Multi-trip drop-and-pull transshipment method considering elastic time

Abstract

The application discloses a multi-trip drop and pull connection transportation method considering elastic time. The method comprises a problem description module, a mixed integer programming model module, an effective inequality module and a self-adaptive large neighborhood search algorithm module. A mixed integer programming model based on a state is established for a one-truck-two-trailer problem, the model is expanded to be applicable to solving the restriction problem of different trailer numbers, the model is simplified by using a logic constraint IF-THEN, and the model is applied to a multi-trip drop and pull connection transportation problem considering vehicle elastic working time, and a self-adaptive large neighborhood search algorithm is proposed to solve the problem. The method optimizes the required number and total working time of the tractor, and can be widely applied to different capacity limited drop and pull transportation problems. Meanwhile, considering the vehicle elastic working time can effectively reduce unnecessary waiting time of the vehicle, reduce the total working time, improve the transportation efficiency, and effectively solve the actual scale combination optimization problem.

Description

Technical Field

[0001] This invention relates to the field of transportation scheduling technology and combination optimization, and in particular to a multi-trip trailer swapping transportation method that takes into account flexible time. Background Technology

[0002] Trailer-swapping is a transportation mode in which a tractor unit tows one or more container trailers, and performs operations such as unloading, towing, or swapping trailers at designated locations. The tractor unit is the power source in trailer-swapping, while the trailers are unpowered and only responsible for loading cargo. During transportation, the tractor unit transports the trailers to the designated location, drops them off, and then continues its subsequent transportation tasks. The tractor unit and trailers work together, flexibly paired according to actual needs, achieving rapid loading and unloading of cargo through "dropping" and "attaching," allowing for simultaneous loading, unloading, and transportation. Compared to traditional container transportation, trailer-swapping, due to its parallel loading, unloading, and transportation capabilities, improves vehicle utilization, reduces the number of tractor units required, and significantly lowers logistics costs. In trailer-swapping, the tractor unit flexibly loads and unloads cargo, greatly reducing waiting time and keeping it almost constantly operational, accelerating vehicle turnover and effectively improving transportation efficiency. The high efficiency of trailer-swapping reduces energy consumption per unit of cargo, contributing to energy conservation and emission reduction.

[0003] With the continuous development of economic globalization and the rapid increase in trade volume, container transshipment has received increasing attention, and trailer-swapping transportation, with its high efficiency and advanced characteristics, has been applied to the transshipment industry. Although trailer-swapping transportation has greatly improved upon traditional methods, there are still some shortcomings in its own development and research:

[0004] (1) At present, domestic research on trailer swapping is mainly limited to one-truck-one-trailer transportation. Although the transportation method of one truck with multiple trailers can effectively improve transportation efficiency and productivity, the complexity of the problem and the difficulty of solving it are much greater than that of one truck with one trailer. Therefore, there is little related research and application, and the efficiency of trailer swapping has not yet been significantly improved.

[0005] (2) During transportation, tractor units often experience unnecessary waiting because customers have not yet completed loading and unloading of containerized goods. During the waiting period, the tractor unit is stationary, which wastes time and resources and reduces transportation efficiency.

[0006] (3) Current research on multiple trailers on a single vehicle is limited to solving two trailers on a single vehicle and lacks universality. The relevant mathematical models are not robust enough and are difficult to apply to more extensive and general practical problems.

[0007] Therefore, effectively improving the efficiency of trailer-swapping container transshipment has become a crucial issue urgently needing resolution in the field of transportation scheduling. This invention establishes a state-based mixed-integer programming model for the one-vehicle-two-trailer and multi-trailer problems. In multi-trip problems, the introduction of state variables effectively solves the logical connections between different trips. To reduce model complexity, the logical constraint IF-THEN is further employed, establishing a mixed-integer programming model based on IF-THEN. Based on a thorough analysis of the problem, several effective inequalities are proposed to improve the model's solution efficiency. Finally, to solve problems of practical scale, an adaptive large neighborhood search algorithm (ALNS) is designed for solution. Summary of the Invention

[0008] This invention addresses the shortcomings of existing research by providing a multi-trip trailer swapping transportation method that considers flexible working time. The method establishes a planning model for the one-truck-two-trailer problem and extends this model to solve problems with varying numbers of trailers (one truck, multiple trailers). The model is simplified using the logical constraint IF-THEN and applied to the multi-trip trailer swapping transportation problem considering the flexible working time of vehicles. An adaptive large neighborhood algorithm is proposed for solving this problem. This method optimizes the required number of tractor units and the total working time to minimize transportation costs and maximize transportation efficiency.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A multi-trip trailer-swapping transport method considering flexible time is applied to a transport network consisting of tractor-trailers, trailers, storage yards, task nodes, and import / export transport areas, and includes the following modules:

[0011] The module includes a problem description module, a mixed integer programming model module, an effective inequality module, and an adaptive large neighborhood search algorithm module.

