A Port Truck-Ground Crane Cluster Control Method Based on Cutting Plane Algorithm

Abstract

This invention provides a port truck-yard crane cluster control method based on the cutting plane algorithm, belonging to the technical field of port multi-equipment cluster control. The port truck-yard crane cluster control method is an iterative algorithm. In each iteration, three optimization models are solved, and the upper and lower bounds of the cutting plane algorithm are updated. When the upper and lower bounds are equal, the cutting plane algorithm obtains the optimal solution, thus yielding the cluster control strategy for port trucks and yard cranes. This invention avoids directly solving the coordinated scheduling optimization problem of all trucks and yard cranes within the port. On the one hand, it significantly reduces the model size, facilitating the rapid acquisition of port equipment cluster control schemes; on the other hand, managing port equipment as a cluster unit reduces the coupling between equipment, simplifying equipment operation and maintenance.

Description

Technical Field

[0001] This invention belongs to the field of port multi-equipment cluster control technology, and relates to a port truck-yard crane cluster control method based on the cutting plane algorithm. Background Technology

[0002] In container terminal landside operations, trucks handle container transfers between the landside and the quay, while yard cranes handle the stacking, retrieval, loading, and unloading of trucks within the yard. If a truck arrives at the yard too early, it must queue at the yard crane; if the yard crane is idle but the truck has not arrived, yard crane resources are wasted. Coordinated scheduling between trucks and yard cranes helps reduce ineffective operation time caused by mutual waiting, playing a crucial role in improving the overall operational efficiency of the terminal. Currently, commonly used equipment joint scheduling methods based on experience or heuristic rules often ensure stable solution quality. However, existing mathematical models, which consider optimal strategies under all equipment collaboration scenarios, are often limited by the solution scale and difficult to apply to the production scenarios of multiple equipment operating together in actual ports, failing to provide reliable scheduling solutions.

[0003] While some research has explored device control schemes from a swarm control perspective, most focuses on collaboration and safety among similar devices, with few studies classifying different devices into swarms and discussing the coordinated scheduling of different devices within a swarm. For example, Chinese invention patent (application number 202510327679.3) proposes a method for UAV networking and trajectory planning, which determines the lead UAV by calculating weight indicators, clusters the UAV group by calculating communication delays between UAVs, and further selects the secondary lead UAVs in each group. Another Chinese invention patent (application number 202510847721.4) provides a method for controlling an autonomous underwater vehicle (AUV) swarm, which determines the next position and speed of the follower UAVs by obtaining the current positions of the lead and follower UAVs and the distances between them, thereby improving the efficiency and safety of the swarm. However, none of these inventions provide a method for classifying different types of devices into swarms, nor do they address the problem of coordinated control of different devices within the same swarm.

[0004] Therefore, there is an urgent need for a port land-based equipment scheduling strategy based on cluster control, which divides a large number of port equipment into several groups and achieves efficient operation of the port's overall equipment based on the coordinated scheduling of equipment within the groups. Summary of the Invention

[0005] To address the problems of existing technologies, this invention provides a port truck-yard crane cluster control method based on the cutting plane algorithm. Based on the "cluster control" strategy, port equipment is divided into several clusters, each containing several trucks and yard cranes. The equipment within each cluster collaboratively performs loading and unloading tasks. This invention can quickly provide an efficient scheduling scheme, solving the problems of low solution efficiency and difficulty in generating stable scheduling strategies in existing algorithms, and effectively reducing the difficulty of port equipment management.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A port truck-yard crane cluster control method based on the cutting plane algorithm is disclosed. This method is an iterative algorithm that solves three optimization models in each iteration, updating the upper and lower bounds of the cutting plane algorithm. The three optimization models are designated as a first optimization model, a second optimization model, and a third optimization model. When the upper and lower bounds are equal, the cutting plane algorithm obtains the optimal solution, thus yielding the cluster control strategy for the port trucks and yard cranes. The method includes the following steps:

[0008] The first step is to collect port data, generate truck, yard crane, and container sets based on existing port equipment resources, and generate virtual container sets and cluster sets according to cluster control strategies. Specifically:

[0009] Step 1.1: Based on the collected port data, generate a set of existing container trucks for the port. , field bridge assembly Container assembly Each yard bridge Container collection that requires loading and unloading operations ,in .

[0010] In the overall container assembly, each container needs to be transported by truck from its starting point at the yard to its final destination at the quayside, or by truck from its starting point at the quayside to its final destination at the yard; the container assembly middle, This refers to a specific yard crane in the port, and each yard crane needs to complete... The loading and unloading operations of containers in China do not overlap between different yard cranes.

[0011] Step 1.2: Generate virtual container nodes to ensure the subsequent model construction, including the virtual starting container. Virtual termination container Generate the set of clusters to be partitioned. Cluster collection Multiple clusters Composition, which will be distributed to each cluster in subsequent steps. A certain number of container trucks and yard bridges are designated in the middle.

