost under the current allocation Estimate expected adjustment costs:

[0172]

[0173] (4.3) Optimize inventory allocation by evaluating the total cost under different inventory allocations using the parameters returned in each iteration. Calculate the expected adjustment cost under the current inventory allocation and adjust accordingly. To reduce total cost Choose the one with the smallest objective function. As the final allocation scheme.

[0174] (4.4) Rollback strategy. If optimization fails to find a better solution, a uniform distribution strategy is adopted, that is, the inventory is distributed equally and the remainder is distributed.

[0175] Step 5: In the second stage, a two-layer Variable Neighborhood Search (VNS) algorithm is used to solve the large-scale optimization problem. First, the upper-level VNS algorithm is used to solve the user incentive task. The upper-level VNS optimizes the overall scheduling task allocation between users and operators to determine the user incentive task.

[0176] (5.1) Constructing the initial solution. In the process of constructing the initial solution, firstly, a primary excitation is applied... arrive The incremental incentive cost generated by users The task allocation is performed, and if one of the following conditions is met, more scheduling tasks are allocated to the user first: (i) The penalty cost for not meeting demand is less than Second The cost is less than the truck's operating cost. The above two conditions indicate that when the user incentive cost exceeds the penalty cost for unmet demand or the operating cost of truck transportation, maintaining the existing imbalance or choosing operator transportation is less costly than incentivizing user scheduling. In this case, user incentives are no longer necessary. The steps to construct the initial solution are as follows.

[0177] S1: Initialization. Settings The initial value is 0.

[0178] S2: Conditional judgment. First, take the smallest value. Check if the cost constraint is met. If not, execute S5.

[0179] S3: Variable update. For the current... , allocate original The right user Subsequently, an update was made. Site Balanced number of vehicles ,as well as Remaining quantity Recalculate .

[0180] S4: Termination condition. If arc All remaining quantities If all values ​​are 0, proceed to S5; if all stations reach a balanced state, stop the allocation; otherwise, return to S2 to continue execution.

[0181] S5: Nested Truck Scheduling Algorithm. For the remaining unbalanced demand in the system, truck scheduling is used. This sub-problem will be solved by the inner nested VNS algorithm.

[0182] (5.2) Perturbation Phase. The perturbation strategy is used to escape local optima and prevent the algorithm from getting trapped in local optima. Perturbation methods include randomly removing some users from their assigned tasks and recalculating the optimal incentive price; and randomly adjusting the scheduling paths of some users, such as changing the users' departure or destination stations.

[0183] (5.3) Variable Neighborhood Descent (VND) Local Search. During the local search process, a neighborhood structure adjustment strategy is used to optimize user task allocation. This involves randomly selecting a combination of stations from the solution set of the initial user incentive allocation, and then... For each selected station and its incentivized combination, the number of bicycles transported by the user is adjusted. That is, the portion of the bicycles transported by the user incentive in the initial solution is used for truck scheduling, and the remaining unbalanced demand within the system is adjusted by the transport trucks.

[0184] Step 6: Solve the lower-level VNS algorithm for the truck dispatching task. The lower-level VNS algorithm further optimizes the operator's shared bicycle redistribution strategy, including route planning for the dispatching fleet and decision-making regarding loading and unloading volumes at each station.

[0185] (6.1) Constructing the initial solution. The truck scheduling result is implemented by the lower-level VNS algorithm. The construction of the initial route follows the logic below:

[0186] The route starts at the warehouse and returns to the warehouse. First, add the nearest unincluded stop to the route. The first stop added should be one with a surplus of bicycles, and the last added stop should be one with a shortage. If the last added stop has a surplus of bicycles, try replacing it with another unsaturated, recently added stop. Second, check if the truck's capacity and budget are feasible. If adding a stop causes the truck to overload, select the next nearest unvisited stop. Repeat these steps until all stops are properly arranged.

