Post-earthquake two-stage multi-scenario vehicle-machine collaborative site selection and scheduling method and system

Abstract

The application provides a post-earthquake two-stage multi-scene vehicle-machine coordination site selection and scheduling method and system, relates to the technical field of unmanned vehicle intelligent scheduling, and aims to solve the problems of the existing model in the multi-target optimization, the dependence on subjective weight setting, and the interruption of materials when the facilities fail due to the split of pre-disaster site selection and post-disaster response. The method comprises the following steps: acquiring basic data columns of a post-earthquake rescue network, constructing a two-stage double-target mixed integer programming model based on the basic data, solving the two-stage double-target mixed integer programming model by using a two-stage randomization greedy construction algorithm, obtaining a Pareto non-dominated solution set, and screening the final pre-disaster resource allocation and post-disaster response scheme based on the obtained Pareto non-dominated solution set. Through multi-scene robust optimization and dynamic reallocation, the total waiting time under the worst failure condition is improved, the interruption of materials is avoided, and the robustness and effectiveness of the post-earthquake rescue scheme are improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent scheduling technology for unmanned aerial vehicles (UAVs), and in particular relates to a site selection and scheduling method and system for multi-scenario vehicle-UAV collaboration in two stages after an earthquake. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In today's society, major emergencies occur frequently, giving rise to truck-drone collaborative transportation systems. The collaborative operation of these two types of vehicles can effectively integrate their respective advantages and provide new solutions for emergency logistics.

[0004] However, existing truck-drone collaborative transportation models often rely on subjective weight settings in multi-objective optimization, using a weighted summation method to merge multiple objectives into a single objective. When both district-level and community distribution centers fail simultaneously in a scenario, leading to a sharp drop in available transportation capacity, such models cannot directly use the response time under the worst-case scenario as an optimization guide. Consequently, the generated resource allocation scheme may suffer from insufficient coverage and forced outsourcing of a large number of demand points under the worst-case failure situation, resulting in increased response time. Furthermore, existing methods do not recognize the correlation between pre-disaster site selection and resource allocation decisions and the actual availability of facilities after a disaster. When a district-level distribution center fails in a scenario, the lack of a method to dynamically redistribute community distribution centers and their subordinate demand points based on facility availability leads to the interruption of supplies to community distribution centers that have lost their superior supply sources, and demand points are unable to receive relief due to the lack of supplies to be delivered. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, this invention provides a site selection and scheduling method and system based on post-earthquake two-stage multi-scenario vehicle-machine collaboration. It provides a method that takes into account both economy and timeliness for the planning and decision-making of post-earthquake urban collaborative rescue networks, and can provide quantitative decision support for emergency management departments in pre-disaster resource allocation and post-disaster response scheduling.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration, comprising: Obtain basic data from the post-earthquake relief network; Based on the aforementioned basic data, a two-stage, dual-objective mixed integer programming model is constructed. The model aims to minimize the pre-disaster fleet purchase cost and minimize the total waiting time in the worst-case scenario, with constraints including site selection, availability allocation, truck transfer, and drone delivery. A two-stage randomized greedy construction algorithm is used to solve the two-stage bi-objective mixed integer programming model. For each generated pre-disaster plan, the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario are calculated and stored in the plan set. Pareto non-dominated screening is performed on the plan set to obtain the Pareto non-dominated solution set. The solution process includes: random generation, greedy construction and Pareto screening. The final pre-disaster resource allocation and post-disaster response plan are obtained by filtering the Pareto non-dominated solution set.

[0007] Furthermore, the basic data includes the set of district-level distribution centers, the set of candidate community distribution centers, the set of demand points, the facility failure status of district-level distribution centers and candidate community distribution centers, fluctuations in truck travel time, and changes in the demand for materials at the demand points. Furthermore, the site selection and attribution constraints specifically include: site selection uniqueness constraints, truck attribution constraints, truck configuration quantity counting constraints, drone configuration prerequisite constraints, and drone attribution constraints. Furthermore, the available allocation constraints specifically include: facility availability constraints and allocation coupling constraints; Furthermore, the truck transfer constraints specifically include: truck origin selection constraints, truck route flow balance constraints, truck jurisdiction constraints, time recursion constraints, truck departure time constraints, community material availability time definition constraints, total truck unloading constraints, unloading and access association constraints, district-level distribution center total capacity constraints, and district-level distribution center inventory constraints. Furthermore, the constraints on drone delivery specifically include: single flight and single demand point constraint, endurance constraint, drone physical ownership constraint, drone availability center prerequisite constraint, drone payload constraint, community distribution center material conservation constraint, unique demand point coverage constraint, coverage status definition constraint, drone arrival time calculation constraint, flight sequence constraint, community center first flight waiting constraint, and district-level center first flight immediate constraint. Furthermore, the random generation specifically includes: Randomly select one of the three heuristic scoring strategies: weighted distance sum, maximum distance, and weighted combination of weighted distance sum and distance to the nearest district-level distribution center. Calculate the score of the candidate community distribution center, take the reciprocal of the score and normalize it to a probability, and randomly select the candidate point through a roulette wheel mechanism. The selected community distribution centers will be assigned to the nearest district-level distribution center according to a preset probability of one, and to the next nearest district-level distribution center according to a preset probability of two. Calculate the base number of trucks, add random fluctuations, and allocate trucks proportionally, ensuring that each district-level distribution center with a community distribution center allocation receives at least one truck. The configuration of drones is determined based on the number of demand points allocated to each node, using the number of points / R+1 as the base, and adding random disturbances, where R represents the maximum number of flights that the drone is allowed to perform. Furthermore, the greedy construct specifically includes: If a district-level distribution center fails in the current scenario, all community distribution centers that were assigned to the failed district-level distribution center will be reassigned to the nearest unfailed district-level distribution center; if all district-level distribution centers fail, all demand points in this scenario will be outsourced. For each available district-level distribution center, the community distribution centers it is responsible for are arranged in ascending order of distance, and the load is allocated sequentially using a load balancing strategy. Each time, a truck with the smallest current cumulative load that can accommodate the demand of the community distribution center is selected, the community distribution center is inserted at the end of the truck's route, and the arrival time is calculated by accumulating the travel time. In all available distribution centers, maintain the earliest available time and remaining flight count for each drone. Iterate through all unserved demand points, calculate the earliest arrival time for each drone on each available node if it were to perform that flight, select the earliest globally reachable demand point-drone-node combination to perform the service, update the earliest available time of the drone and decrement the remaining flight count until all reachable demand points are served or there are no more flights to perform. The total waiting time for the current scenario is calculated based on the sum of truck arrival times, the sum of drone arrival times, and the outsourcing penalty. The maximum value among all scenarios is taken as the minimum worst-case total waiting time for this solution. Furthermore, the Pareto screening specifically includes: deduplicating and merging the solution set, comparing the dominance relationships between solutions one by one through bi-objective non-dominated comparison, retaining all solutions that are not dominated by other solutions, forming the Pareto front, and obtaining the Pareto non-dominated solution set.

