Sea-air cooperative emergency material delivery optimization method in remote group island scene

Abstract

The invention discloses a sea-air cooperative emergency material delivery optimization method in a remote group island scene, and the method comprises the steps: obtaining the coordinate and material demand of each island, and the weight, speed and loading and unloading speed data of a rescue ship and a helicopter, and building a sea-air cooperative emergency material delivery optimization model based on the data; solving the sea-air cooperation emergency material delivery optimization model through a customized column generation algorithm for embedding variable neighborhood search of a fusion column generation framework and a variable neighborhood search framework, and generating a preliminary sea-air cooperation path; and adopting an improved genetic algorithm to optimize the sea-air cooperation path, feeding back an optimization result to the column generation framework, and finally obtaining an optimal sea-air cooperation path. According to the invention, the material delivery efficiency and the resource cooperative utilization level of remote group island emergency rescue are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of operations research and optimization, and in particular to an optimization method for sea-air coordinated emergency material delivery in remote archipelago scenarios. Background Technology

[0002] Remote archipelagos, due to geographical isolation and limited transportation, are prone to shortages of supplies and delays in rescue efforts during major emergencies. Efficient delivery of emergency supplies is crucial for ensuring the safety of lives. Current technological solutions employ a combined sea-air approach for emergency supply delivery, where ships and helicopters transport various emergency supplies independently. Helicopters and ships depart separately from the rescue center, and helicopter transport is limited to round-trip and circular transport between the affected islands and the rescue center, failing to integrate ships and helicopters for coordinated operations. Helicopters cannot rely on ships for faster replenishment of supplies or to conduct more delivery missions, failing to fully leverage the advantages of large ship capacity and rapid helicopter response. Furthermore, current technological solutions prioritize delivery to the nearest affected island, lacking a global perspective and prone to local optima. This approach fails to effectively coordinate the timing of sea and air transport, resulting in low resource utilization efficiency. Summary of the Invention

[0003] This invention provides an optimized method for sea-air coordinated emergency material delivery in remote archipelago scenarios, which overcomes the problem of existing technologies being prone to getting trapped in local optima and failing to effectively coordinate the timing relationship of sea and air transportation, resulting in low resource utilization efficiency.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows: An optimized method for sea-air coordinated emergency material delivery in remote archipelago scenarios includes: S1. Obtain the coordinates of each island and the amount of relief supplies needed for each island; at the same time, obtain the load, speed and loading / unloading speed data of rescue ships and rescue helicopters respectively; S2. Based on the data obtained in S1, construct an optimization model for the coordinated sea-air delivery of emergency supplies to remote islands; S3. Solve the optimization model of sea-air coordinated emergency material delivery to remote islands by embedding a customized column generation algorithm with variable neighborhood search to obtain the sea-air coordinated path; the customized column generation algorithm with embedded variable neighborhood search includes a column generation framework and a variable neighborhood search framework. S4. Optimize the sea-air cooperative path using a genetic algorithm to obtain an optimized sea-air cooperative path; S5. Based on the optimized sea-air coordinated path and column generation framework, the optimal sea-air coordinated path is obtained for emergency material delivery to remote islands.

[0005] Beneficial effects: This invention provides an optimization method for sea-air coordinated emergency material delivery in remote archipelago scenarios. It decouples the complex sea-air coordinated delivery problem into a ship and helicopter scheduling sub-problem, and uses a customized column generation algorithm with embedded variable neighborhood search to solve them efficiently. This method can quickly plan a coordinated path that takes into account load, speed and loading and unloading characteristics. The solution is achieved through a customized column generation algorithm embedded with a variable neighborhood search, which consists of a column generation framework and a variable neighborhood search framework. The column generation framework is responsible for handling the core of large-scale problems, while the variable neighborhood search enhances the ability to find local depths and escape local optima by dynamically changing the search strategy, thus making up for the shortcomings of the column generation algorithm under complex constraints. This collaborative solution mechanism ensures that the algorithm can continuously approach and ultimately obtain a high-quality global optimum or near-optimal solution, significantly improving the scientificity and reliability of the material delivery plan. Attached Figure Description

[0006] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0007] Figure 1 This is a schematic diagram of the optimized sea-air coordinated emergency material delivery method of the present invention; Figure 2 This is a flowchart illustrating the sea-air coordinated emergency material delivery process in an embodiment of the present invention. Figure 3 This is a flowchart illustrating the algorithm process in an embodiment of the present invention. Figure 4 This is a simulation diagram of a sea-air coordinated rendezvous scenario in an embodiment of the present invention; Figure 5 This is a simulation diagram of the virtual task dynamic elimination mechanism in an embodiment of the present invention; Figure 6 This is a diagram showing the optimized results of the first round of rescue delivery in an embodiment of the present invention; Figure 7 This is a diagram showing the optimized results of subsequent rescue delivery in an embodiment of the present invention; Figure 8 This is a schematic diagram of chromosome encoding in a genetic algorithm embodiment of the present invention; Figure 9 This is a schematic diagram of the crossover operation of the heritage algorithm in an embodiment of the present invention; Figure 10 This is a schematic diagram of the mutation operation of the heritage algorithm in an embodiment of the present invention; Figure 11This is a diagram showing the structure of the initial solution for the variable neighborhood search in an embodiment of the present invention. Figure 12 This is a schematic diagram of the variable neighborhood search neighborhood operator operation in an embodiment of the present invention; Figure 13 This is a schematic diagram of the operation of repair strategy 1 in an embodiment of the present invention; Figure 14 This is a schematic diagram of the operation of repair strategy 2 in an embodiment of the present invention; Figure 15 This is a comparison chart of the solution results for independent sea-air transport and sea-air cooperative transport in the embodiments of the present invention. Detailed Implementation

[0008] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0009] This embodiment provides an optimized method for sea-air coordinated emergency material delivery in remote archipelago scenarios, such as... Figure 1 As shown, it includes: S1. Obtain the coordinates of each island and the amount of relief supplies needed for each island; at the same time, obtain the load, speed and loading / unloading speed data of rescue ships and rescue helicopters respectively; S2. Based on the data obtained in S1, construct an optimization model for the coordinated sea-air delivery of emergency supplies to remote islands; S3. Solve the optimization model of sea-air coordinated emergency material delivery to remote islands by embedding a customized column generation algorithm with variable neighborhood search to obtain the sea-air coordinated path; the customized column generation algorithm with embedded variable neighborhood search includes a column generation framework and a variable neighborhood search framework. S4. Optimize the sea-air cooperative path using a genetic algorithm to obtain an optimized sea-air cooperative path; S5. Based on the optimized sea-air coordinated path and column generation framework, the optimal sea-air coordinated path is obtained for emergency material delivery to remote islands.