[0187] For a given route, a greedy algorithm is used to determine the loading and unloading quantity at each station. The greedy algorithm aims to determine the maximum number of bicycles a station can accommodate in a single unloading operation, or the maximum number of excess bicycles it can support. Let represent the nodes that appear sequentially in a truck's path. Then, the mathematical expression for the above algorithm is:

[0188]

[0189] (6.2) Perturbation Stage. In each iteration, a perturbation operator is randomly selected, and constraints are checked to generate feasible solutions. The following neighborhood structures are applied sequentially, and the optimal improvement strategy is used for searching. These classic neighborhood structures have proven effective in various vehicle routing problems. The feasibility of all candidate routes is checked during this process. For each feasible solution, a greedy algorithm is used to determine the loading and unloading quantities. The stopping condition is set to the maximum number of iterations between two improvements. Table 2 provides operator descriptions, and schematic diagrams of the operators are shown below. Figures 1 to 3 As shown.

[0190] Table 2 Operator Description

[0191]

[0192] (6.3) Variable Neighborhood Descent (VND) Local Search. The lower-level variable neighborhood descent stage also uses the neighborhood structure. The feasible solution generated during the search perturbation phase neighborhood until the optimal solution in that neighborhood is obtained. .if Superior ,make , Otherwise, The process continues until the maximum number of iterations is reached, at which point a local optimum is output. The optimal solution includes the original driving route as follows: Motivated as The incentive price, the The first type of vehicle Did the vehicle come from Click Point, and the The first type of vehicle Vehicles from the area Transported to the area The loading and unloading volume.

[0193] This invention verifies the solution performance of the proposed two-stage stochastic programming algorithm through numerical simulation. Random numbers with station distances in the interval [1,3] are randomly generated as the distance matrix for each scenario. Monte Carlo sampling was used to obtain the corresponding demand matrix. Truck handling employed truck fleets with capacities of 30, 40, and 50 vehicles, fixed costs of 10, 12, and 15 yuan respectively, and a unit transportation cost of 0.2 yuan / km. System parameter settings are shown in Table 3.

[0194] Table 3 System Parameters

[0195]

[0196] The results of the site parameter generation are shown in Table 4:

[0197] Table 4 Site Parameter Settings

[0198]

[0199] Point 0 is the warehouse node, and arcs between all nodes are randomly generated. The distance matrix and the demand matrix are obtained by Monte Carlo sampling, and the specific steps are as follows:

[0200] Initialize minimum and maximum OD matrices: Generate minimum (0,5) and maximum (5,15) OD matrices using a uniform distribution.

[0201] Generate probability matrix: Calculate probability values ​​for each pair of different stations and normalize them.

[0202] Generate scene matrices: Generate multiple scene matrices based on the minimum and maximum OD matrices.

[0203] Calculate the mean and standard deviation matrix: Calculate the mean and standard deviation of the OD matrix for all scenarios.

[0204] Generate the demand matrix: Use a normal distribution to generate the demand matrix and stack it into a three-dimensional array.