[0012] The aforementioned problem description module defines the scenario and related objects, analyzes the problem, and determines the proposed solution objective. It studies the container drop-and-go transportation problem considering the flexible working hours of vehicles. Vehicles can freely choose their start time to reduce unnecessary waiting at customer locations and lower overall transportation costs. This problem involves multiple constraints, requiring simultaneous satisfaction of deadlock-free constraints, trailer quantity constraints, planning period constraints, and access order constraints. To address these issues, a node decomposition strategy is first employed to break down the same task into first-stage subtasks and second-stage subtasks.

[0013] The aforementioned mixed-integer programming model module comprises two sub-modules. The first sub-module introduces an improved state-variable method to address the logical connections between different trips in a multi-trip system and establishes a mixed-integer programming model to solve the trailer-swapping and docking transportation problem. The second sub-module simplifies the model using the logical constraint IF-THEN, establishing a mixed-integer programming model based on IF-THEN constraints, reducing model complexity, and making the model easier to solve.

[0014] The above-mentioned effective inequality module proposes an effective inequality that can effectively improve the quality of the upper and lower bounds, thereby reducing the solution space, increasing the solution speed, and enhancing the solution capability of the established mathematical model.

[0015] The aforementioned Adaptive Large Neighborhood Search (ALNS) algorithm module is designed to solve large-scale problems. This module consists of three sub-modules: the first sub-module is used for initial solution construction; the second sub-module is used for operator design; and the third sub-module is used for adaptive mechanism design.

[0016] The present invention has the following advantages:

[0017] (1) The proposed improved model is universal and can be used to solve the problem of trailer quantity limitation, improve vehicle utilization, reduce the number of tractor purchases, and significantly reduce logistics costs.

[0018] (2) Considering that flexible working hours for vehicles can effectively reduce unnecessary waiting time for vehicles, reduce total working time, and improve transportation efficiency.

[0019] (3) The adaptive large neighborhood search algorithm (ALNS) proposed in this invention can effectively solve combinatorial optimization problems of real scale. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the module structure according to an embodiment of the present invention.

[0021] Figure 2 This is a flowchart illustrating the adaptive large neighborhood search algorithm according to an embodiment of the present invention. Detailed Implementation

[0022] Example:

[0023] like Figure 1As shown, this invention comprises four main modules and two sub-modules: a problem description module 1, a mixed integer programming model module 2, an effective inequality module 3, and an adaptive large neighborhood search algorithm module 4. The mixed integer programming model module 2 includes: a state-based mixed integer programming model sub-module 2-1 and a mixed integer programming model sub-module 2-2 based on the logical constraint IF-THEN. The adaptive large neighborhood search algorithm module 4 includes: an initial solution construction sub-module 4-1, an operator sub-module 4-2, and an adaptive mechanism sub-module 4-3.

[0024] The problem description module 1 is used to determine the solution objective for the container swapping and relay transportation problem:

[0025] A trucking company provides import and export container transshipment services in a certain area. The company owns a yard with ample tractors and trailers. One tractor can tow two trailers simultaneously; the tractor and trailer are detachable. Each trailer carries one container, and the two always exist as a single unit. Based on the type of cargo loaded in the containers, trailers can be categorized into three types: trailers carrying imported goods, trailers carrying exported goods, and trailers carrying empty containers. The trucking company has a set of import tasks (set I) and an export task set (set O), each task consisting of a first-stage subtask and a second-stage subtask. Let the first and second-stage subtask sets for import tasks be I1 and I2, and for export tasks be O1 and O2. The first-stage subtask for imports requires delivering an import trailer from the yard to the corresponding importer, while the second-stage subtask requires returning the empty trailer to the yard or transporting it to the exporter after the container is emptied. The first phase of the export sub-task requires delivering an empty trailer to the corresponding exporter, while the second phase sub-task requires towing the exported loaded trailer back to the yard after cargo loading is completed. The tractor unit can tow any type and number of trailers, provided it does not exceed the towing limit.