[0012] The second step involves constructing the first optimization model based on the trucks, cranes, containers, container sets, and virtual container and cluster sets created in the first step. The first optimization model is a mixed-integer linear programming model, containing several variables, an objective function, and several constraints. The construction process of the first optimization model is as follows:

[0013] Step 2.1, Define the first variable The value is Set the objective function as follows:

[0014] (1)

[0015] Step 2.2, Define the second variable The value is , indicating containers Clustered During the loading and unloading operations of trucks and yard cranes, the completion time of the container loading and unloading operation is as follows: , Specifically, virtual starting container. Virtual termination container All are in each cluster All equipment loading and unloading operations, .therefore, Represents a cluster The time it takes for all the equipment in the system to complete its work. Add constraints as shown in formula (2) to make the first variable... The total time for all port equipment to complete all operations:

[0016] (2)

[0017] Step 2.3: Assign field bridges to the cluster. Define a third variable. The value can be 0 or 1, if the field bridge Classified as a cluster Then take 1, otherwise take 0, where , Add constraints as shown in formula (3) to indicate that each yard bridge is assigned to a cluster:

[0018] (3)

[0019] Step 2.4, add the constraint shown in formula (4), indicating that at least one field bridge is allocated to each cluster:

[0020] (4)

[0021] Step 2.5: Assign trucks to the cluster. Since all trucks in the port have the same operating capacity, it is only necessary to determine the number of trucks in each cluster. Define the fourth variable. The value is a positive integer, indicating that it has been assigned to a cluster. The number of cluster cards. Add constraints as shown in formula (5) to represent all clusters. The total number of trucks allocated equals the total number of trucks at the port:

[0022] (5)

[0023] Step 2.6, Define the fifth variable The value can be 0 or 1, if the cluster A certain truck in the middle completed container delivery. Immediately after loading and unloading of containers If the loading and unloading operation is successful, a value of 1 is used; otherwise, a value of 0 is used. In other words, This reflects the sequence of loading and unloading operations on the container trucks. for The precursor mission. for The subsequent task. For example, given a set of containers. , =1 indicates a cluster A container truck inside the container terminal completed its virtual container start operation. Container handling should be carried out immediately after loading and unloading operations. Loading and unloading operations; =1 indicates a cluster A container truck inside the container terminal completed its container handling operations. Virtual termination of container operations immediately after loading and unloading. Loading and unloading operations.

[0024] Add constraints as shown in formulas (6) and (7) to represent clusters. Each truck in the process starts loading and unloading operations from a virtual starting container 0 and ends with a virtual ending container. As the last loading and unloading operation, specifically, the left-hand side of the constraint equation in formula (6) limits the cluster. After the container truck in the middle executed the virtual starting container 0, a total of [number] executions were performed. The subsequent container loading and unloading tasks, namely those assigned to the cluster Each truck in the cluster performs a task; constraint (7) on the left side of the equals sign limits the cluster. The container trucks in the middle perform virtual termination of containers Previously, a total of One front-wheel-drive container loading and unloading task.

[0025] (6)

[0026] (7)

[0027] Step 2.7, add constraints as shown in formulas (8) and (9), indicating that when assigning loading and unloading tasks to container trucks, the set Each container in the system has one and only one preceding task and one succeeding task, thus ensuring that each container is assigned to a single truck.

[0028] (8)

[0029] (9)

[0030] Step 2.8, add constraints as shown in formulas (10) and (11) to limit the cluster. The scope of container loading and unloading operations by internal trucks. Specifically, if... =0, i.e., field bridge Not included in the cluster Then cluster Internal container truck non-loading and unloading operation collection Any container in the cluster is used to ensure that loading and unloading tasks do not overlap between different clusters. To achieve this logic, the summation term on the left side of equation (10) represents the cluster. A certain truck in the area completed container delivery. After the loading and unloading operations, several follow-up tasks need to be performed. Because a container truck can only load and unload one container at a time, the maximum value of this summation term is 1. If =0, the summation term on the left side of formula (10) is 0, that is, in the cluster China, containers There is no follow-up task. Similarly, if =0, formula (11) limits the cluster China Container There is no precursor mission. Therefore, if =0, cluster The container trucks in the middle do not load or unload the containers Any container in the container.

[0031] (10)

[0032] (11)

[0033] Step 2.9, Define the sixth variable The value can be 0 or 1, if the cluster A container bridge in a certain area was completed. Immediately after loading and unloading of containers The value is 1 for loading and unloading operations, and 0 otherwise. This sixth variable has the same meaning as the fifth variable defined in step 2.6. Similar in meaning, but This reflects the sequence of loading and unloading operations on container trucks. The order of loading and unloading operations for the bridge at the site.