[0010] Specifically, in the embodiments, such as Figure 2 As shown, the concept of a collaborative transportation model between ships and helicopters for rescue operations on remote islands is as follows: A rescue team consisting of several ships and helicopters departs from the rescue base to provide support to the disaster-stricken islands. The first category of supplies transportation is the initial rescue, while the second and third categories of supplies replenishment are for subsequent rescues. Each helicopter is attached to a ship to form a fixed coordination unit, and efficient cooperation is achieved through dynamic convergence to give full play to the complementary advantages of sea and air transportation. Ships not only undertake long-distance transportation of various materials, but also serve as mobile resupply platforms for helicopters. They must adjust their positions in real time and accurately plan routes and docking times to support aerial operations. Due to load limitations, helicopters are mainly responsible for the rapid delivery of Category I and II supplies. They take off from the attached ships, deliver supplies to the disaster-stricken islands, and then return to the ships at their real-time location, forming an efficient and flexible supply delivery chain.

[0011] Preferably, by obtaining data on the coordinates of each island, the island's demand for relief supplies, and the load, speed, and loading / unloading speed data of rescue vessels and helicopters, and based on the concept of a collaborative transportation model for ships and helicopters in remote island rescue, an optimization model for the coordinated sea-air delivery of emergency supplies to remote archipelagos is constructed; the objective function of the optimization model for the coordinated sea-air delivery of emergency supplies to remote archipelagos is: (1) In the formula, Indicates the time when all rescue missions were completed; Equation (1) represents the operation time of the ship-helicopter rescue team that minimizes the total time. The constraints of the optimization model for the coordinated sea-air delivery of emergency supplies to remote islands are as follows: (2) In the formula, Indicates a collection of affected islands; Represents an archipelago set; Indicates the affected islands; Indicates an island; Represents a set of material types; Indicate the type of supplies; Indicates the affected islands and islands The distance between them; Indicates whether the ship passed by the disaster-stricken islands. To the island Decision variables between arcs; Indicates the ship's speed; This indicates that ships are being deployed to the affected islands. The quantity of this type of material; Indicates the speed at which a ship delivers supplies; This indicates the assembly of a ship-helicopter rescue team; An index representing the set of ship-helicopter rescue teams; (3) In the formula, Represents a set of helicopter flights; Indicates the helicopter's flight number; Indicates the helicopter on a flight China delivers supplies to the disaster-stricken islands The quantity of this type of material; Indicating the affected islands Demand for this type of material; This refers to the first category of supplies, namely the most urgent supplies, which must be delivered within 12 hours of the start of the rescue operation. This indicates the second category of supplies, namely secondary emergency supplies, which are stipulated to be delivered by helicopter; (4) In the formula, This indicates the third category of supplies, which are in the largest demand and are delivered by ships. (5) In the formula, Indicates the ship's maximum deadweight; (6) (7) In the formula, Indicates a ship Should we provide assistance to the affected islands? Decision variables for delivering supplies; Represents a sufficiently large positive number; (8) In the formula, Indicates whether the ship has passed through rescue base 0 to island Decision variables between arcs; Indicates whether the ship passes by the island. The decision variables for the arc between the rescue base and point 0; (9) In the formula, Indicates whether the ship passes by the island. to the disaster-stricken islands Decision variables between arcs; (10) In the formula, This represents the set of intersection points between ships and helicopters. Indicates the meeting point between the ship and the helicopter; Indicates the helicopter on a flight Did it pass through the intersection? To the island Decision variables between arcs; This indicates that the helicopter is on a flight. Did China pass through the disaster-stricken islands? To the junction Decision variables between arcs; (11) In the formula, Indicates the number of helicopter flights The meeting point of ships and helicopters in China; Indicates the helicopter on a flight Did China pass through the disaster-stricken islands? To the island Decision variables between arcs; Indicates the helicopter on a flight Did China pass through islands? to the disaster-stricken islands Decision variables between arcs; (12) In the formula, Indicates whether the ship is heading to the disaster-stricken islands. Decision variables for delivering supplies; (13) (14) (15) In the formula, Indicates the helicopter on a flight Whether China will provide assistance to the affected islands Decision variables for delivering supplies; (16) (17) Indicates the helicopter on a flight Does it return to the rendezvous point at the end? Decision variables; (18) In the formula, Indicates that the ship has arrived at the rendezvous point. Time; Indicates the helicopter on a flight The time it takes for them to arrive at the rendezvous point; (19) (20) In the formula, Indicates the current voyage Intersection Physical coordinates; Indicates the next voyage Intersection Physical coordinates; Indicates the ship is on a voyage The amount of supplies China sent to the disaster-stricken islands; Indicates the helicopter will be on the next flight Arrive at the next intersection Time; Indicates the helicopter on a flight The time when the middle leaves the intersection point; (twenty one) In the formula, This indicates that the ship has arrived at the island. Time; Indicates that the ship has left the disaster-stricken island. Time; (twenty two) In the formula, Indicates that the ship has arrived at the disaster-stricken island. Time; (twenty three) In the formula, Indicates the helicopter on a flight Arrival at the island Time; Indicates the helicopter on a flight China leaves the disaster-stricken island Time; Indicates the helicopter's flight speed; (twenty four) In the formula, Indicates the helicopter on a flight China arrives at the disaster-stricken island Time; (25) (26) In the formula, Indicates the helicopter on a flight The ship departed earlier than it arrived at the disaster-stricken island. The decision variable based on time; (27) (28) (29) In the formula, Indicates the affected islands The latest time when Category I supplies are satisfied; Indicates whether the ship is heading to the disaster-stricken islands. Decision variables for delivering Category I supplies; (30) (31) In the formula, Indicates the helicopter on a flight Should we provide assistance to the affected islands? Decision variables for delivering Category I supplies; (32) (33) (34) (35) Among them, Equation (2) is the longest time to calculate all ship-helicopter rescue teams; Equations (3) and (4) are to ensure that the needs of various materials on the disaster-stricken islands are met; Equation (5) specifies the capacity limit of ships; Equation (6) specifies the capacity limit of helicopters; Equation (7) is the relationship between the amount of helicopter material delivery and its visit behavior; Equations (8), (9), (10), and (11) are the path flow balance constraints of ships and helicopters; Equation (12) restricts each disaster-stricken island to be visited by ships only once; Equation (13) allows helicopters to deliver materials to each disaster-stricken island only once in a flight; Equations (14), (15), and (16) clarify the visit status and binding relationship of ships and helicopters; Equations (17) and ( ) are used to define the visit status and binding relationship of ships and helicopters. 18) Equation (19) stipulates that the ship-helicopter rescue team selects only one rendezvous point in each voyage, and the arrival times of both are consistent; Equation (20) represents the connection constraints between voyages; Equations (21), (22), (23), and (24) stipulate the navigation and operation times of ships and helicopters; Equations (25), (26), (27), and (28) stipulate that the time for helicopters to arrive at the disaster-stricken islands must not be later than that of ships, and require that disaster-stricken islands visited by ships do not require repeated helicopter deliveries; Equations (29), (30), (31), and (32) stipulate that the first category of materials for all disaster-stricken islands must be met within the specified time window; Equations (33), (34), and (35) represent the range of variable values.