[0026] The problem under study can be described as a graph G = (N, A). Here, N = I1∪I2∪O1∪O2∪{0} is the set of nodes, and A = {(0,i)|i∈N\{0}}∪{(i,0)|i∈N\{0}}∪A TRF Let A be an arc set, where A TRFLet {(i,j)|i∈N\{0},j∈N\{0,i}}\{(δ(i),i)|i∈I1∪O1} be the intermediate arc set. I1 and I2 are the first and second stage sub-task nodes of the inlet, respectively. O1 and O2 are the first and second stage sub-task nodes of the outlet, respectively. 0 is the yard node. δ(j) represents the second stage sub-task node corresponding to the first stage sub-task node j∈I1∪O1. Node j∈I1∪O1 must be visited before δ(j), which is referred to as the priority constraint. The travel time of the tractor between any two nodes i and j is τ. ij For any three nodes i, j, and k, the following condition is met: τ ij +τ jk >τ ik .

[0027] A sufficient number of tractor-trailers and trailers are responsible for container intermodal transport services. One tractor-trailer can tow K trailers, where K ≥ 2 (hereinafter referred to as the capacity constraint). The types of trailers towed are combinations of imported loaded trailers, exported loaded trailers, and empty trailers. A tractor-trailer can perform one or more transport trips. A trip refers to the tractor-trailer departing from the yard node, visiting several sub-task nodes, and then returning to the yard node. One or more trips performed by a tractor-trailer constitute a path. After returning to the yard, the tractor-trailer does not need to ditch all trailers; it can ditch or attach appropriate types and numbers of trailers as needed to begin the next transport trip. The tractor-trailer can freely choose when to leave the yard and begin work.

[0028] The goal of the problem is to complete all transportation tasks within the planning period [0, H] with the minimum total transportation cost. The total transportation cost consists of the fixed usage cost of the tractor and the total working time cost of the tractor. The working time of the tractor refers to the time from when the tractor leaves the yard to when it completes its first transportation service and returns to the yard after completing its last transportation service.

[0029] The mixed integer programming model module 2 includes a state-based mixed integer programming model submodule 2-1 and a logic constraint IF-THEN-based mixed integer programming model submodule 2-2, which are used to solve the trailer-swapping and docking transportation problem.

[0030] The state-based mixed-integer programming model submodule 2-1 can be described by the following formula:

[0031] minβ1∑ i∈N\{0} x 0i +β2(∑ i∈N\{0} x i0 (s i +τ i0 )-∑ i∈N\{0} x 0i (s i -τ0i )) Formula (1)

[0032] Objective function (1) minimizes the fixed usage cost of the tractor and the total working time cost of the tractor, where ∑ i∈N\{0} x 0i For the number of tractor units used, β1 is the fixed operating cost per tractor unit. ∑ i∈N\{0} x i0 (s i +τ i0 )-∑ i∈N\{0} x 0i (s i -τ 0i Let ) represent the total working time of all tractor units, and β2 represent the cost per unit working time of a tractor unit. Where ∑ i∈N\{0} x i0 (s i +τ i0 ∑ represents the sum of the times it takes for the tractor to return to the yard after completing its final journey. i∈N\{0} x 0i (s i -τ 0i This is the sum of the times when the tractor leaves the yard during its first trip.

[0033]

[0034] Constraint (2) limits the number of times each node can be accessed, ensuring that each node is accessed only once, thereby guaranteeing the completion of all container transfer and transportation tasks. Constraint (3) achieves flow balance, where, Constraint (4) ensures the temporal continuity of two nodes visited by the same tractor, where M is a positive number. Constraint (5) establishes the sequential relationship between the first and corresponding second-stage subtasks. Constraint (6) establishes tractor capacity constraints. Imported heavy-duty trailers need to be delivered to the importer, and export heavy-duty trailers need to be transported from the exporter to the yard. Therefore, constraint (7) ensures that the tractor does not tow imported heavy-duty trailers when returning to the yard, and does not tow export heavy-duty trailers when leaving the yard.

[0035]

[0036] Constraints (8)-(10) respectively construct the state variables for the number of imported loaded trailers, the number of unloaded trailers, and the total number of trailers towed by the tractor. Where ∈ is a sufficiently small positive number. For constraint (8), when When both sides of the constraint are equal to 0, we can obtain Conversely, when When constraint (8) is greater than 0 on the left and greater than or equal to 1 on the right, combined with... The range of variables can be obtained Similarly, in constraint (9), when At that time, it can be obtained when At that time, it can be obtained when When both sides of constraint (10) are equal to 1, we can obtain Conversely, when When the left side of constraint (10) is less than or equal to 0, and the right side is less than 1, according to The range of variables can be obtained

[0037]

[0038] Constraints (11)-(15) describe the changes in the number of various trailers when the tractor visits the first stage subtask node j∈I1 at the import port. When the tractor is towing an import heavy trailer, i.e. You can directly access node j∈I1. Otherwise, you need to return to the storage yard to perform a swap operation before accessing node j∈I1.