[0205] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A shared bike rebalancing method considering operator and user incentives, characterized in that, The initial allocation and multi-type rebalancing problem of shared bicycles is abstracted into a two-stage stochastic programming model and solved; the decision elements of the model include the initial allocation of each service area, the incentive price for users in the rebalancing stage, and the specific plan of the truck dispatching; the objective function is to maximize the net income under random demand; including the following steps: S1: describe the first-stage initial allocation optimization problem, including total bicycle quantity constraint and budget constraint; S2: describe the second-stage rebalancing allocation problem, after the initial allocation, in the second-stage rebalancing problem, describe the user incentive constraint and the truck dispatching related constraint, complete the dispatching task by incentivizing users or adopt multi-type truck dispatching; S3: generating a random demand scenario each demand scenario representing different user demands; S4: solve the first-stage initial allocation optimization problem, use SAA algorithm to solve the initial allocation of bicycles, minimize the total expected cost; S5 in the second stage, use VNS algorithm with double-layer structure to solve the rebalancing allocation problem; solve the user incentive task based on the upper-layer VNS algorithm; determine the user incentive task by optimizing the overall dispatching task allocation between users and operators through the upper-layer VNS; S6: solve the truck dispatching task based on the lower-layer VNS algorithm; further optimize the shared bicycle reallocation strategy of the operator, including the path planning of the dispatching truck fleet and the loading and unloading quantity decision of each station, through the lower-layer VNS. 2.The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The net income is equal to the demand satisfaction income minus the total cost; the total cost includes initial allocation cost, penalty cost of unmet demand, overflow management cost of station vehicle quantity exceeding capacity, fixed dispatching cost of truck dispatching, handling cost and user incentive cost. 3.The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The implementation process of step S1 is as follows: Shared bike flow is expressed as a directed graph wherein is a set of nodes comprising a central depot labeled 0 and a set of stations , is a set of directed arcs in the network; a directed arc represents the number of bikes moving from node to node ; represents the initial allocation decision of the operator, service area The initial allocation cost of , represents the initial allocation budget of a single bike, represents the total number of allocable bikes, represents the set of service area points, the initial allocation cannot exceed the maximum number of shared bikes and the budget constraint. 4.The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The implementation process of the user incentive constraint described in step S2 is as follows: Motivated user traffic The number of users who are willing to relocate their bicycles, i.e. the difference between the price discount and the additional costs associated with relocating the detour road, is a monotonic increasing non-linear function of the difference: ； wherein, is the number of users whose original travel path is is the price incentive coefficient, is the additional time cost coefficient; the price incentive coefficient corresponds to the average level parameter of the price sensitivity coefficient; considering that the original travel path of the user is , the user may change to a similar starting point after being motivated by the price and travel along the route , set as the incentive price, as the additional time cost of the motivated user due to the detour of the repositioning road; The expression is as follows:​ ； The price incentive needs to satisfy the budget constraint, assuming that when the incentive reaches the final number of users incentivized on this route is fixed, i.e. after the price threshold is reached, some users still do not participate in the transport, then ; in addition, the traffic brought by the users from point to point is: 。 5.The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The implementation process of the truck dispatching related constraint described in step S2 is as follows: The distribution truck departs from the warehouse and finally returns to the warehouse: ； ； wherein, represents the th vehicle of the th vehicle of the th vehicle of the th vehicle of the Flow balance of truck dispatching: 　； Sub-loop elimination constraint, ensure that there is no loop in the route that does not include the warehouse: ； wherein is an auxiliary variable to avoid subrings; The distribution truck departs empty, and all the bicycles loaded on the truck are unloaded during the entire distribution process: ； wherein, is the first of a first vehicle from the area to the area of the load; The distribution truck can return to the warehouse empty: ； The constraint (11) represents The number of shared bikes loaded or unloaded at each access site cannot exceed the capacity of the truck, i.e. it is equal to zero if the truck does not visit the site: The number of shared bikes loaded or unloaded at each access site cannot exceed the capacity of the truck, i.e. it is equal to zero if the truck does not visit the site: ； wherein, is the capacity limit of the haul vehicle; Truck load constraint: ； ； ； wherein is the first vehicle at the departure point;​​ The capacity constraint of the station needs to be met, the number of bicycles taken away from the station by the user and the number of bicycles handled by the truck do not exceed the initial allocated number of the station: ； If the number of bicycles allocated by the user and handled by the truck exceeds the capacity of the station, the overflow capacity management cost will be generated: ； wherein, representing nodes number of bikes over capacity; Actual flow in the network: ； wherein is the total demand of the user from node to node , is the demand that is not satisfied from node to node ; Station flow balance constraint: ； Variable constraint: ； ； 。 6. The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The implementation process of step S4 is as follows: S 4.1 : Initialize variables: Use uniform allocation to initialize the site initial inventory variables ; S4.2: Compute expected adjustment cost: Set demand scenario probabilities , compute total demand at each site under the scenario , average dispatch cost under current allocation , estimate expected adjustment cost: ； S4.3: optimize inventory allocation: evaluate the total cost under different inventory allocation through the parameters returned by each iteration; computing the expected adjustment cost under the current inventory allocation, adjusting to reduce the total cost , selecting the final allocation scheme with the minimum objective function ​ S4.4: rollback strategy: if optimization fails to find a better solution, use the uniform allocation strategy, i.e. evenly allocate the inventory and allocate the remainder.