[0012] Specifically, the optimization model for the coordinated sea-air delivery of emergency supplies to remote islands is a mixed-integer quadratic constraint programming model. Mixed-integer quadratic constraint programming models have two main problems. First, they contain multidimensional variables, complex constraints, and nonlinear terms, leading to a sharp increase in computational complexity as the problem size increases. Commercial solvers and traditional exact algorithms struggle to solve large-scale problems within a reasonable timeframe. Second, emergency logistics scenarios in remote islands during major emergencies place stringent demands on solution speed, requiring the generation of high-quality delivery plans within a short period to support decision-making. Therefore, a customized column generation algorithm with embedded variable neighborhood search, including a column generation framework and a variable neighborhood search framework, is designed to solve the optimization model problem of sea-air coordinated emergency material delivery in remote islands. The customized column generation algorithm with embedded variable neighborhood search decouples the optimization model problem of sea-air coordinated emergency material delivery in remote islands into a ship scheduling problem and a helicopter scheduling problem.

[0013] Specifically, based on the objective function of the optimization model for the coordinated sea-air delivery of emergency supplies to remote islands, the problem is decoupled into a ship routing problem and a helicopter routing problem; the decoupling method is existing technology and will not be elaborated here. Preferably, the process of generating a framework using the columns to obtain the ship's route specifically includes: S311. Construct a set partitioning model for the ship routing problem; the objective function of the set partitioning model for the ship routing problem is: (36) In the formula, For ship routes; For the set of ship routes; Indicates the ship's path The time required for ships to deliver supplies; The decision variable representing whether a ship's route is chosen; Equation (36) represents minimizing the ship's operation time; The constraints of the set partitioning model for the ship routing problem are: (37) In the formula, The decision variables represent whether a ship's route passes through the affected islands; (38) (39) In this context, Equation (37) indicates that each affected island is covered by a single path; Equation (38) indicates that the number of selected paths does not exceed the number of available vessels; and Equation (39) indicates the range of values ​​for the decision variable regarding whether a vessel path is selected. S312. Solve the set partitioning model of the ship routing problem using the Gurobi solver to obtain the dual variables; Specifically, let's set and Let the dual variables corresponding to equations (37) and (38) be respectively, and the test number of the pricing subproblem can be expressed as: ,in, The pricing subproblem aims to determine which paths should be included in the main problem to improve the quality of the overall solution by calculating the verification number of the ship paths. The verification number comprehensively considers the original time cost of the path and its dual benefit. In this embodiment, the pricing subproblem can be transformed into a shortest path problem with resource constraints. S313. Based on the dual variables, the pricing subproblem of the column generation framework is constructed into a shortest path problem model with resource constraints; the objective function of the shortest path problem model with resource constraints is: (40) In the formula, and For the affected islands; Indicates the order in which the affected islands are visited. and Decision variables; Indicates the affected islands and The distance between them; Indicates the affected islands in each iteration. The total material requirements that need to be met by ships; and Table dual variables; Equation (40) represents the difference between the operation time and dual benefits of minimizing the ship path; The constraints of the shortest path problem model with resource constraints are as follows: (41) In the formula, Indicates the order in which the affected islands are visited. and Decision variables; (42) In the formula, Indicates the order in which the affected islands are visited. and Decision variables; (43) In the formula, The route indicates that the rescue base and the disaster-stricken island were visited in sequence. Decision variables; Indicates the order in which the affected islands are visited. Decision variables for rescue bases; (44) In the formula, Indicates the affected islands in each iteration. The total material requirements that need to be met by ships; (45) In the formula, Indicates the affected islands The order in which they are accessed in the path; Indicates the affected islands The order in which they are accessed in the path; (46) In the formula, Indicates the affected islands The order in which they are accessed in the path; (47) In the formula, Represents a set of integers; Equations (41) and (42) represent the flow balance constraints for the visited disaster-stricken islands; Equation (43) stipulates that ships must depart from and return to the rescue base; Equation (44) limits the total demand along the path to no more than the ship's capacity; Equations (45) and (46) eliminate sub-loops in the path; and Equation (47) represents the disaster-stricken islands. The order in which the routes are visited and the range of values ​​for the decision variables regarding the islands affected by the disaster. S314. Solve the shortest path problem model with resource constraints using a customized genetic algorithm to obtain the ship path.