[0039]

[0040] Constraints (6-16)-(6-20) describe the changes in the number of various types of trailers when the tractor visits the exit at the first-stage subtask node j∈O1. When the tractor is towing an empty trailer, i.e. You can directly access node j∈O1. Otherwise, you need to return to the storage yard to perform a swap operation before accessing node j∈O1.

[0041]

[0042]

[0043] Constraints (21)-(25) describe the changes in the number of various types of trailers when the tractor visits the second-stage subtask node j∈I2 at the import port. When the total number of trailers towed by the tractor reaches K, i.e. You need to return to the yard to perform the swapping operation before accessing node j∈I2. Conversely, you can directly access node j∈I2.

[0044]

[0045] Constraints (26)-(29) describe the changes in the number of various types of trailers when the tractor visits the exit at the second-stage subtask node j∈O2. When the total number of trailers towed by the tractor reaches the upper limit K of the total number of trailers, i.e. You need to return to the storage yard to perform the swap operation before accessing j∈O2. Conversely, you can directly access node j∈O2.

[0046]

[0047] Constraints (30)-(32) are used to calculate the transition time on the intermediate arc. When At that time, from constraint (11), we can obtain t ij =τ ij Conversely, we can obtain t. ij =τ i0 +τ 0j Similarly, from constraint (31), we can obtain that when At that time, t ij =τ ij , and when At that time, t ij =τ i0 +τ 0j For constraint (32), when At that time, t ij =τ i0 +τ 0j , and when At that time, t ij =τ ij .

[0048]

[0049] Constraints (33)-(36) define decision variables. Among them, constraint (34) limits the earliest and latest start times for the tractor to serve the node, ensuring that all tasks are completed within the planning period.

[0050] The mixed-integer programming model submodule 2-2 based on the logical constraint IF-THEN is described as follows:

[0051] Formulas (11)-(29) are constraints on the change in the number of trailers, and constraints (30)-(32) are constraints on the calculation of the conversion time. These constraints are established based on the state variables introduced by constraints (8)-(10). However, the introduction of state variables makes the model extremely complex. Since both the constraints on the change in the number of trailers and the constraints on the calculation of the conversion time can be regarded as consisting of two parts: the IF part, which indicates the condition for the constraint to hold, and the THEN part, which indicates the result, this module uses the logical constraints IF-THEN of the commercial solver to redefine the constraints on the change in the number of trailers and the constraints on the calculation of the conversion time.

[0052] By using logical constraints, constraints (11), (12), (16), (17), (21), (22), (26), and (27) can be described as

[0053]

[0054] After applying logical constraints, constraints (3), (15), (18), (20), (23), and (28) can be described as follows:

[0055]

[0056] Constraints (14), (19), (24), (25), and (29) can be described as follows:

[0057]

[0058] Constraints (6-30)-(6-32) can be described as follows:

[0059]

[0060] The objective function (1) and constraints (2)-(7) and (34)-(40) constitute a mixed integer programming model based on the logical constraint IF-THEN.

[0061] To enhance the solution capability of the established mathematical model, the effective inequality module 3 proposes a lower bound inequality for vehicle operating time. This improves the quality of the upper and lower bounds, thereby reducing the solution space and increasing the solution speed.

[0062] First of all, let and These are the times the tractor returns to the yard after completing its visit to the last node i∈N\{0} of the last trip, and the times the tractor leaves the yard when it visits the first node i∈N\{0} of the first trip, respectively. Using a method that minimizes the linearization of the objective function, the objective function (1) can be linearized as follows:

[0063]

[0064] For the mixed-integer programming model based on the logical constraint IF-THEN, by replacing the objective function (1) with the objective function (41) and constraints (42)-(46), the following inequality can be obtained.

[0065]

[0066] The adaptive large neighborhood search algorithm module 4 includes an initial solution construction submodule 4-1, an operator submodule 4-2, and an adaptive mechanism submodule 4-3, the flowchart of which is shown below. Figure 2 As shown, the process includes the following:

[0067] First, an initial solution S is generated. This is then used as the current optimal solution S. B and the current solution S C The current solution is then fed into an iterative destructive reconstruction process. This iterative process is divided into several segments, each containing N... SEGThe process involves several iterations. In each iteration, a destruction operator and an insertion operator are selected sequentially according to an adaptive mechanism. Based on the current solution, the selected operators are used to perform destruction and insertion operations. If a neighborhood solution S is successfully generated... N If the solution in the neighborhood is not found, a local search operator is used to further improve it. Whether to accept the resulting solution is determined by a threshold-based simulated annealing mechanism with backtracking. At the end of each iteration search segment, the weights of the various destruction and reconstruction operators are updated. Finally, when the number of iterations reaches a given upper limit N... ITE The algorithm terminates when the time is right.