[0008] The second aspect of the present invention provides a location scheduling system based on post-earthquake two-stage multi-scenario vehicle-machine collaboration, including a data acquisition module, a model building module, a model solving module and a scheme output module; The data acquisition module is configured to acquire basic data from the post-earthquake relief network. The model building module is configured to: build a two-stage, dual-objective mixed integer programming model based on the basic data. The model aims to minimize the pre-disaster fleet purchase cost and minimize the total waiting time in the worst-case scenario, with constraints including site selection, availability allocation, truck transfer, and drone delivery. The model solving module is configured to: use a two-stage randomized greedy construction algorithm to solve the two-stage bi-objective mixed integer programming model; for each generated pre-disaster solution, calculate the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario and store them in the solution set; perform Pareto non-dominated screening on the solution set to obtain a Pareto non-dominated solution set; the solving process includes: random generation, greedy construction and Pareto screening. The solution output module is configured to: filter the obtained Pareto non-dominated solution set to obtain the final pre-disaster resource allocation and post-disaster response scheme.

[0009] The above one or more technical solutions have the following beneficial effects: This invention uses a set of discrete scenarios to describe the uncertainty of district-level distribution centers and community distribution centers, and further uses the total waiting time in the worst scenario as the optimization target. This overcomes the problem that existing solutions rely on subjective weights and cannot directly optimize the performance of extreme scenarios, so that the total waiting time of the final generated resource allocation scheme is improved in the worst failure case, avoiding the problems of insufficient coverage and increased response time in the drone delivery link from the distribution center to the demand point. This invention considers pre-disaster community distribution center site selection, truck and drone resource allocation, post-disaster truck route planning, drone flight allocation, and dynamic reallocation based on facility availability in a two-stage decision-making process. It solves the problem of the disconnect between pre-disaster site selection and post-disaster response in existing methods. When a district-level distribution center fails, it can reallocate community distribution centers whose material supply has been cut off to available district-level distribution centers based on facility availability. This avoids the problem of material interruption at lower-level nodes and the inability of demand points to receive rescue due to the failure of higher-level nodes, thus enhancing the effectiveness of the solution in the case of facility failure.

[0010] Advantages of additional aspects 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

[0011] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0012] Figure 1 A flowchart of a location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the post-earthquake urban collaborative rescue network structure provided in an embodiment of the present invention; Figure 3 A flowchart of a two-stage randomized greedy construction algorithm provided in an embodiment of the present invention; Figure 4Pareto front distribution map provided for embodiments of the present invention; Figure 5 The convergence curve of the hypervolume index as a function of the number of samplings is shown in the embodiment of the present invention. Detailed Implementation

[0013] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0014] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0015] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0016] Example 1 like Figure 1 As shown, this embodiment discloses a location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration, including the following steps: Step S1: Obtain basic data from the post-earthquake relief network; Step S2: Construct a two-stage, dual-objective mixed integer programming model based on the aforementioned basic data. The model aims to minimize the pre-disaster fleet purchase cost and the worst-case total waiting time. It uses pre-disaster site selection and resource allocation variables, as well as post-disaster truck route and drone flight allocation variables, as decision variables. It also uses site selection attribution, availability allocation, truck transfer, and drone delivery as constraints. Step S3: A two-stage randomized greedy construction algorithm is used to solve the two-stage bi-objective mixed integer programming model. For each generated pre-disaster plan, the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario are calculated and stored in the plan set. Pareto non-dominated screening is performed on the plan set to obtain the Pareto non-dominated solution set. The solution process includes: random generation, greedy construction and Pareto screening. Step S4: Based on the obtained Pareto non-dominated solution set, the final pre-disaster resource allocation and post-disaster response plan are obtained by filtering.

[0017] Next, combined Figure 1 This embodiment provides a detailed description of a location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration.

[0018] (I) Model Assumptions and Parameter Definitions The rescue network in this embodiment includes three types of nodes: a set of district-level distribution centers G (fixed locations, with initial inventory and strong survivability), a set of candidate community distribution centers J (selected from each region, with exactly one center to be converted in each region), and a set of demand points D (residential areas or temporary shelters that need to receive relief supplies). Figure 2 As shown, the transportation method is divided into two levels: trucks are responsible for transferring bulk materials from district-level distribution centers to community distribution centers; drones are responsible for the last-mile delivery from distribution centers (including district-level distribution centers and community distribution centers) to the demand points, and each drone can perform multiple round trips.

[0019] Furthermore, existing models do not adequately characterize the multiple uncertainties such as post-disaster facility failure and road damage. The post-earthquake scenario presents the following uncertainties: First, district-level and community distribution centers may be unusable due to earthquake damage (using binary parameters). , describe, The value is 1 if candidate community distribution center j fails in scenario s, and 0 otherwise. (1 indicates that the district-level distribution center g is invalid in scenario s, and 0 otherwise); secondly, truck travel time fluctuates due to changes in road conditions; thirdly, the demand for materials at each demand point varies with the degree of disaster (based on scenario-related parameters). describe, This represents the demand at demand point d under scenario s (which is a constant if demand fluctuations are not considered). However, most existing methods only consider the single type of uncertainty mentioned above. Therefore, this embodiment also utilizes a discrete scenario set S for modeling, where each scenario represents a possible post-disaster realization state, and the above three types of uncertainty parameters are defined as relevant variables of the scenario.

[0020] After defining the rescue network and transportation methods, the decision-making process in this embodiment is divided into two stages: Phase 1 (Pre-Disaster): Before the disaster occurs, determine the location of community distribution centers, the district-level distribution centers to which each community distribution center belongs, and the number of trucks allocated to each district-level distribution center. And the number of drones deployed at each distribution center (including district and community levels). The decision-making at this stage is independent of specific scenarios and aims to build a basic resource network with minimal fleet acquisition costs.

[0021] Phase Two (Post-Disaster): For each earthquake scenario s, emergency response is implemented based on available facilities. Trucks depart from their respective district-level distribution centers, transporting supplies to their assigned community distribution centers (if available); drones take off from available distribution centers, with delivery methods including: delivery from their own community distribution center, direct flight from the district-level distribution center, or cross-district support from other community distribution centers. The model automatically selects the optimal delivery allocation by minimizing wait time. If a demand point d cannot be covered by any drone under any of the above methods, outsourcing is allowed, with an equivalent wait time penalty.

[0022] In addition, the key decisions in this case include: (1) the location and district-level allocation of community distribution centers; (2) the number of trucks configured for each district-level distribution center; (3) the number of drones configured for each distribution center; (4) the route and unloading plan for each truck after the disaster; and (5) the flight allocation and take-off time arrangement for each drone.

[0023] To facilitate modeling and solving, this embodiment makes the following assumptions: ① The driving speeds of both the truck and the drone are constant, and the drone flies along a straight path between the distribution center and the demand point; ② The truck's load is measured only by the number of packages, ignoring volume differences, and all supplies are homogeneous relief packages; ③ The outsourcing penalty coefficient P is a pre-set constant used to equivalently measure the equivalent waiting time caused by the uncovered demand point.

[0024] In summary, the model constructed in this embodiment describes uncertainty using discrete scenarios, separates pre-disaster preparation and post-disaster response through a two-stage decision-making process, integrates key elements such as truck-drone collaborative transportation, facility failure, material inventory and flight scheduling, and ultimately constructs a mixed integer programming model with the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario as the objectives. This provides an optimization method that balances economy and timeliness for the design of post-earthquake urban rescue networks.