[0014] Preferably, the shortest path problem model with resource constraints is solved using a customized genetic algorithm, specifically including: S321. Generate the initial ship path based on the Gurobi solver and the greedy criterion; Specifically, the ship path generation method is as follows: starting from the rescue base, affected islands are gradually selected to form the ship path. Island selection follows a heuristic principle, that is, priority is given to visiting islands with high dual value and shorter distances, until the path length reaches the upper limit, or the total path demand exceeds the capacity; for example, Figure 8 As shown, the upper layer represents the number of the affected islands, which is encoded as an integer; the lower layer represents the island selection, which is encoded as a binary code (1 indicates that the path contains the island, and 0 indicates that it does not). The initial solution only defines the task allocation information, and its optimal access order is further optimized and determined by calling the Gurobi model to solve the pricing subproblem model of the given task allocation. S322. Perform crossover and mutation operations on the initial ship path in sequence to obtain a new ship path; Specifically, such as Figure 9 As shown, in the crossover operation, two cutting points are randomly selected from the path, and the segments divided by the cutting points in the parent path are interchanged to generate two child paths; child path 1 is formed by splicing the first segment of parent path 1 (to cutting point 1) and the second segment of parent path 2 (starting from cutting point 2); child path 2 is the opposite. like Figure 10 As shown, in the mutation operation, a disaster-stricken island in the path is randomly selected and its access status is flipped (i.e., 0 becomes 1 or 1 becomes 0) to enhance the local search capability. S323. Calculate the fitness of the new ship path and retain the offspring with the highest ship path fitness based on the elite retention strategy; S324. Iterate through S322 to S323 until the maximum number of iterations is reached, and output the ship path.

[0015] Preferably, the variable neighborhood search framework, such as Figure 3 As shown, based on the ship paths output by the column generation framework, the sea-air cooperative path is obtained, specifically including: S331. Calculate the consecutive intersection points of ships and helicopters; S332. Based on the continuous intersection points of ships and helicopters, and through a greedy algorithm, the initial solution, i.e. the initial sea-air cooperative path, is obtained. S333. Within the current neighborhood, the initial solution is optimized using a perturbation-local search iterative strategy: During the perturbation phase, perturbation candidate solutions are obtained by applying different neighborhood operators to the current solution; During the local search phase, the perturbation candidate solutions are searched to obtain new candidate solutions; S334. Perform feasibility repair and virtual task elimination on new candidate solutions, and calculate the target value; S335. If the objective value of the new candidate solution is greater than the objective value of the optimal solution, then update the new candidate solution to the optimal solution and return to the first neighborhood; otherwise, switch to the next neighborhood. S336. Iterate through S333 to S335 until the maximum number of iterations is reached, and output the optimal solution, i.e. the optimal sea-air coordinated path.

[0016] Specifically, in the helicopter scheduling problem, helicopters need to perform multiple missions and return to the ship for resupply after each mission. Since the ship moves dynamically during transport, accurate and real-time calculation of rendezvous points is crucial for optimizing air-sea coordination, ensuring that helicopters can accurately return to the ship for resupply after each mission. The dynamic adjustment of rendezvous points not only affects the continuity of mission operations but also directly relates to the feasibility of path planning and the optimization effect of the overall scheduling scheme. Therefore, a continuous rendezvous point coordinate calculation method is used to calculate continuous rendezvous points. The scenario of rendezvous points is as follows: Figure 4 As shown; Preferably, the specific steps for calculating the consecutive intersection points of ships and helicopters include: S341. Calculate the time parameters based on the island parameters, ship parameters, and helicopter parameters; The island parameters include island coordinates; The ship parameters include the amount of supplies the ship delivers to the disaster-stricken islands, the ship's sailing speed, and the ship's supply delivery speed. The helicopter parameters include helicopter flight speed and helicopter cargo delivery speed; The time parameters include the rescue start time, the time when ships arrive at the disaster-stricken island, the time when ships leave the disaster-stricken island, and the time when helicopters arrive at the disaster-stricken island. The expression for calculating the time it takes for a ship to arrive at the disaster-stricken island is as follows: (48) In the formula, For ships to reach the disaster-stricken islands Time; The coordinates of the affected island 1; The coordinates of the affected island 2; The speed at which the ship sails; The expression for calculating the time it takes for a ship to leave a disaster-stricken island is: (49) In the formula, For ships to leave the disaster-stricken islands Time; For ships to reach the disaster-stricken islands The amount of supplies delivered; For the speed of cargo delivery by ships; The expression for calculating the time it takes for a helicopter to reach the disaster-stricken island is: (50) In the formula, To allow helicopters to reach the disaster-stricken islands Time; Indicates the helicopter's flight speed; S342. Calculate the rendezvous time between the ship and the helicopter based on the island parameters, ship parameters, helicopter parameters, and time parameters. The rendezvous time between the ship and the helicopter can be one of three cases: the rendezvous point and the helicopter's flight end point are not on the same ship path arc, the rendezvous point is on the disaster-stricken island, and the rendezvous point and the helicopter's flight end point are on the same ship path arc. Among them, according to The fsolve function is used to calculate the rendezvous time when the rendezvous point and the helicopter flight end point are not on the same ship path arc. ; Based on the ship's unloading time on the island, the helicopter's flight time, and the helicopter's unloading time, the fsolve function is used to calculate the rendezvous time of the intersection point on the affected island. ; according to The fsolve function is used to calculate the rendezvous time of the rendezvous point and the helicopter flight end point, which are on the same ship path arc. ; S343. Calculate the coordinates of the intersection point between the ship and the helicopter based on the time of their intersection. The expression for the coordinates of the intersection point and the helicopter voyage end point, which are not on the same ship path arc, is as follows:

[0017] In the formula, The coordinates of the intersection point and the helicopter voyage end point are not on the same ship path arc; The moment of convergence; Coordinates of the rescue base; The time it takes for the ship to arrive at the disaster-stricken island 2; The expression for the coordinates of the intersection point on the disaster-stricken island is:

[0018] In the formula, The coordinates of the intersection point on the affected island; The expression for the coordinates of the rendezvous point and the helicopter voyage termination point on the same ship's path arc is:

[0019] In the formula, The coordinates of the intersection point and the end point of the helicopter voyage lie on the same ship path arc; The time it takes for the ship to arrive at the disaster-stricken island 1; The time it takes for the ship to leave the disaster-stricken island 2.