[0068] The initial solution construction submodule 4-1 is used to construct the initial solution. A process can be represented as (0, v1, v2, ..., v...). n ,0),v i ∈N\{0}, i=1,2,…,n. One or more journeys constitute a path, and one or more paths constitute a solution.

[0069] First, initialize |N|-1 processes, each process containing only one node v. i ∈I1∪O1∪I2∪O2. First, consider nodes containing only node v. i The routes ∈I1∪O1 are merged. Then, the resulting routes are merged with the remaining routes. (Based on the routes...) and For example, fusion and This refers to deletion. The last storage node and The first storage node will Attached to The process always selects two paths that produce the minimum tractor working time for merging. Path construction is performed by sequentially using path merging and path insertion operations. The loop ends when the number of paths no longer decreases. Path merging refers to directly appending one path to another, merging the two paths into one. This operation always selects two paths that produce the minimum total tractor working time for merging. If the merged path r... i and r j If a feasible solution can be successfully generated, then it is called a solution. <r i ,r j > represents a path pair; path insertion, on the other hand, involves taking each node i∈N{0} of a path and inserting it into a node P that is not on the path. B In (i), if this operation succeeds, the path is deleted. For a given solution, this operation is performed on all paths.

[0070] The operator sub-module 4-2 is used to design the destruction operator and the insertion operator.

[0071] For a given solution, each destruction operator will pairwisely take out the first and the corresponding second-stage sub-task nodes therefrom until a total of q nodes are taken out.

[0072] The specific operation process of the similarity-based destruction operator is as follows:

[0073] First, given a solution S and an empty set Q, randomly select a node i∈I1∪O1 from S, and move i and the corresponding δ(i) into Q. Then randomly select a node j∈I1∪O1 from Q. Select a node i∈I1∪O1 from S such that is minimized, and move the node i and its corresponding node δ(i) from S into Q. Here, μ is a random number in the range of 0 to 1, and |S| is the total number of remaining non-yard nodes in S. If |Q|<q, return to the previous process and continue the operation; otherwise, output S and end the operation.

[0074] The specific operation process of the depth greedy search-based insertion operator is as follows:

[0075] First, check all trips, insert the removed nodes into the trips that violate the capacity constraint, and repair them to meet the capacity constraint. Then, insert the remaining removed nodes into the optimal candidate positions. If some trips cannot be repaired all the time, or some nodes cannot be inserted successfully all the time, the operator ends the execution.

[0076] The local search includes three operators, namely the trip segment insertion operator, the node exchange operator, and the node insertion operator. The three operators are executed in the order shown.

[0077] The trip segment insertion operator: A trip segment refers to a segment composed of k∈{1,2,…,K} consecutive nodes within a trip, where K is the K in the above capacity constraint. For a trip containing n non-yard nodes, if n≥K, then the trip contains n + 1 - K trip segments, and each trip segment is composed of K consecutive nodes; otherwise, the trip only contains a unique trip segment composed of n consecutive nodes. Taking the trip (0,v1,v2,v3,0) as an example, assuming K = 2, then this trip contains two trip segments: (v1,v2) and (v2,v3). And the trip (0,v4,0) only contains one trip segment (v4). The trip segment insertion operator takes out the best trip segment and inserts it into the corresponding optimal position to generate a solution with the minimum tractor working time. The trip segment cannot be inserted into its original position.

[0078] The node exchange operator: This operator exchanges two optimal nodes to make the tractor working time corresponding to the generated solution the minimum.

[0079] The node insertion operator is similar to the travel segment insertion operator. It extracts the optimal node and inserts it into the corresponding optimal position.

[0080] The adaptive mechanism submodule 4-3 is used to design the adaptive mechanism, and the specific operation process is as follows:

[0081] First, to calculate the weights of the destruction and insertion operators, the mechanism assigns a score to each operator. The entire destruction-reconstruction iteration process is divided into several segments. Then, at the beginning of each segment, the scores of all operators are reset to zero. Within each segment, the selected destruction and insertion operators are rewarded with scores based on their performance. Finally, if the selected destruction and insertion operators find a new current optimal solution, σ1 is added to the scores of both operators; if a better solution is found, σ2 is added to the scores of both operators; if a worse solution is found but is accepted, σ3 is added to the scores of both operators.

[0082] In summary, the multi-trip trailer swapping transportation method of the present invention, which considers flexible time, can be widely applied to trailer swapping transportation problems with different capacity limitations. Furthermore, considering the flexible working time of vehicles can effectively reduce unnecessary vehicle waiting time, decrease total working time, and improve transportation efficiency.