7. The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The implementation process of step S5 is as follows: S5.1: Construct initial solution: in the process of constructing the initial solution, first, for each original to the user, the incremental cost of the generated incentive is divided, and if one of the following conditions is met, the user is first allocated more scheduling tasks: ① is less than the penalty cost of not meeting the demand ; ② is less than the driving cost of the truck; S5.2: perturbation stage: perturbation strategy is used to jump out of local optimum and prevent the algorithm from falling into local optimal solution; perturbation methods include randomly removing part of the user allocation task and recalculating the optimal incentive price; randomly adjust part of the user's dispatching path; S5.3: Variable neighborhood descent local search: In the local search process, the neighborhood structure adjustment strategy is adopted to optimize the user task allocation, and the station combination is randomly selected in the solution set of the initial user incentive allocation. In the interval above, for each selected station combination, the number of user bicycle handling is adjusted, that is, the number of parts handled by the user incentive in the initial solution construction is used for the scheduling of the truck, and the remaining unbalanced part of the demand in the system is adjusted by the handling truck.

8. The rebalancing method of shared bikes considering operator and user incentives according to claim 7, characterized in that, The implementation process of step S5.1 is as follows: 1) Setup the initial value of the counter is 0; 2) take the minimum whether the cost constraint is satisfied, and if not, Step 5.1.5 is executed; 3) for the current , the original pair of users to ; then, update , the site the number of vehicles after balancing , and the remaining number , recalculate ; 4) If arc All remaining quantities are 0, go to Step 5.1.5; if all sites are in equilibrium, stop allocation; otherwise, return to Step 5.1.2 and continue execution; 5) For the remaining unbalanced demand in the system, dispatch a truck. 9.The rebalancing method of shared bikes considering operator and user incentives according to claim 1, wherein, The step S6 is implemented as follows: S6.1: Construction of initial routes follows the logic: Routes start and end at the warehouse; first, the nearest site not yet included in the route is added where, where the first site added to the route should be the one with excess bikes, and the last site added to the route is the one with shortage of bikes; if the last site added has excess bikes, try to replace it with another unsaturated, last added site; second, check the truck's load capacity and budget for feasibility; if adding a site causes the truck to overload, select the next nearest unvisited site; repeat the above steps until all sites are properly arranged; For a given route, the number of stations to be loaded or unloaded is determined by a greedy algorithm; the number of bicycles that can be unloaded at a station or the number of bicycles that can be loaded at a station is determined by the maximum number of missing bicycles or the maximum number of excess bicycles, respectively, and denotes the nodes that occur in the path of a truck, then the mathematical expression of the above algorithm is: ； S 6.2: Perturbation phase: in each iteration, a perturbation operator is randomly selected, and the constraints are checked to generate a feasible solution; the following neighborhood structures will be applied in order, and the best improvement strategy is used for search; check the feasibility of all candidate routes, and for each feasible scheme, use a greedy algorithm to determine the number of loads and unloads; Step 6.3: Variable neighborhood descent local search: The lower variable neighborhood descent phase also uses the neighborhood structure feasible solution resulting from the search perturbation phase neighborhood of until an optimal solution of the neighborhood is obtained ; if is better than , let , ; otherwise, ; until the maximum number of iterations is reached, output the locally optimal solution .

10. The rebalancing method of shared bikes considering operator and user incentives according to claim 9, wherein, The local optimal solution includes the original driving route as follows: Motivated as The incentive price, the The first type of vehicle Did the vehicle come from Click Point, and the The first type of vehicle Vehicles from the area Transported to the area The loading and unloading volume.

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