[0020] Specifically, in the helicopter scheduling problem, several ship routes and information on the affected islands along each route are known. Since the needs of the affected islands can be broken down and involve constraints on material types and time windows, the generation of the initial solution must fully consider the helicopter's carrying capacity and the reasonable allocation of delivery tasks. In this embodiment, the encoding result is set based on the characteristics of the helicopter scheduling problem as follows: Figure 11 As shown, the coding results only consider the voyage information of the first and second categories of materials, while the third category of materials is delivered by ships; exist Figure 11 In the diagram, M1, M2 to M6 represent the locations where the helicopter returns to the ship for resupply. Each resupply point corresponds to the return point (i.e., consecutive rendezvous points) after the helicopter completes a batch of material delivery missions. The initial solution is divided into two parts according to the type of material: the left side represents the delivery voyages for the first type of material (E), and the right side represents the delivery voyages for the second type of material (B). Under the weight limit, the helicopter needs to perform multiple delivery missions. Among them, voyage 1 delivers material E to islands 1 and 2, voyage 2 delivers material E to islands 2, 3 and 4, and voyage 3 delivers material B to island 1. After each voyage is completed, the helicopter returns to the rendezvous point for resupply and then continues to the next round of missions. based on Figure 11 The encoding rules, based on the continuous intersection points of ships and helicopters, and using a greedy algorithm, yield an initial solution. The specific steps are as follows: Step 1: Based on the ship's route and material requirements, set the helicopter's starting position and initialize the delivery path; Step 2: Sort the resource needs of each island by quantity and prioritize the allocation to islands with high demand to optimize resource allocation; Step 3: Based on the helicopter's carrying capacity, select suitable tasks from the remaining demands and insert them into the current path; Step 4: After inserting the mission, update the path and adjust the remaining payload; if the payload reaches the limit, start a new voyage; Step 5: Repeat steps 3–4 until all island requirements have been allocated, generating complete and constrained delivery paths.

[0021] In a specific embodiment, the perturbation-local search iteration strategy employed is designed... to Six neighborhood operators are used for perturbation operations and local searches; the operation diagrams of the six neighborhood operators are shown below. Figure 12 As shown, the specific design is as follows: (Intra-Trip Swap): Randomly select a voyage and swap the order of any two mission points within that voyage; (Parallel Inter-Trip Swap): During voyages carrying two types of supplies, a mission point is randomly selected from each voyage to carry out an inter-voyage swap; (Intra-Trip Reversal): Randomly select a voyage and reverse the order of all mission points within that voyage; (Trip-Cargo Hybrid Swap): Randomly select a voyage and swap any two mission points within that voyage. At the same time, select one mission point from each of the different voyages carrying the first type of supplies and swap it across voyages. (Trip-Cargo Hybrid Reversal): Select one mission point from each of the different voyages to exchange, and randomly select one voyage from the first category of supplies, reversing all its mission points; (Global Cargo Reversal & Inter-Trip Swap): Select the first type of cargo voyage, reverse the order of mission points, and select one mission point from each voyage to swap.

[0022] Specifically, the feasibility repair involves introducing two types of repair strategies to improve the feasibility of new candidate solutions. The specific repair strategies are as follows: (Load Constraint Repair): By adjusting the task allocation scheme of the initial solution, resource delivery tasks exceeding the single-voyage load limit are split into multiple voyages for execution; for example... Figure 13 As shown, before the repair, the helicopter delivered a total of 16 units of supplies in Flight 1, exceeding its single-flight payload capacity (14 units). Through the repair operation, the mission was re-divided into two parts: 8 units of the mission remained in Flight 1, and 2 units of the mission were transferred to Flight 2, thus ensuring that the amount of supplies delivered in each flight did not exceed the helicopter's maximum payload limit. This operation not only ensured the feasibility of the repair but also enhanced the space for subsequent optimization through the reasonable division of the mission, which is conducive to achieving global optimization. (Task Consolidation Repair): This involves refactoring task allocation within a flight by merging task loads to improve resource utilization and reduce redundant deployments; for example... Figure 14 As shown, before the repair, the affected island 2 was assigned two delivery missions in voyage 2, with delivery volumes of 2 and 7 units respectively; after the repair, these two missions were merged into a single delivery mission of 9 units; this operation simplified the mission execution process within the voyage and improved the overall scheduling efficiency.

[0023] Specifically, the virtual mission elimination means that if the material needs of a disaster-stricken island have already been met by ships, then subsequent helicopter flights should exclude missions related to that island to avoid duplicate deliveries and resource waste; for example... Figure 5 As shown, the upper-level solution contains all potential helicopter delivery missions. The search space is expanded through neighborhood search to enhance the algorithm's global search capability and avoid getting trapped in local optima. The lower-level solution is the actual helicopter flight number and route arrangement obtained by applying a virtual mission dynamic elimination mechanism on the basis of the upper-level solution. It is used to calculate the objective function value to improve the solution speed and accuracy.

[0024] Specifically, the sea-air cooperative path is optimized using a genetic algorithm. The optimized sea-air cooperative path is the existing technology and will not be elaborated here.

[0025] In a specific embodiment, the data collected consisted of 21 islands in a certain sea area, one of which was a rescue base (0#) responsible for coordinating the allocation of emergency supplies; the remaining 20 islands (1# to 20#) were islands that needed rescue after the disaster; the geographical coordinates and material requirements of each island are shown in Tables 1 and 2. Table 1. Island Geographic Coordinate Data

[0026] Table 2. Data on the material needs of each island

[0027] Assume there are 5 ships available, each with a maximum load capacity of 3000t, a speed of 30 nautical miles per hour, and an unloading speed of 60t / h; and 5 helicopters available, each with a maximum load capacity of 14t, a flight speed of 140 nautical miles per hour, and an unloading speed of 30t / h. The material needs are divided into three categories: Category 1 materials account for 5% of the island's total needs and must be met within 12 hours of the start of the rescue; Category 2 materials account for 20%; and Category 3 materials account for 75%.

[0028] The virtual experiment was run on a computer with a Windows 11 system, an AMD Ryzen 7 7840H 3.80 GHz processor, and 32GB of RAM, using Python 3.12.0. The parameters were set as follows: column generation iterations: 20; genetic algorithm (for solving the pricing subproblem): population size 50, crossover probability 0.6, mutation probability 0.1, maximum iterations 50; variable neighborhood search (for solving the helicopter subproblem): maximum iterations 500; ensemble algorithm framework iterations: 60.