[0083] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-trip trailer swapping transportation method considering flexible time, characterized in that... include: The system comprises a problem description module, a mixed-integer programming model module, an effective inequality module, and an adaptive large neighborhood search algorithm module. The mixed-integer programming model module includes a state-based mixed-integer programming model submodule and a mixed-integer programming model submodule based on the logical constraint IF-THEN. The adaptive large neighborhood search algorithm module includes an initial solution construction submodule, an operator submodule, and an adaptive mechanism submodule. The problem description module is used to determine the objective of solving the container swapping and docking transportation problem. A trucking company provides import and export container transshipment services in a certain area. The company owns a yard with ample tractors and trailers. One tractor can tow two trailers simultaneously; the tractor and trailer are detachable. Each trailer carries one container, and the two always exist as a single unit. Based on the type of cargo loaded in the containers, trailers can be categorized into three types: trailers carrying imported goods, trailers carrying exported goods, and trailers carrying empty containers. A set of these is... The import task and a set of Export tasks need to be completed by trucking companies, and each task consists of a first-stage sub-task and a second-stage sub-task; let the first and second-stage sub-task sets of the import tasks be respectively... and Let the first and second phase sub-task sets of the export task be respectively... and The first phase of the import task requires delivering an import trailer from the yard to the corresponding importer, while the second phase task requires towing the empty trailer back to the yard or to the exporter after the container is emptied. The first phase of the export task requires delivering an empty trailer to the corresponding exporter, while the second phase task requires towing the export trailer back to the yard after the cargo loading is completed. The tractor unit can tow trailers of any type and within the limit number of trailers that can be towed. The problem studied can be described as a graph. ;in, For a set of nodes, Let be an arc set, where It is an intermediate arc set; and These are the first and second phase sub-task nodes for import; and These are the first and second phase sub-task nodes for the export stage, respectively. For storage yard nodes; Indicates the first phase subtask node The corresponding second-stage subtask node; node To Previously visited, hereinafter referred to as the sequential constraint; the tractor is at any two nodes and The travel time between them is Any three nodes , and Between, satisfy ; A sufficient number of tractor-trailers and trailers are available for container transshipment services; one tractor-trailer can tow... One trailer truck, Hereinafter referred to as capacity constraint; the type of trailer being towed is a combination of imported loaded trailers, exported loaded trailers, and empty trailers; the tractor can perform one or more transport services; a trip refers to the tractor starting from the yard node, visiting several sub-task nodes, and then returning to the yard node, and one or more trips performed by a tractor constitute a path; after returning to the yard, the tractor does not need to drop off all trailers, and can drop off or attach appropriate types and numbers of trailers according to transport needs to carry out the next transport operation; the tractor can freely choose when to leave the yard to start working; The goal of the problem is during the planning period Within the scope, all transportation tasks are completed with the minimum total transportation cost. The total transportation cost consists of the fixed usage cost of the tractor and the total working time cost of the tractor. The working time of the tractor refers to the time from when the tractor leaves the yard to when it completes its first transportation service and returns to the yard after completing its last transportation service.