[0025] (II) Model Construction The two-stage, dual-objective mixed-integer programming model in this embodiment is as follows: (1) (2) (3) The objective function of the model includes: (1) minimizing the pre-disaster fleet purchase cost F1, which includes the fixed costs of all trucks and drones. (2) minimizing the total waiting time F2 in the worst-case scenario using the minmax criterion, where the total waiting time consists of three parts: the cumulative time for trucks to reach the community distribution center, the cumulative time for drones to reach the demand point, and the equivalent waiting time for uncovered demand points calculated using outsourcing penalties. Where, For the fixed cost of each truck, The number of trucks configured for a district-level distribution center g, where G is the set of district-level distribution centers, where , For the fixed cost of each drone, Let i be the number of drones configured for node i, where i∈I, I is the set of all distribution center nodes, I=J∪G, and J is the set of all candidate community distribution centers. S is a set of earthquake scenarios, where , Let be the total waiting time in scenario s. This represents the time (scenario s) when the drone u arrives at the required point d on its r-th flight. , This represents the time it takes for truck m to arrive at community distribution center j in scenario s. , This indicates that if requirement point d is covered in scenario s (at least one flight service), and If it is 1, then it is 1; otherwise it is 0. This represents the demand at demand point d in scenario s. If demand fluctuations are not considered, it is a constant. P represents the outsourcing penalty coefficient.

[0026] Model constraints include site selection, availability allocation, truck transfer, and drone delivery.

[0027] Among them, the location allocation constraints specifically include formulas (4)-(9). (4) (5) (6) (7) (8) (9) Formula (4) is a site selection uniqueness constraint to ensure that exactly one community distribution center is transformed in each area; Formula (5) is a truck affiliation constraint to ensure that each truck must and can only belong to one district-level distribution center; Formula (6) is a truck configuration quantity counting constraint to associate this affiliation with the truck configuration quantity Ω of each district-level distribution center. g The association ensures consistent counting; Formula (7) is a prerequisite constraint for drone configuration, ensuring that community distribution centers must be selected before drones can be configured; Formulas (8)-(9) are drone affiliation constraints, stipulating that each drone must belong to a distribution center, and the number of drones allocated to each center is equal to its configuration quantity. .

[0028] In the formula, This is a collection of candidate community distribution centers within region z. This indicates that if candidate community distribution center j is selected, and If the expression is true, then the expression is 1; otherwise, it is 0. Z represents the set of all regions, where... , This means that if truck m belongs to the district-level distribution center g, and If it is 1, then it is 1; otherwise it is 0. Let M be the number of trucks configured for the district-level distribution center g, where M is the set of trucks. , This indicates the number of drones configured in community distribution center j. This indicates that if drone u belongs to node i, and If it is 1, then it is 1; otherwise it is 0. A collection of drones, among which .

[0029] The available allocation constraints specifically include formulas (10)-(12). (10) (11) (12) Formulas (10)-(11) are facility availability constraints, which characterize that community distribution centers are available if and only if they are selected and not invalid, and district-level distribution centers are available if and only if they are not invalid; Formula (12) is an allocation coupling constraint, which requires that each available community distribution center must be allocated to exactly one available district-level distribution center, linking post-disaster availability with pre-disaster site selection decisions.

[0030] In the formula, This indicates that if community delivery center j is available in scenario s, and If it is 1, then it is 1; otherwise it is 0. This indicates that if candidate community distribution center j is selected, and If it is 1, then it is 1; otherwise it is 0. The value is 1 if candidate community distribution center j fails in scenario s, and 0 otherwise. This indicates that if the district-level distribution center g is available in scenario s, and If it is 1, then it is 1; otherwise it is 0. The value is 1 if the district-level distribution center g is invalid in scenario s, and 0 otherwise. This means that if, in scenario s, community distribution center j is assigned to district-level distribution center g, and If the result is positive, the value is 1; otherwise, it is 0.

[0031] The truck transfer constraints specifically include formulas (13)-(23). (13) (14) (15) (16) (17) (18) (19) (20) (twenty one) (twenty two) (twenty three) Formula (13) is the truck origin selection constraint. Each truck can only depart from one available district-level distribution center to which it belongs. Formulas (14) and (15) are the truck path flow balance constraints, which respectively characterize the flow conservation from the origin and the flow balance of intermediate nodes. If a truck arrives at a community distribution center, it must leave or end its journey. One of the two must be true. Formula (16) is the truck jurisdiction constraint, which ensures that trucks can only access community distribution centers under the jurisdiction of their respective district-level distribution centers, thus avoiding the chaos of cross-district distribution. Formula (17) is the time recursion constraint, which establishes the arrival time relationship between consecutively accessed nodes. Formula (18) is the truck departure zero-time constraint, which stipulates that the departure time of the district-level distribution center is 0, serving as the origin of the entire time axis. Formula (19) is the community material availability time definition constraint, which defines the material availability time of the community distribution center. The maximum arrival time for all trucks arriving at the center is a critical time point connecting truck transfers and drone last-mile delivery; the first drone flight from the community distribution center must be executed after this time.

[0032] Formula (20) is the total unloading limit for trucks, ensuring that the unloading volume of each truck does not exceed its maximum load capacity. Formula (21) is the unloading and access association constraint, ensuring that unloading can only be carried out at the community distribution center where the truck actually arrives. Formula (22) is the total transport capacity constraint for district-level distribution centers, ensuring that the total amount of goods transported by all trucks departing from the center does not exceed the total load capacity of the configured vehicles. Formula (23) is the inventory constraint for district-level distribution centers, ensuring that the sum of the total amount of goods transported by trucks and those flown directly by drones does not exceed its initial inventory, thus incorporating material reserves and distribution capacity into a unified framework.

[0033] In the formula, This means that if, in scenario s, truck m departs from district-level distribution center g, and If it is 1, then it is 1; otherwise it is 0. This indicates that if the district-level distribution center g is available in scenario s, and If it is 1, then it is 1; otherwise it is 0. This means that if truck m belongs to the district-level distribution center g, and If it is 1, then it is 1; otherwise it is 0. This means that if, in scenario s, truck m travels from district-level distribution center g to community distribution center j, and If it is 1, then it is 1; otherwise it is 0. This means that in scenario s, truck m travels from community distribution center j to community distribution center j. ,and If it is 1, then it is 1; otherwise it is 0. This indicates that if, in scenario s, truck m ends its journey at community delivery center j, and If it is 1, then it is 1; otherwise it is 0. This means that in scenario s, truck m travels from community distribution center j to community distribution center j. ,and If it is 1, then it is 1; otherwise it is 0. This means that if, in scenario s, truck m travels from node i to node j, and If it is 1, then it is 1; otherwise it is 0. This means that if, in scenario s, community distribution center j is assigned to district-level distribution center g, and If it is 1, then it is 1; otherwise it is 0. This represents the time it takes for truck m to arrive at community distribution center j in scenario s. , This represents the time it takes for truck m to reach node i in scene s. , This represents the travel time of the truck from node i to node j. , This represents the time when truck m departs from the district-level distribution center g in scenario s. , This indicates the earliest available time of supplies for community distribution center j in scenario s. , Let M be the number of trucks configured for the district-level distribution center g, where M is the set of trucks. This represents the amount of supplies that truck m unloads at community distribution center j in scenario s. , Let D represent the truck's load capacity (number of packages) and D be the set of demand points. Let [R] be the set of drone flights, where R is the maximum number of flights allowed for each drone, and r∈[R]={1,2,…,R}. This indicates that if, in scenario s, the drone u's r-th flight departs from the distribution center g to the demand point d, and If it is 1, then it is 1; otherwise it is 0. This represents the initial inventory of the district-level distribution center g. , This represents the demand at demand point d in scenario s. If demand fluctuations are not considered, it is a constant.