[0029] Table 3 shows all the route plans for ships and helicopters obtained based on the above settings; the scheduling arrangements for ships and helicopters in the first and subsequent rescue operations are as follows: Figure 6 and Figure 7 As shown; Table 3 Optimization Results of Sea-Air Coordination Emergency Material Delivery to Remote Islands

[0030] According to Table 3, the maximum mission completion time for the five ship-helicopter rescue teams is 34.84 hours (objective function value). Taking the mission plan of rescue team 1 as an example, the mission completion time of rescue team 1 is 33.9 hours. The ship route is Base 0 - Island 13 - Island 12 - Island 11 - Island 10 - Base 0, indicating that ship 1 departs from rescue base 0, visits the disaster-stricken islands 13, 12, 11, and 10 in sequence, and then returns to the rescue base; (Base 0 - Island 13 (7.5) - Island 11 (6.5) - ),( -Island 12 (7.5)-Island 10 (6.5)- The first two flights of helicopter 1 will depart from rescue base 0, dropping 7.5 tons of supplies to disaster-stricken island 13, and then dropping 6.5 tons of supplies to disaster-stricken island 11 before returning to the first rendezvous point with ship 1. The second voyage from After departing, supplies will be delivered to the affected islands 12 and 10 in sequence before returning to the second rendezvous point with the ships. The subsequent path information is similar; see Table 3, Figure 6 , Figure 7 During the delivery mission, all ships and helicopters consistently met constraints such as flow conservation and maximum helicopter load, verifying the effectiveness of the method.

[0031] In a specific embodiment, the material delivery optimization method of this embodiment is compared with the greedy (nearest) principle and the first-come, first-served (FCFS) principle; the greedy principle is that ships and helicopters visit the nearest disaster-stricken island each time; the FCFS principle is that helicopters deliver materials to each disaster-stricken island in sequence according to the ship's route; the comparison results are shown in Table 4; Table 4 Comparison of Solution Results for Different Schemes

[0032] Table 4 shows that, in calculations of different scales, the objective function value of the proposed solution is superior to both the greedy principle and the FCFS principle. The maximum difference between the proposed solution and the greedy solution is 6.76 hours, while the maximum difference between the proposed solution and the FCFS solution is 4.92 hours. This superiority stems from the fact that the proposed solution achieves globally optimal allocation of rescue resources through dynamic task allocation and path optimization. In contrast, the greedy principle is prone to getting stuck in local optima due to the lack of a global perspective, while the FCFS principle fails to effectively coordinate the temporal relationship of sea and air transportation, resulting in low resource utilization efficiency. The above results highlight the efficiency and applicability of the proposed solution in responding to major emergencies.

[0033] In a specific embodiment, the material delivery optimization method of this embodiment is compared with the existing independent sea and air transportation scheme to verify its superiority; each set of calculations is calculated ten times to obtain the objective function evaluation value and the comparison results are as follows. Figure 15 As shown in the figure, in different calculation examples, the objective function value of the material delivery optimization method in this embodiment is better than that of the independent sea-air transport scheme (the difference between the two is the smallest 1.54h, the largest 4.72h, and the maximum optimization rate reaches ((41.26–36.54) / 41.26=11.44%). This is because, compared with the independent sea-air transport scheme, the material delivery optimization method in this embodiment allows helicopters to replenish materials more quickly and carry out more delivery tasks, fully combining the advantages of large ship carrying capacity and fast helicopter response speed. The above comparison results verify the superiority and application value of the material delivery optimization method in this embodiment compared with the independent sea-air transport scheme.

[0034] The present invention has the following beneficial effects: The present invention provides an optimization method for sea-air coordinated emergency material delivery in remote archipelago scenarios, which decouples the complex sea-air coordinated delivery problem into a ship and helicopter scheduling sub-problem, and uses a customized column generation algorithm with embedded variable neighborhood search to solve them efficiently, which can quickly plan a coordinated path that takes into account load, speed and loading and unloading characteristics. The solution is achieved through a customized column generation algorithm embedded with a variable neighborhood search, which consists of a column generation framework and a variable neighborhood search framework. The column generation framework is responsible for handling the core of large-scale problems, while the variable neighborhood search enhances the ability to find local depths and escape local optima by dynamically changing the search strategy, thus making up for the shortcomings of the column generation algorithm under complex constraints. This collaborative solution mechanism ensures that the algorithm can continuously approach and ultimately obtain a high-quality global optimum or near-optimal solution, significantly improving the scientificity and reliability of the material delivery plan.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing sea-air collaborative emergency material delivery in a remote island scenario, characterized in that, The application relates to a method for optimizing sea-air collaborative emergency material delivery for remote islands. S1, obtaining island coordinates and island emergency material demand data; meanwhile, obtaining ship and helicopter load, travel speed and loading and unloading speed data; S2, constructing a sea-air collaborative emergency material delivery optimization model for remote islands according to the data obtained in S1; S3, solving the sea-air collaborative emergency material delivery optimization model for remote islands by embedding a variable neighborhood search customized column generation algorithm to obtain a sea-air collaborative path; the variable neighborhood search customized column generation algorithm comprises a column generation framework and a variable neighborhood search framework; S4, optimizing the sea-air collaborative path by a genetic algorithm to obtain an optimized sea-air collaborative path; S5, obtaining an optimal sea-air collaborative path according to the optimized sea-air collaborative path and the column generation framework, and using the optimal sea-air collaborative path for emergency material delivery for remote islands.