2. The multi-trip trailer swapping transportation method considering flexible time according to claim 1, characterized in that, The mixed integer programming model module includes a state-based mixed integer programming model submodule and a mixed integer programming model submodule based on logical constraints IF-THEN, which are used to solve the trailer-swapping and docking transportation problem. The state-based mixed-integer programming model submodule can be described by the following formula: Official (1) Objective function (1) minimizes the fixed operating cost of the tractor and the total working time cost of the tractor, where, The number of tractor units used. It is the fixed operating cost of a single tractor unit; The total working time of all tractor units. It is the cost per unit working time of the tractor; among which, This is the sum of the time it takes for the tractor to return to the yard after completing its final journey. This is the sum of the times the tractor leaves the yard when it first performs its first stroke; Official (2) Official (3) Official (4) Official (5) Official (6) Official (7) Constraint (2) limits the number of times each node can be accessed, ensuring that each node is accessed only once, thereby guaranteeing the completion of all container transfer and transportation tasks. Constraint (3) achieves flow balance, where, Constraint (4) ensures the temporal continuity of two nodes visited by the same tractor, where, It is a positive number; constraint (5) establishes the sequential relationship between the first and corresponding second stage sub-tasks; constraint (6) establishes the tractor capacity constraint; imported heavy-duty trailers need to be delivered to the importer, and exported heavy-duty trailers need to be transported from the exporter to the yard. Therefore, constraint (7) ensures that the tractor does not tow imported heavy-duty trailers when returning to the yard, and does not tow exported heavy-duty trailers when leaving the yard. Official (8) Official (9) Official (10) Constraints (8)-(10) respectively construct the state variables of the number of imported loaded trailers, the number of unloaded trailers, and the total number of trailers towed by the tractor; among which, For sufficiently small positive numbers; for constraint (8), when When both sides of the constraint are equal to 0, we can obtain On the contrary, when When constraint (8) is greater than 0 on the left and greater than or equal to 1 on the right, combined with... The range of variables can be obtained Similarly, in constraint (9), when At that time, it can be obtained ;when At that time, it can be obtained ;when When both sides of constraint (10) are equal to 1, we can obtain On the contrary, when When the left side of constraint (10) is less than or equal to 0, and the right side is less than 1, according to The range of variables can be obtained ; Official (11) Formula (12) Official (13) Official (14) Official (15) Constraints (11)-(15) apply to the first phase sub-task nodes of the tractor access import. The text describes the changes in the number of various types of trailers; when a tractor unit is towing an imported heavy-duty trailer, that is... You can directly access the node. Conversely, it is necessary to return to the yard to perform a swapping operation before accessing the node. ; Official (16) Official (17) Official (18) Official (19) Official (20) Constraints (16)-(20) apply to the first phase subtask nodes of the tractor access exit. The text describes the changes in the number of various types of trailers; when a tractor is towing an empty trailer, that is... You can directly access the node. Conversely, it is necessary to return to the yard to perform a swapping operation before accessing the node. ; Official (21) Official (22) Official (23) Official (24) Official (25) Constraints (21)-(25) apply to the second phase sub-task nodes of the tractor access import. Describe the changes in the number of various types of trailers; when the total number of trailers towed by the tractor reaches At that time, that is It is necessary to return to the yard to perform the swapping operation before accessing the node. Conversely, nodes can be accessed directly. ; Official (26) Official (27) Official (28) Official (29) Constraints (26)-(29) apply to the second phase sub-task nodes of the tractor access exit. The text describes the changes in the number of various types of trailers; it also mentions the situation when the total number of trailers towed by a tractor reaches the maximum limit for the total number of trailers. At that time, that is It is necessary to return to the yard first for swapping operations, and then visit the site. Conversely, nodes can be accessed directly. ; Official (30) Official (31) Official (32) Constraints (30)-(32) calculate the transition time on the intermediate arc; when Then, from constraint (11), we can obtain Conversely, we can obtain Similarly, from constraint (31), we can obtain that when hour, , and when hour, For constraint (32), when hour, , and when hour, ; Official (33) Official (34) Official (35) Official (36) Constraints (33)-(36) define decision variables; among them, constraint (34) limits the earliest and latest start times for the tractor to serve the node, ensuring that all tasks are completed within the planning period; The mixed-integer programming model submodule based on the logical constraint IF-THEN is described as follows: Constraints (11)-(29) are constraints on the change in the number of trailers, and constraints (30)-(32) are constraints on the calculation of conversion time. These constraints are established based on the state variables introduced by constraints (8)-(10). However, due to the introduction of state variables, the model becomes extremely complex. Since the constraints on the change in the number of trailers and the constraints on the calculation of conversion time can both be regarded as consisting of two parts: the IF part which indicates the condition for the constraint to be valid and the THEN part which indicates the result, this module uses the logical constraints IF-THEN of the commercial solver to redescribe the constraints on the change in the number of trailers and the constraints on the calculation of conversion time. By using logical constraints, constraints (11), (12), (16), (17), (21), (22), (26), and (27) can be described as Official (37) After applying logical constraints, constraints (3), (15), (18), (20), (23), and (28) can be described as follows: Official (38) Constraints (14), (19), (24), (25), and (29) can be described as follows: Official (39) Constraints (30)-(32) can be described as: Official (40) The objective function (1) and constraints (2)-(7) and (34)-(40) constitute a mixed integer programming model based on the logical constraint IF-THEN.

3. The multi-trip trailer swapping transportation method considering flexible time according to claim 1, characterized in that, To enhance the solution capability of the established mathematical model, the effective inequality module proposes a lower bound inequality for vehicle working time; this improves the quality of the upper and lower bounds, thereby reducing the solution space and increasing the solution speed. First of all, let and These are the last nodes where the tractor ends its final journey. ∈ The time for the return to the yard after accessing {0} and the tractor's journey to the first node in the first trip. ∈ The time spent leaving the storage yard when accessing {0}; by minimizing the linearization method of the objective function, the objective function (1) can be linearized as Official (41) Official (42) Official (43) Official (44) Official (45) Official (46) For the mixed-integer programming model based on the logical constraint IF-THEN, by replacing the objective function (1) with the objective function (41) and constraints (42)-(46), the following inequality can be obtained. Official (47).