[0034] The constraints on drone delivery specifically include formulas (24)-(35). (twenty four) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) Formula (24) is a single-flight single-demand-point constraint, stipulating that each UAV flight can serve at most one demand point; Formula (25) is a flight endurance constraint, the round-trip flight distance of the UAV shall not exceed the maximum flight range L of the UAV; Formula (26) is a physical affiliation constraint of the UAV, limiting the UAV to only depart from the distribution center to which it belongs; Formula (27) is a UAV available center prerequisite constraint, used to limit the total number of flights of each UAV to no more than the upper limit R, the two together ensure the physical affiliation and operational capability boundary of the UAV; Formula (28) is a UAV payload constraint; Formula (29) is a community distribution center material conservation constraint, the total amount of materials transported by UAV from the community distribution center shall not exceed the amount of materials received by the center by truck, tightly coupling the first-mile transfer and the last-mile delivery; Formula (30) is a demand point unique coverage constraint, ensuring that each demand point is covered at most once; Formula (31) is a coverage state definition constraint, defining the coverage indicator variable Defined as whether there is a demand for drone flights, this provides a basis for calculating outsourcing penalties.

[0035] Formula (32) is the constraint for calculating the arrival time of the UAV, which depends on the take-off time and flight time. Formula (33) is the flight sequence constraint, which requires that the next flight can only take off after the previous flight has returned, reflecting the physical operation sequence of the UAV. Formula (34) is the waiting constraint for the first flight of the community center, which stipulates that the UAV must wait for the materials to be available before it takes off for the first time from the community distribution center. Formula (35) is the immediate constraint for the first flight of the district-level center, which allows the UAV to take off immediately from the district-level distribution center. The essential difference in the timing logic between the two types of centers is thus characterized.

[0036] In the formula, This indicates that if, in scenario s, the drone u's r-th flight departs from distribution center i to demand point d, and If it is 1, then it is 1; otherwise it is 0. This represents the distance from node i to the required point d (used by drones). M is the set of trucks, where This indicates the drone's payload (number of packages / flights), and R is the maximum number of flights allowed per drone. This indicates that if drone u belongs to node i, and If it is 1, then it is 1; otherwise it is 0. This indicates that if distribution center i is available in scenario s, and If it is 1, then it is 1; otherwise it is 0. This indicates that if requirement point d is covered in scenario s (at least one flight service), and If it is 1, then it is 1; otherwise it is 0. This represents the demand at demand point d in scenario s. It is a constant if demand fluctuations are not considered. This represents the amount of supplies that truck m unloads at community distribution center j in scenario s. , This represents the time (scenario s) when the drone u arrives at the required point d on its r-th flight. This indicates the takeoff time of the drone u on its r-th flight in scenario s. , This indicates the earliest available time of supplies for community distribution center j in scenario s. , This represents the flight time of the drone from node i to the demand point d. , This indicates the takeoff time of the drone u in scenario s for its first flight (from its center). , This represents the takeoff time of drone u in scenario s for the (r+1)th flight. , This indicates that if, in scenario s, the drone u's r-th flight departs from community delivery center j to demand point d, and .

[0037] Finally, formulas (36) and (37) define the range of values ​​for all decision variables: the former defines all 0-1 variables, and the latter defines the range of values ​​for all decision variables. and The variables are non-negative integers, while the remaining time and material quantities are continuous non-negative variables. This constraint system organically connects pre-disaster preparation and post-disaster response through a two-stage structure. From site selection and configuration, facility failure, truck routes, and material flow to UAV flight scheduling and time coordination, it progressively and completely depicts the operational logic of the post-earthquake urban collaborative rescue network.

[0038] (36) (37) (III) Two-phase randomized greedy construction algorithm Based on the model construction section, this embodiment addresses the post-earthquake urban collaborative rescue network optimization problem by constructing a two-stage, dual-objective, multi-scenario mixed-integer linear programming model. This model involves multiple decision dimensions, including pre-disaster site selection and resource allocation, post-disaster truck route planning, UAV flight allocation, material flow balancing, and time coordination. However, this approach leads to the constructed mixed-integer linear programming model exhibiting high dimensionality, strong coupling, and combinatorial explosion issues. To address this, this embodiment further designs a two-stage randomized greedy construction algorithm (TS-RGCA). This algorithm combines multiple random sampling with greedy simulation to generate a set of high-quality Pareto non-dominated solutions within a reasonable timeframe, providing decision-makers with diverse solution options.

[0039] The algorithm employs a three-layer framework of random generation, greedy construction, and Pareto selection, decoupling pre-disaster site selection and post-disaster response simulation into two stages. During the iteration process, it explores the solution space through diverse strategies, such as... Figure 3 As shown, its core process is as follows: Step 1: Initialization and Parameter Setting. Load the problem instance data (distance matrix, requirement point information, candidate node set, etc.), set the algorithm control parameters (maximum number of iterations MAX_ITER, maximum drone range L, maximum number of flights R, outsourcing penalty coefficient P, etc.), initialize the random number seed, and create a data structure to store all solutions and Pareto solutions.

[0040] Step Two (Phase One): Randomized Site Selection, Allocation, and Resource Configuration. This phase is completed before the disaster and is independent of the specific scenario. It includes three sub-steps: 1. Multi-strategy random site selection: For each region, one of three heuristic scoring strategies is randomly selected: Strategy S1 is a weighted distance sum (weighted by demand), Strategy S2 is the maximum distance, and Strategy S3 is a weighted combination of the weighted distance sum and the distance to the nearest district-level distribution center. After calculating the score for each candidate community distribution center, the reciprocal of the score is normalized to a probability, and a candidate point is randomly selected through a roulette wheel mechanism to achieve diversity in site selection schemes.

[0041] 2. Random perturbation allocation: The selected community distribution center is allocated to the nearest district-level distribution center with an 80% probability and to the next nearest district-level distribution center with a 20% probability. While maintaining the principle of proximity, a controllable random perturbation is introduced to increase the diversity of allocation schemes.

[0042] 3. Resource Allocation: First, the demand allocation function is called to assign each demand point to the nearest and reachable distribution center, summarizing the total demand and the number of demand points for each node. Based on the total demand in the area managed by each district-level distribution center, the number of basic trucks is calculated (total demand / The trucks are allocated according to the demand ratio of each center after adding a random fluctuation amount [1,3], ensuring that each district-level distribution center with a community distribution center allocation receives at least one truck. The drone configuration is determined based on the number of demand points allocated to each node, using (number of points / R+1) as the base, and adding a random disturbance to ensure coverage while avoiding excessive resource redundancy. Here, R represents the maximum number of flights that the drone is allowed to perform.

[0043] Step 3 (Second Phase): Scenario-Driven Multi-Scenario Greedy Simulation. Based on the pre-disaster generated site selection and resource allocation scheme, sequentially traverse all failure scenarios (36 in total, covering no failure, single district-level center failure, single community center failure, combined district-level and community failure, and dual community failure, etc.), and execute the following post-disaster response simulation: 1. Dynamic reallocation: If a district-level distribution center fails in the current scenario, all community distribution centers that were assigned to the failed district-level distribution center will be reassigned to the nearest and not failed district-level distribution center; if all district-level distribution centers fail, all demand points in this scenario will be outsourced.

[0044] 2. Truck Route Construction: For each available district-level distribution center, the community distribution centers it is responsible for are arranged in ascending order of distance. A load balancing strategy is used to allocate them sequentially. Each time, the truck with the smallest current cumulative load that can accommodate the demand of that community distribution center is selected, and the community distribution center is inserted at the end of the truck's route. The arrival time is calculated by accumulating the travel time. This strategy minimizes the load difference between trucks while ensuring load constraints.