2. The method according to claim 1, wherein, The objective function of the sea-air collaborative emergency material delivery optimization model for remote islands is as follows: （1） In the formula, denotes the time at which all rescue tasks are completed; Wherein, formula (1) represents the minimum operation time of the ship-helicopter rescue group with the longest total time; The constraint condition of the sea-air collaborative emergency material delivery optimization model for remote islands is as follows: （2） wherein, denotes a set of affected islands; denotes a set of islands; denotes an affected island; denotes an island; denotes a set of material types; denotes a material type; denotes an affected island and an island between them; denotes a decision variable for whether the ship passes through the arc between the affected island and the island ; denotes a ship's sailing speed; denotes the number of units of the material type that the ship delivers to the affected island; denotes a ship's material delivery speed; denotes a set of ship-helicopter rescue teams; denotes an index into the set of ship-helicopter rescue teams; （3） wherein represents a set of missions of the helicopter; represents a mission of the helicopter; represents the delivery of the first type of material by the helicopter to the affected island during the mission represents the quantity of the first type of material; represents the affected island; represents the quantity of the second type of material; represents the first type of material, i.e. the most urgent material; represents the second type of material, i.e. the less urgent material;​ （4） In the formula, represents the third type of materials, i.e. the largest demand for materials; （5） In the formula, Dmax represents the maximum deadweight of the ship; （6） （7） wherein represents a ship whether to deliver supplies to a disaster-stricken island a decision variable; represents a sufficiently large positive number; （8） wherein denotes the decision variable for the arc between the ship and the island i; denotes the decision variable for the arc between the ship and the island i; denotes the decision variable for the arc between the ship and the island i; denotes the decision variable for the arc between the ship and the island i; （9） wherein indicates whether the ship passed the island to the affected island decision variable for the arc between （10） In the formula, This represents the set of intersection points between ships and helicopters. Indicates the meeting point between the ship and the helicopter; Indicates the helicopter on a flight Did it pass through the intersection? To the island Decision variables between arcs; Indicates the helicopter on a flight Did China pass through the disaster-stricken islands? To the junction Decision variables between arcs; （11） wherein denotes the set of intersection points of the ship and the helicopter during the mission of the helicopter denotes the decision variable whether the helicopter passes the arc between the island denotes the decision variable whether the helicopter passes the arc between the island denotes the decision variable whether the helicopter passes the arc between the island​​​​​​ （12） wherein denotes whether the ship is heading towards the affected island decision variable for the delivery of goods; （13） （14） （15） wherein represents the decision variable of whether the helicopter delivers supplies to the affected island during the voyage ; （16） （17） a decision variable representing whether the helicopter returns to the rendezvous point at the end of the mission a decision variable representing whether the helicopter returns to the rendezvous point at the end of the mission a decision variable representing whether the helicopter returns to the rendezvous point at the end of the mission （18） wherein represents the time at which the ship reaches the intersection point; represents the time at which the helicopter reaches the intersection point during the voyage; represents the time at which the helicopter reaches the intersection point during the voyage;​ （19） （20） wherein represents the current voyage intersection point physical coordinates; represents the next voyage intersection point physical coordinates; represents the quantity of goods delivered by the ship to the affected island during the voyage ; represents the time of arrival of the helicopter at the next intersection point during the next voyage ; represents the time of departure of the helicopter from the intersection point during the voyage ; represents the time of departure of the helicopter from the intersection point during the voyage ; （21） wherein denotes the time at which the ship arrives at the island ; denotes the time at which the ship leaves the affected island ; （22） In the formula, represents the time of arrival of the ship at the affected island ; （23） In the formula, Indicates the helicopter on a flight Arrival at the island Time; Indicates the helicopter on a flight China leaves the disaster-stricken island Time; Indicates the helicopter's flight speed; （24） In the formula, represents the time at which the helicopter arrives at the affected island during the voyage . （25） （26） wherein represents the decision variable of the time at which the helicopter leaves the ship earlier than the time at which the ship arrives at the affected island during the voyage . （27） （28） （29） wherein denotes the affected islands the latest time when the first type of goods is satisfied; denotes whether the ship sails to the affected islands the decision variable for delivering the first type of goods （30） （31） In the formula, represents the helicopter in the voyage whether to send the first type of material to the disaster-stricken island the decision variable of sending the first type of material （32） （33） （34） （35） Wherein, formula (2) is used for calculating the longest time of all ship-helicopter rescue groups; formula (3) and formula (4) are used for ensuring that the demand of all types of materials of the disaster-stricken islands is met; formula (5) is used for stipulating the capacity limitation of the ship; formula (6) is used for stipulating the capacity limitation of the helicopter; formula (7) is used for the relationship between the helicopter material delivery amount and the visiting behavior; formula (8), formula (9), formula (10) and formula (11) are used for ship and helicopter path flow balance constraints; formula (12) is used for limiting that each disaster-stricken island is visited only once by the ship; formula (13) is used for the fact that the helicopter can deliver materials to each disaster-stricken island only once in one voyage; formula (14), formula (15) and formula (16) are used for clearly defining the visiting state and binding relationship of the ship and the helicopter; formula (17), formula (18) and formula (19) are used for the fact that the ship-helicopter rescue group selects only one intersection point in each voyage, and the arrival time of the ship and the helicopter is consistent; formula (20) represents the connection constraint between voyages; formula (21), formula (22), formula (23) and formula (24) are used for stipulating the sailing and operation time of the ship and the helicopter; formula (25), formula (26), formula (27) and formula (28) are used for stipulating that the arrival time of the helicopter at the disaster-stricken island cannot be later than the arrival time of the ship, and the disaster-stricken island visited by the ship does not need to be repeatedly delivered by the helicopter; formula (29), formula (30), formula (31) and formula (32) are used for the fact that the first type of material of all disaster-stricken islands must be met within a specified time window; formula (33), formula (34) and formula (35) are used for the value range of the variable.