4. The multi-trip trailer swapping transportation method considering flexible time according to claim 1, characterized in that, The adaptive large neighborhood search algorithm module includes an initial solution construction submodule, an operator submodule, and an adaptive mechanism submodule, and includes the following process: First, generate an initial solution. ; take it as the current optimal solution and the current solution The current solution is then fed into an iterative destructive reconstruction process; this iterative process is divided into several segments, each containing... The next iteration; In each iteration, a destruction operator and an insertion operator are selected sequentially according to an adaptive mechanism; Based on the current solution, perform destruction and insertion operations using the selected operator; if a neighborhood solution is successfully generated... If the solution is not found, the local search operator is used to further improve the solution in the neighborhood; whether to accept the generated solution is determined by the threshold-type simulated annealing mechanism with backtracking. At the end of each iteration search segment, the weights of each destruction and reconstruction operator are updated; finally, when the number of iterations reaches a given upper limit... The algorithm terminates when the time comes. The initial solution construction submodule is used to construct the initial solution; A trip can be represented as , , One or more journeys constitute a path, and one or more paths constitute a solution. First, initialize Each process contains only one node. ; First, for nodes only The itineraries are merged; then the resulting itineraries are merged with the remaining itineraries; and so on. and For example, fusion and This refers to deletion. The last storage node and The first storage node will Attached to Above; this process always selects two routes that can produce the solution with the minimum tractor working time for merging; path construction is performed by sequentially using path merging and path insertion operations in a loop; the loop ends when the number of paths no longer decreases; where path merging refers to directly appending one path to another path, merging the two paths into one path; this operation always selects two paths that can produce the solution with the minimum total tractor working time for merging; if the merged path and If a feasible solution can be successfully generated, then it is called a solution. For a path pair, path insertion is, for a path, attempting to insert each node... Take it out and then insert it into a path that is not on that path. If the operation succeeds, the path is deleted; for a given solution, this operation is performed on all paths. The operator submodule is used to design destruction operators and insertion operators; For a given solution, each destruction operator will extract the first and corresponding second-stage subtask nodes in pairs, until the total number of extracted nodes is [number missing]. Up to the node; The specific operation process of the similarity-based destruction operator is as follows: First, given a solution and an empty set ,from Randomly select a node ,Will and corresponding move in Then from Randomly select a node ;from Select a node , making Minimum, this node and its corresponding node from move in ;in, It is a random number in the range of 0 to 1. yes The total number of remaining non-stockyard nodes; if If the condition is met, return to the previous step and continue the operation; otherwise, output the result. End the operation; The specific operation process of the insertion operator based on depth-greedy search is as follows: First, all processes are checked, and the removed nodes are inserted into processes that violate capacity constraints to fix them and make them satisfy the capacity constraints. Then, the remaining removed nodes are inserted into the optimal candidate positions. If some processes cannot be fixed or some nodes cannot be successfully inserted, the operator terminates. The local search comprises three operators: a journey segment insertion operator, a node swapping operator, and a node insertion operator; these three operators are executed sequentially as shown. The travel segment insertion operator: a travel segment refers to a travel segment within a travel period. A segment consisting of consecutive nodes, here This refers to the capacity constraints mentioned above. For those containing For a non-stockyard node's journey, if The itinerary includes Each of the three travel segments consists of [number] segments. The process consists of a series of consecutive nodes; otherwise, the process contains only a single node. A journey segment consisting of consecutive nodes; a journey For example, suppose Therefore, the trip consists of two segments: and The itinerary Only contains A travel segment; the travel segment insertion operator takes the best travel segment and inserts it into the corresponding optimal position in order to generate the solution with the minimum working time of the tractor; a travel segment cannot be inserted into its original position; The node swapping operator: This operator swaps two optimal nodes to minimize the working time of the tractor corresponding to the generated solution; The node insertion operator: This operator is similar to the travel segment insertion operator, which extracts the optimal node and inserts it into the corresponding optimal position; The adaptive mechanism submodule is used to design the adaptive mechanism, and the specific operation process is as follows: First, to calculate the weights of the destruction and insertion operators, the mechanism assigns a score to each operator. The entire destruction-reconstruction iteration process is divided into several segments. Then, at the beginning of each segment, the scores of all operators are reset to zero. Within each segment, the selected destruction and insertion operators are rewarded based on their performance. Finally, when a selected destruction or insertion operator finds a new current optimal solution, the scores of both operators are increased. If a better solution is found than the current solution, then the scores of both operators are increased. If a solution worse than the current solution is found, but that solution is accepted, then the scores of both operators are increased by [amount missing]. .

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