[0045] 3. Greedy Drone Scheduling: For each drone, maintain its "earliest available time" and "remaining flight count" across all available delivery centers (both district-level and community-level centers that are not yet expired). Iterate through all unserved demand points, calculate the earliest arrival time for each drone on each available node to perform that flight, and select the globally earliest reachable demand point-drone-node combination to execute the service; update the drone's earliest available time (takeoff time + 2). d i,d The remaining number of flights will be reduced until all reachable demand points are served or there are no more flights available. Demand points not covered by any drone will be counted as outsourced and penalized.

[0046] 4. Scene Target Calculation: The total waiting time for the current scene is calculated based on three parts: the cumulative arrival time of the truck, the cumulative arrival time of the drone, and the outsourcing penalty. The maximum value among all scenarios is taken as the F2 value of the solution.

[0047] Step 4: Target Calculation and Solution Recording. Calculate the pre-disaster fleet acquisition cost F1 (the sum of fixed costs for trucks and drones) for this solution. Store (F1, F2) along with complete decision details (site selection, allocation, truck configuration, drone configuration, worst-case truck routes and drone flight records, etc.) in the solution set. Periodically (every 500 iterations), record the overvolume metric to track the algorithm's convergence progress.

[0048] Step 5: Pareto Screening and Result Output. After iteration, the solution set is deduplicated and merged according to (F1, F2), and then Pareto non-dominated screening is performed. Through bi-objective non-dominated comparison, the dominance relationships between solutions are compared one by one, and all solutions not dominated by other solutions are retained, forming the Pareto front and obtaining the Pareto non-dominated solution set. The complete decision information of the front solution is output to a text file, and the Pareto front curve and hypervolume convergence curve are plotted to provide decision-makers with visual analysis basis.

[0049] The key technologies of the algorithm in this embodiment are reflected in several aspects: First, the multi-strategy random location selection and perturbation allocation mechanism transforms the three deterministic scores into probabilistic selections, introducing controllable randomness in local optimization and avoiding premature entrapment in local optima; Second, the coupling of resource allocation and demand pre-allocation ensures that the number of trucks and drones configured precisely matches the actual load; Third, traversing multiple failure scenarios and using the worst-case waiting time as a guide enhances the robustness of the solution to facility damage; Fourth, the balanced load truck route construction and the greedy scheduling of drones with the earliest completion time work together to form a progressive optimization; Fifth, the integration of hypervolume tracking and Pareto screening endows the algorithm with self-monitoring and convergence analysis capabilities.

[0050] Furthermore, this embodiment proposes a two-stage stochastic greedy construction framework for robust optimization across multiple scenarios, achieving synchronous coupling between pre-disaster solution generation and post-disaster multi-scenario assessment, generating high-quality Pareto fronts while maintaining low computational complexity. The algorithm integrates failure scenario generation and hypervolume convergence tracking modules, providing decision-makers with convergence evidence and robustness quantification beyond the objective function value. This algorithm can serve as an independent heuristic solver for emergency decision-making, offering managers multiple trade-offs between fleet costs and response efficiency, demonstrating significant practical value.

[0051] (iv) Numerical Experiments This embodiment implements a two-stage randomized greedy algorithm on the Python platform to conduct experimental analysis of the model and algorithm using a test network containing 2 district-level distribution centers, 6 candidate community distribution centers (belonging to 3 regions), and 33 demand points. The node distribution of the test network is constructed based on the actual road network of a certain region. The test network is configured with a variable number of trucks and drones, considering a total of 36 failure scenarios, including two types of uncertain combinations: the first type is the combination of a single district-level distribution center failure and a single candidate community distribution center failure (2×6=12 scenarios), and the second type is the combination of any two of the 6 candidate community distribution centers failing simultaneously. =15 scenarios), plus 1 no-failure baseline scenario, 2 scenarios with failure only at the district-level distribution center, and 6 scenarios with failure only at the community distribution center, totaling 36 scenarios, comprehensively covering the multiple uncertainties of post-earthquake facility failure. The algorithm parameters are set as follows: maximum number of iterations MAX_ITER=30000, maximum number of flights per drone R=4, maximum drone range L=60, outsourcing penalty coefficient P=200, truck load capacity Packages, drone payload Package and truck fixed costs Fixed costs of drones .

[0052] 1. Pareto Front and Convergence Analysis After 30,000 iterations, the algorithm generated 23,655 non-repeating solutions. After Pareto non-dominated filtering, 18 non-dominated approximate Pareto optimal solutions were obtained. The total running time of the algorithm was 3239.93 seconds (54.00 minutes), indicating that the algorithm effectively explored the solution space within an acceptable computational cost. Figure 4 It shows the distribution of the Pareto front in the target space, with the horizontal axis representing the team acquisition cost F1 and the vertical axis representing the total waiting time in the worst-case scenario F2.

[0053] Depend on Figure 4As can be seen, the Pareto front exhibits a clear diminishing marginal return pattern, which can be divided into two observable phases. The first phase is a steep decline (F1=1400~2250): when F1 increases from 1400 to 2250, F2 drops sharply from 15492.32 to 4368.24, a decrease of 71.8%. On average, every 100 units of fleet cost increase can be exchanged for approximately 1448 units of waiting time reduction. In this phase, the extremely low configuration scheme with F1=1400 (only 5 drones in total at each node) is forced to outsource 25 demand points in the worst-case scenario, with an extremely high outsourcing penalty ratio; while when F1 increases to around 2250, the total number of drones increases to about 12, and the outsourcing demand points are reduced to 5, achieving a qualitative leap in response capability. This steep decline phase means that under conditions of extreme scarcity of emergency resources, a small amount of additional investment can quickly make up for the shortcomings in end-point coverage, with extremely high marginal benefits. It is a key investment range with significant marginal benefits in emergency decision-making.

[0054] The second stage is a gradual approach to saturation (F1=2250~3200): F1 continues to increase from 2250 to 3200, while F2 only decreases from 4368.24 to 3919.23, with the reduction narrowing to 10.3%. On average, every 100 units of increased cost only yields about 56 units of waiting time reduction. In this stage, the increased fleet resources are mainly used to optimize the response timing of already covered demand points, rather than expanding the coverage area, so the improvement effect diminishes with each increase. In particular, after F1=2700, F2 has already decreased to 3948.03, and a further increase to 3200 only results in a further decrease of 28.80, with marginal benefits approaching negligible levels. At the end of the front line, F2 approaches the lower limit of about 3900, indicating that under given network structure and range constraints, even with a significant increase in fleet resources, the total waiting time in the worst-case scenario is unlikely to exceed this theoretical lower bound. To further reveal the internal structural differences of different front line solutions, a comparative analysis of typical non-dominated solutions is conducted below.

[0055] The structural differences between the two ends of the frontier significantly reflect the correspondence between resource input and service guarantee capabilities. Taking the extremely low-configuration scheme with F1=1400 as an example (drone configuration: 1 drone each for district-level distribution center 0 and community distribution centers 4 and 6, with no drones for district-level distribution center 1), its worst-case scenario is the simultaneous failure of candidate community distribution centers 2 and 4, resulting in 25 out of 33 demand points being uncovered, and an F2 as high as 15492.32, indicating that the failure of dual facilities when resources are severely insufficient will cause a large-scale service outage. In contrast, the high-configuration scheme with F1=3200 (total of 22 drones and 2 trucks) reduces the number of outsourced demand points to 5 in all 36 failure scenarios (demand points 20, 22, 23, 24, and 25), and the worst-case F2 drops to 3919.23, demonstrating excellent robustness. It is worth noting that even with the highest configuration, there are still 5 remote demand points that cannot be covered. This indicates that these demand points are limited by the drone's range (L=60) or the location of the road network topology and belong to "inaccessible blind spots". Simply increasing fleet resources cannot solve the problem. It is necessary to break through by adding temporary take-off and landing points or deploying relay drones.