3. The method according to claim 2, wherein, The ship path is obtained through the column generation framework, and the ship path problem set partitioning model is constructed, and the objective function of the ship path problem set partitioning model is as follows: Wherein, formula (36) represents the minimum ship operation time; （36） wherein is a ship route; is a set of ship routes; denotes the operation time of a ship delivering goods on a ship route ; denotes a decision variable indicating whether a ship route is selected or not. The constraint condition of the ship path problem set partitioning model is as follows: ​ （37） In the formula, Decision variable indicating whether the ship route passes through the disaster-stricken island. （38） （39） In the formula (37), each affected island is covered by a path; in the formula (38), the number of selected paths does not exceed the number of available ships; and in the formula (39), the value range of the decision variable of whether the ship path is selected. S312, solving the ship path problem set partitioning model through the Gurobi solver to obtain a dual variable; S313, constructing a shortest path problem model with resource constraints according to the dual variable; the objective function of the shortest path problem model with resource constraints is: （40） wherein and are the affected islands; is the decision variable representing the order of visiting the affected islands and ; is the distance between the affected islands and ; is the total amount of supplies that the affected islands need to be satisfied by the ships in each iteration; and are the dual variables; In the formula (40), the difference between the operation time of the ship path and the dual profit is minimized. The constraint condition of the shortest path problem model with resource constraints is: （41） wherein denotes the path order visiting the disaster-stricken islands and the decision variable; （42） wherein denotes the path order visiting the disaster-stricken islands and the decision variable; （43） In the formula, The route indicates that the rescue base and the disaster-stricken island were visited in sequence. Decision variables; Indicates the order in which the affected islands are visited. Decision variables for rescue bases; （44） wherein represents the affected islands in each iteration total amount of supplies that needs to be satisfied by the ships; （45） In the formula, indicates the affected islands the order of visits in the path; indicates the affected islands the order of visits in the path; （46） In the formula, indicates the affected islands Visited order in the path; （47） In the formulae, denotes a set of integers; Wherein, formula (41) and (42) are flow balance constraints of the visited disaster island; formula (43) is a constraint that the ship must depart from the rescue base and return to the base; formula (44) is a constraint that the total amount of demand on the path does not exceed the capacity of the ship; formula (45) and (46) are constraints for eliminating sub-loops in the path; formula (47) is a constraint that the disaster island The value range of the decision variable of the visited order in the path and the ship path passing through the disaster island S314, solving the shortest path problem model with resource constraints through a customized genetic algorithm to obtain a ship path.

4. The method according to claim 3, wherein, Solving the shortest path problem model with resource constraints through a customized genetic algorithm specifically includes: S321, generating an initial ship path based on the Gurobi solver and the greedy criterion; S322, sequentially performing crossover and mutation operations on the initial ship path to obtain a new ship path; S323, calculating the fitness of the new ship path, and based on the elite reservation strategy, reserving the offspring with the highest ship path fitness; S324, iteratively performing S322 to S323 until the maximum number of iterations is reached, and outputting the ship path.

5. The method of claim 4, wherein the method is characterized by, According to the column generation framework output ship path, the ship-air coordination path is obtained, specifically including: S331, calculating the continuous intersection point of the ship and the helicopter; S332, obtaining an initial solution, i.e., an initial sea-air coordination path, according to the continuous intersection point of the ship and the helicopter and through a greedy algorithm; S333, in the current neighborhood, a perturbation-local search iterative strategy is adopted to optimize the initial solution: In the perturbation stage, different neighborhood operators are applied to the current solution to obtain perturbation candidate solutions; In the local search stage, the perturbation candidate solutions are searched to obtain new candidate solutions; S334, performing feasibility repair and virtual task elimination on the new candidate solution, and calculating the target value; S335, if the target value of the new candidate solution is greater than the target value of the optimal solution, updating the new candidate solution as the optimal solution and returning to the first neighborhood; otherwise, switching to the next neighborhood; S336, iteratively performing S333 to S335 until the maximum number of iterations is reached, and outputting the optimal solution, i.e., the optimal sea-air coordination path.

6. The method according to claim 5, wherein, The specific steps of calculating the continuous intersection point of the ship and the helicopter include: S341, calculating time parameters according to island parameters, ship parameters, and helicopter parameters; The island parameters include island coordinates; The ship parameters include the amount of supplies delivered by the ship to the affected island, the ship's navigation speed, and the ship's supply delivery speed; The helicopter parameters include the helicopter's flight speed and the helicopter's supply delivery speed; The time parameters include the start time of the rescue, the time when the ship arrives at the affected island, the time when the ship leaves the affected island, and the time when the helicopter arrives at the affected island; The expression for calculating the time when the ship arrives at the affected island is: （48） wherein is the time of arrival of the ship to the affected island; is the time of arrival of the ship to the affected island; is the coordinates of the affected island 1; is the coordinates of the affected island 2; is the sailing speed of the ship; The expression for calculating the time when the ship leaves the affected island is: （49） wherein is the time for the ship to leave the affected island; is the time for the ship to leave the affected island; is the amount of supplies delivered by the ship to the affected island; is the amount of supplies delivered by the ship to the affected island; is the speed of supply delivery by the ship; The expression for calculating the time for the helicopter to reach the disaster island is: （50） In the formula, To allow helicopters to reach the disaster-stricken islands Time; Indicates the helicopter's flight speed; S342, according to the island parameters, ship parameters, helicopter parameters and time parameters, the intersection time of the ship and the helicopter is calculated; the intersection time of the ship and the helicopter is three cases, including: the intersection point and the end point of the helicopter voyage are not on the same ship path arc, the intersection point is on the disaster island, and the intersection point and the end point of the helicopter voyage are on the same ship path arc; Wherein, according to , the intersection time of the intersection point and the end point of the helicopter voyage not on the same ship path arc is calculated by the fsolve function ; According to the unloading time period of the ship on the island, the flight time of the helicopter and the unloading time of the helicopter, the meeting time of the meeting point on the disaster island is calculated by the fsolve function ; According to , the intersection time of the intersection point and the end point of the helicopter voyage on the same ship path arc is calculated by the fsolve function ; S343, according to the intersection time of the ship and the helicopter, the intersection point coordinates of the ship and the helicopter are calculated; Wherein, the expression of the coordinates of the intersection point and the end point of the helicopter voyage not on the same ship path arc is: In the formula, is the coordinate of the intersection point and the end point of the helicopter voyage, which is not on the same ship path arc; is the intersection time; is the rescue base coordinate; is the time of the ship arriving at the disaster island 2; The expression of the coordinates of the intersection point on the disaster island is: In the formula, is the intersection point on the affected island coordinates; The expression of the coordinates of the intersection point and the end point of the helicopter voyage on the same ship path arc is: wherein is the coordinate of the intersection point and the end point of the helicopter voyage on the same ship path arc; is the time of the ship's arrival at the affected island 1; is the time of the ship's departure from the affected island 2.

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