[0056] Figure 5 This is the convergence curve of the hypervolume index (HV) with the number of samplings. HV is a core comprehensive index for evaluating multi-objective optimization, measuring both the convergence (how close the solution is to the true Pareto front) and diversity (the breadth of solution distribution in the objective space) of the solution set. A larger HV value indicates a higher quality solution set.

[0057] from Figure 5As can be seen, the HV curve exhibits a monotonically rising trend throughout, with the rate of increase gradually narrowing, displaying three distinct stages. The first stage is a rapid climb (0-5000 iterations): HV jumps almost vertically from approximately 4.8×10⁷ to over 5.05×10⁷, an increase of 5.2%, accounting for the vast majority of the overall HV growth. This rapid growth indicates that the algorithm has extremely high search efficiency in the early stages of solution space exploration. The randomized greedy construction mechanism can quickly locate high-quality regions in the target space, completing the main framework of the Pareto front in only about 5000 iterations. The second stage is a slow, oscillating climb (5000-19000 iterations): HV gradually rises from approximately 5.09×10⁷ to around 5.13×10⁷, with a significant slowdown in the growth rate, exhibiting a step-like alternating pattern of "small increases - brief periods of stagnation". In this stage, the algorithm continuously discovers new non-dominated solutions, constantly refining and expanding the details of the Pareto front. However, the high-quality regions in the search space have been fully explored, leading to diminishing marginal returns. The third stage is the convergence and stability phase (19,000-30,000 iterations): After HV jumps to above 5.2 × 10⁷, it remains relatively stable, with a flat overall curve and only a very slight rise at the end. This indicates that the range of the Pareto front and the distribution density of solutions have stabilized in the later stages of the algorithm's iterations, and the hypervolume index has reached a state of saturated convergence. Further increasing the number of iterations has very little marginal benefit in improving the overall quality of the solution set. This convergence curve fully demonstrates the effective convergence of the TS-RGCA algorithm in multi-objective optimization solutions.

[0058] 2. Comparison of Typical Solutions and Analysis of Resource Allocation To reveal the internal structural differences and evolutionary patterns of different Pareto front solutions, this section selects three representative non-dominated solutions for comparative analysis: Transitional Solution I (F1=2100), Inflection Point Solution (F1=2800), and Transitional Solution II (F1=3000). The selection criteria are as follows: F1=2100 is located at the end of the steep descent phase, where the number of outsourcing demand points has decreased from 25 to 9, and coverage expansion is nearing completion, representing the "coverage expansion period"; F1=2800 is at the turning point where marginal returns plummet from "extremely limited" to "approaching zero," corresponding to the "performance saturation critical period"; F1=3000 is located within the gradual approaching saturation phase, where the number of outsourcing demand points has stabilized at 5, and further investment can only produce minor time-series optimization, representing a typical solution in the "redundancy investment period." These three solutions together outline the complete evolutionary path from coverage expansion and performance saturation to the investment of redundancy. The lowest-cost solution (F1=1400) has the lowest cost, but in the worst-case scenario, 25 demand points are forced to be outsourced, making it impractical for emergency situations. The highest-cost solution (F1=3200) increases cost by 14.3% compared to the inflection point solution, while F2 only improves by 0.6%, with marginal benefits approaching zero. Therefore, the three solutions in the middle region of the Pareto front are truly valuable for decision-making.

[0059] To measure the efficiency of drone configuration, the drone flight utilization rate is defined as the ratio of the total number of actual flights to the theoretical maximum number of available drones. The theoretical maximum number of flights equals the number of available drones multiplied by the maximum number of flights per drone, R (R=4). The number of available drones refers to the number of drones remaining after excluding the drones belonging to the failed node in the worst-case failure scenario. The actual number of flights equals the number of covered demand points (each demand point is served at most once). In the three schemes presented in this paper, all uncovered demand points are outsourced; therefore, the actual number of flights is 33 minus the number of outsourced demand points. The comparison results of the three schemes are shown in Table 1.

[0060] Table 1. Comparison of resource allocation and performance of typical Pareto solutions

[0061] The utilization rate of drone flights in the three schemes showed a monotonically decreasing trend (100%→46.7%→41.2%). In the transitional solution I, only 6 drones were available, and only by operating at full capacity (each drone completing all 4 flights) could 24 demand points be covered. In the inflection point solution, the number of available drones jumped to 15, and the number of demand points covered increased to 28, but the utilization rate dropped sharply, indicating that only 4 of the 9 newly available drones were converted into effective coverage expansion, and the rest were mainly used to optimize the service timing of already covered demand points.

[0062] From Transitional Solution I to Inflection Point Solution, the worst-case failure scenario undergoes a fundamental shift. Transitional Solution I is characterized by "0 failures at the district-level distribution center + 4 failures at the community distribution center," where 5 drones become unusable due to node failures, leaving only 6 drones available. The Inflection Point Solution is characterized by "simultaneous failures at community distribution centers 2 and 5," where only 3 drones are out of service, resulting in 15 available drones. This order-of-magnitude increase in available capacity (6 → 15 drones) is due to the reduction of outsourcing demand points from 9 to 5. The direct reason for the 38.7% reduction is that, more importantly, the worst-case scenario for the system has changed from "involving the failure of district-level distribution centers" to "involving only the failure of community distribution centers," indicating that resource investment has made the failure of district-level distribution centers no longer a bottleneck for system performance.

[0063] From the inflection point solution to the transitional solution II, the location selection and allocation relationship remains unchanged. The number of drones at district-level distribution center 1 decreases from 6 to 5, while the number at community distribution center 6 increases from 3 to 6, resulting in a net increase of 2 drones and a cost increase of 200. The number of outsourcing points decreased by only 0.5%, but the total number remains at 5. This adjustment attempts to strengthen the last-mile delivery capability of the only available community distribution center 6 in the worst-case scenario (when community distribution centers 2 and 5 fail), but the addition of drones failed to reduce any outsourcing points. All 5 outsourcing points (20, 22, 23, 24, and 25) are located at the edge of the road network. The failure of community distribution centers 2 and 5 cuts off their last-mile coverage channels, and community distribution center 6, constrained by its range (L=60), is also unable to provide coverage. Direct flights to district-level distribution centers are also insufficient to reach them. Therefore, the performance bottleneck lies in the physical endurance limit, not the number of drones.

[0064] The above analysis shows that the inflection point solution offers the best overall cost-effectiveness across the entire frontier: it achieves a reduction in outsourcing demand points from 9 to 5 at a moderate cost, improving the worst-case scenario from "district-level distribution center failure" to "double failure of community distribution centers," significantly enhancing system resilience. Subsequent resource additions only produce marginal improvements. Furthermore, the district-level distribution center configuration at the inflection point solution stage is already redundant—the fact that reducing one drone at district-level distribution center 1 in transitional solution II had almost no impact on system performance serves as a counter-evidence. For decision-makers with higher resilience requirements, priority should be given to adding redundant drones or pre-setting temporary take-off and landing points at key edge nodes such as community distribution centers 2 and 5, rather than continuing to add homogeneous capacity to existing nodes, as the latter, constrained by physical range, has marginal benefits approaching zero.

[0065] This embodiment addresses the complex conditions of facility failure, road network fluctuations, and demand uncertainty in post-earthquake urban rescue. It constructs a two-stage, dual-objective, multi-scenario truck-drone collaborative rescue network optimization model and designs the TS-RGCA algorithm for efficient solution. Through experimental network examples involving 2 district-level distribution centers, 6 candidate community distribution centers, and 33 demand points, totaling 36 failure scenarios, the effectiveness of the model and algorithm is verified, leading to the following conclusions: (1) The two-stage multi-scenario modeling framework effectively integrates pre-disaster site selection and post-disaster response decision-making, providing a systematic optimization tool for the design of post-earthquake relief networks. The model takes minimizing the fleet purchase cost and the total waiting time in the worst-case scenario as its dual objectives, and can generate 18 Pareto non-dominated solutions under 36 failure scenarios, covering a complete spectrum of solutions from "low input and high outsourcing risk" to "high input and near saturation", providing sufficient solution reserves for emergency decision-making under different budget constraints.

[0066] (2) The Pareto front reveals the diminishing marginal returns between fleet cost and response time, and clarifies the inflection point of resource input efficiency. When F1 increases from 1400 to 2250, F2 decreases by 71.8%, demonstrating significant cost-effectiveness per unit. When F1 exceeds 2800, the marginal benefit of further investment decreases sharply, and F2 approaches the physical lower bound of approximately 3900. The inflection point solution (F1=2800) has the best overall cost-effectiveness in the entire frontier and is the most valuable solution for practical decision-making.

[0067] (3) The utilization rate of UAV flights decreases monotonically with the increase of resources, indicating that the intensity of single-machine operation will inevitably decrease under the condition of fixed total demand. From the transition solution I to the inflection point solution, the worst scenario of the system changes from "failure of district-level distribution center" to "double failure of community distribution center". The failure of district-level distribution center no longer constitutes a performance bottleneck. Then, from the inflection point solution to the transition solution II, the number of outsourced demand points remains unchanged while the number of community distribution center 6 is increased by 3 UAVs. This proves that the 5 remote demand points are constrained by the flight range (L=60) and belong to the structurally inaccessible blind area. Simply increasing the homogeneous transportation capacity cannot break through this physical limit.

[0068] (4) The TS-RGCA algorithm has good convergence and solution efficiency when solving this complex model. The HV curve monotonically increases from about 4.8×107 to about 5.2×107 within 30,000 iterations, and tends to stabilize after 19,000 iterations, indicating that the algorithm has converged to a high-quality approximate Pareto front; the total running time of the algorithm is about 54 minutes, which completes the effective exploration of the solution space within an acceptable computational cost.

[0069] In summary, the two-stage multi-scenario modeling framework and TS-RGCA algorithm proposed in this paper provide a methodological system that balances economy and timeliness for the planning and decision-making of post-earthquake urban collaborative rescue networks, and can provide quantitative decision support for emergency management departments in pre-disaster resource allocation and post-disaster response scheduling.

[0070] Example 2 This embodiment discloses a location scheduling system based on post-earthquake two-stage multi-scenario vehicle-machine collaboration, including a data acquisition module, a model building module, a model solving module, and a scheme output module; The data acquisition module is configured to acquire basic data from the post-earthquake relief network. The model building module is configured to: build a two-stage, dual-objective mixed integer programming model based on the basic data. The model aims to minimize the pre-disaster fleet purchase cost and minimize the total waiting time in the worst-case scenario. The decision variables are pre-disaster site selection and resource allocation variables and post-disaster truck route and drone flight allocation variables. The constraints are site selection attribution, availability allocation, truck transfer, and drone delivery. The model solving module is configured to: use a two-stage randomized greedy construction algorithm to solve the two-stage bi-objective mixed integer programming model; for each generated pre-disaster solution, calculate the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario and store them in the solution set; perform Pareto non-dominated screening on the solution set to obtain a Pareto non-dominated solution set; the solving process includes: random generation, greedy construction and Pareto screening. The solution output module is configured to: filter the obtained Pareto non-dominated solution set to obtain the final pre-disaster resource allocation and post-disaster response scheme.

[0071] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration, characterized in that: Obtain basic data from the post-earthquake relief network; Based on the aforementioned basic data, a two-stage, dual-objective mixed integer programming model is constructed. The model aims to minimize the pre-disaster fleet purchase cost and minimize the total waiting time in the worst-case scenario, with constraints including site selection, availability allocation, truck transfer, and drone delivery. A two-stage randomized greedy construction algorithm is used to solve the two-stage bi-objective mixed integer programming model. For each generated pre-disaster plan, the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario are calculated and stored in the plan set. The Pareto nondominated sieve is performed on the solution set to obtain the Pareto nondominated solution set. The solution process includes: random generation, greedy construction and Pareto sieve. The final pre-disaster resource allocation and post-disaster response plan are obtained by filtering the Pareto non-dominated solution set. The random generation specifically includes: Randomly select one of the three heuristic scoring strategies: weighted distance sum, maximum distance, and weighted combination of weighted distance sum and distance to the nearest district-level distribution center. Calculate the score of the candidate community distribution center, take the reciprocal of the score and normalize it to a probability, and randomly select the candidate point through a roulette wheel mechanism. The selected community distribution centers will be assigned to the nearest district-level distribution center according to a preset probability of one, and to the next nearest district-level distribution center according to a preset probability of two. Calculate the base number of trucks, add random fluctuations, and allocate trucks proportionally, ensuring that each district-level distribution center with a community distribution center allocation receives at least one truck. The configuration of drones is determined based on the number of demand points allocated to each node, using the number of points / R+1 as the base, and adding random disturbances, where R represents the maximum number of flights that the drone is allowed to perform. The greedy construction specifically includes: Based on the pre-disaster site selection and resource allocation plan, all failure scenarios are sequentially traversed, covering no failure, single district-level center failure, single community center failure, combined district-level and community failure, and dual community failure scenarios. The following post-disaster response simulation is then performed: If a district-level distribution center fails in the current scenario, all community distribution centers that were assigned to the failed district-level distribution center will be reassigned to the nearest unfailed district-level distribution center; if all district-level distribution centers fail, all demand points in this scenario will be outsourced. For each available district-level distribution center, the community distribution centers it is responsible for are arranged in ascending order of distance, and the load is allocated sequentially using a load balancing strategy. Each time, a truck with the smallest current cumulative load that can accommodate the demand of the community distribution center is selected, the community distribution center is inserted at the end of the truck's route, and the arrival time is calculated by accumulating the travel time. In all available distribution centers, maintain the earliest available time and remaining flight count for each drone. Iterate through all unserved demand points, calculate the earliest arrival time for each drone on each available node if it were to perform that flight, select the earliest globally reachable demand point-drone-node combination to perform the service, update the earliest available time of the drone and decrement the remaining flight count until all reachable demand points are served or there are no more flights to perform. The total waiting time for the current scenario is calculated based on the sum of truck arrival times, the sum of drone arrival times, and the outsourcing penalty. The maximum value among all scenarios is taken as the minimum worst-case total waiting time for this solution. The two-stage, dual-objective mixed-integer programming model is specifically as follows: The objective function of the model includes: (1) minimizing the pre-disaster fleet purchase cost F1, which includes the fixed costs of all trucks and drones; and (2) minimizing the total waiting time F2 in the worst-case scenario using the minmax criterion, where the total waiting time consists of three parts: the cumulative time for trucks to arrive at the community distribution center, the cumulative time for drones to arrive at the demand point, and the equivalent waiting time for the uncovered demand point calculated using the outsourcing penalty; where, For the fixed cost of each truck, The number of trucks configured for a district-level distribution center g, where G is the set of district-level distribution centers, where , For the fixed cost of each drone, Let i be the number of drones configured for node i, where i∈I, I is the set of all distribution center nodes, I=J∪G, and J is the set of all candidate community distribution centers. S is a set of earthquake scenarios, where , Let be the total waiting time in scenario s. This indicates the time it takes for the drone u to reach the required point d on its r-th flight. , This represents the time it takes for truck m to arrive at community distribution center j in scenario s. , This indicates that if requirement point d is covered in scenario s, and If it is 1, then it is 1; otherwise it is 0. This represents the demand at demand point d in scenario s. If demand fluctuations are not considered, it is a constant. P represents the outsourcing penalty coefficient.

2. The location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration as described in claim 1, characterized in that, The basic data includes a set of district-level distribution centers, a set of candidate community distribution centers, a set of demand points, the facility failure status of district-level distribution centers and candidate community distribution centers, fluctuations in truck travel time, and changes in the demand for materials at the demand points.

3. The location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration as described in claim 1, characterized in that, The site selection and ownership constraints specifically include: site selection uniqueness constraint, truck ownership constraint, truck configuration quantity counting constraint, drone configuration prerequisite constraint, and drone ownership constraint.

4. The location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration as described in claim 1, characterized in that, The available allocation constraints specifically include: facility availability constraints and allocation coupling constraints.

5. The location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration as described in claim 1, characterized in that, The constraints on truck transfer specifically include: truck origin selection constraints, truck route flow balance constraints, truck jurisdiction constraints, time recursion constraints, truck departure time constraints, community material availability time definition constraints, total truck unloading constraints, unloading and access association constraints, total capacity constraints of district-level distribution centers, and inventory constraints of district-level distribution centers.

6. The location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration as described in claim 1, characterized in that, The constraints on drone delivery specifically include: single flight and single demand point constraint, endurance constraint, drone physical ownership constraint, drone availability center prerequisite constraint, drone payload constraint, community distribution center material conservation constraint, unique demand point coverage constraint, coverage status definition constraint, drone arrival time calculation constraint, flight sequence constraint, community center first flight waiting constraint, and district-level center first flight immediate constraint.

7. The location scheduling method based on post-earthquake two-stage multi-scenario vehicle-machine collaboration as described in claim 1, characterized in that, The Pareto screening specifically includes: deduplicating and merging the solution set; comparing the dominance relationships between solutions one by one through bi-objective non-dominated comparison; retaining all solutions that are not dominated by other solutions; forming the Pareto front; and obtaining the Pareto non-dominated solution set.

8. A site selection and scheduling system based on post-earthquake two-stage multi-scenario vehicle-machine collaboration, characterized in that, It includes a data acquisition module, a model building module, a model solving module, and a solution output module; The data acquisition module is configured to acquire basic data from the post-earthquake relief network. The model building module is configured to: build a two-stage, dual-objective mixed integer programming model based on the basic data. The model aims to minimize the pre-disaster fleet purchase cost and minimize the total waiting time in the worst-case scenario, with constraints including site selection, availability allocation, truck transfer, and drone delivery. The model solving module is configured to: use a two-stage randomized greedy construction algorithm to solve the two-stage bi-objective mixed integer programming model; for each generated pre-disaster plan, calculate the pre-disaster fleet purchase cost and the total waiting time in the worst-case scenario and store them in the plan set. The Pareto nondominated sieve is performed on the solution set to obtain the Pareto nondominated solution set. The solution process includes: random generation, greedy construction and Pareto sieve. The solution output module is configured to: filter the obtained Pareto non-dominated solution set to obtain the final pre-disaster resource allocation and post-disaster response scheme; The random generation specifically includes: Randomly select one of the three heuristic scoring strategies: weighted distance sum, maximum distance, and weighted combination of weighted distance sum and distance to the nearest district-level distribution center. Calculate the score of the candidate community distribution center, take the reciprocal of the score and normalize it to a probability, and randomly select the candidate point through a roulette wheel mechanism. The selected community distribution centers will be assigned to the nearest district-level distribution center according to a preset probability of one, and to the next nearest district-level distribution center according to a preset probability of two. Calculate the base number of trucks, add random fluctuations, and allocate trucks proportionally, ensuring that each district-level distribution center with a community distribution center allocation receives at least one truck. The configuration of drones is determined based on the number of demand points allocated to each node, using the number of points / R+1 as the base, and adding random disturbances, where R represents the maximum number of flights that the drone is allowed to perform. The greedy construction specifically includes: Based on the pre-disaster site selection and resource allocation plan, all failure scenarios are sequentially traversed, covering no failure, single district-level center failure, single community center failure, combined district-level and community failure, and dual community failure scenarios. The following post-disaster response simulation is then performed: If a district-level distribution center fails in the current scenario, all community distribution centers that were assigned to the failed district-level distribution center will be reassigned to the nearest unfailed district-level distribution center; if all district-level distribution centers fail, all demand points in this scenario will be outsourced. For each available district-level distribution center, the community distribution centers it is responsible for are arranged in ascending order of distance, and the load is allocated sequentially using a load balancing strategy. Each time, a truck with the smallest current cumulative load that can accommodate the demand of the community distribution center is selected, the community distribution center is inserted at the end of the truck's route, and the arrival time is calculated by accumulating the travel time. In all available distribution centers, maintain the earliest available time and remaining flight count for each drone. Iterate through all unserved demand points, calculate the earliest arrival time for each drone on each available node if it were to perform that flight, select the earliest globally reachable demand point-drone-node combination to perform the service, update the earliest available time of the drone and decrement the remaining flight count until all reachable demand points are served or there are no more flights to perform. The total waiting time for the current scenario is calculated based on the sum of truck arrival times, the sum of drone arrival times, and the outsourcing penalty. The maximum value among all scenarios is taken as the minimum worst-case total waiting time for this solution. The two-stage, dual-objective mixed-integer programming model is specifically as follows: The objective function of the model includes: (1) minimizing the pre-disaster fleet purchase cost F1, which includes the fixed costs of all trucks and drones; and (2) minimizing the total waiting time F2 in the worst-case scenario using the minmax criterion, where the total waiting time consists of three parts: the cumulative time for trucks to arrive at the community distribution center, the cumulative time for drones to arrive at the demand point, and the equivalent waiting time for the uncovered demand point calculated using the outsourcing penalty; where, For the fixed cost of each truck, The number of trucks configured for a district-level distribution center g, where G is the set of district-level distribution centers, where , For the fixed cost of each drone, Let i be the number of drones configured for node i, where i∈I, I is the set of all distribution center nodes, I=J∪G, and J is the set of all candidate community distribution centers. S is a set of earthquake scenarios, where , Let be the total waiting time in scenario s. This indicates the time it takes for the drone u to reach the required point d on its r-th flight. , This represents the time it takes for truck m to arrive at community distribution center j in scenario s. , This indicates that if requirement point d is covered in scenario s, and If it is 1, then it is 1; otherwise it is 0. This represents the demand at demand point d in scenario s. If demand fluctuations are not considered, it is a constant. P represents the outsourcing penalty coefficient.

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