[0034] Add constraints as shown in formulas (12) and (13) to represent clusters. Each yard crane in the system originates from a virtual starting container. Loading and unloading operations commenced, and the container was virtually terminated. As the last loading and unloading operation. Specifically, the terms on the right-hand side of the constraint equation in formula (12) Indicates partitioning into a set The total number of field bridges, combined with the terms on the left side of the equation, represents the cluster. The yard crane in the middle executed a total of [number] actions after virtual starting container 0. The subsequent container loading and unloading tasks, namely those assigned to the cluster Each of the field bridges performs a task; the left-hand side of the constraint equation in formula (13) limits the cluster. The yard crane in the middle performs virtual termination of the container Previously, a total of One front-wheel-drive container loading and unloading task.

[0035] (12)

[0036] (13)

[0037] Step 2.10, add constraints as shown in formulas (14) and (15), with meanings similar to formulas (8) and (9) in step 2.7, representing the set when assigning container loading and unloading tasks to the yard crane. Each container in the system has one and only one preceding task and one succeeding task, thus ensuring that each container is assigned to a single yard crane:

[0038] (14)

[0039] (15)

[0040] Step 2.11, add constraints as shown in formulas (16) and (17) to limit the cluster. The scope of container loading and unloading operations at the inner yard crane. Specifically, if... =0, i.e., field bridge Not included in the cluster Then cluster Internal yard bridge non-loading and unloading operation collection This ensures that loading and unloading operations between different clusters do not overlap. To achieve this logic, the summation term on the left side of equation (16) represents the cluster. A container bridge within the area was completed. After the loading and unloading operations, several follow-up tasks are performed. If =0, formula (16) restricts the summation term to 0, that is, in the cluster China, containers There is no follow-up task. Similarly, if =0, formula (17) limits the cluster China Container There is no precursor mission. Therefore, if =0, cluster The yard bridge does not load or unload the assembly Any container in the container.

[0041] (16)

[0042] (17)

[0043] The third step is to define the lower bound of the cutting plane algorithm. and the Upper Realm This is used in the fourth step to determine whether the cutting plane algorithm has found the optimal solution, i.e., the optimal cluster partitioning scheme. The upper and lower bounds will be continuously updated in subsequent steps, initially set to... =0, = .

[0044] The fourth step is to calculate the relative difference between the upper and lower bounds. If the difference is less than If the cutting plane algorithm has found the optimal solution and obtained the optimal cluster partitioning scheme, the calculation ends and the process proceeds to step nine; otherwise, the process proceeds to step five.

[0045] The fifth step involves using a mathematical programming solver to solve the first optimization model constructed in the second step. The first variable is then obtained from the optimal solution of the first optimization model. The value is denoted as Update the lower bound of the cutting plane algorithm. Let the upper bound of the cutting plane algorithm be... Obtain the third variable from the optimal solution of the first optimization model. Fourth variable Fifth variable The sixth variable The values ​​are denoted as follows: , , , This is used in subsequent steps to construct the second and third optimization models. Define the set of cutting planes. This is used to store the cutting planes generated in steps six and seven. The cutting planes are essentially constraints, expressed as inequalities below. All cutting planes will be added to the first optimization model in step eight.

[0046] Step 6: Based on the set defined in Step 1 and the set obtained in Step 5... , For each cluster Construct and solve the second optimization model, and then apply it to the set of cutting planes. Add a cutting plane. Specifically:

[0047] Step 6.1: Construct a temporary optimization model A, which will be used to derive and establish the second optimization model in step 6.2. The specific steps are as follows.

[0048] Step 6.1.1, use the second variable defined in step 2.2. Set the objective function (18) to minimize the cluster. Internal virtual termination container The time required to complete the assignment;

[0049] (18)

[0050] Step 6.1.2, Calculate parameters This is used to derive the completion time of container loading and unloading operations, where... and Indicates containers, This parameter indicates: when the truck completes container loading... After loading and unloading operations, what is the minimum time required to complete the container handling? Loading and unloading tasks, including trucks unloading containers The loading and unloading task ends at a specific location on the shore or in the yard, and the vehicle then proceeds to the container. The time of origin (a location on the shore or in the yard), the truck's departure from the container From the starting point to the container The time to the destination, and the time for loading and unloading container j by quay crane or yard crane. All travel times are obtained by dividing the distance by the truck speed. The loading and unloading time for a container by quay crane and yard crane is taken as an average based on the actual port operations. In particular, if , ,but This indicates that a quay crane or yard crane is used for loading and unloading containers. Time; if Then let =0.

[0051] Container collection Any container origin or destination and the virtual origin container Virtual termination container The distance between them is set to zero, thus virtually starting the container loading and unloading operations of the quay crane and the yard crane. Virtual termination container The time is set to zero.

[0052] Step 6.1.3, Define Let represent a sufficiently large constant, taking the value 1e5. Use the second variable defined in step 2.2. Add constraints as shown in formula (19) to represent the inequality relationship between the completion times of the two container loading and unloading operations. Specifically, when When =1, container The loading and unloading operation shall be completed no earlier than the container's loading and unloading operation. Loading and unloading operation completion time and The sum of, among which The value is obtained from step five.

[0053] (19)

[0054] Step 6.1.4, Calculate parameters This is used to derive the completion time of container loading and unloading operations, where... and Indicates containers, This parameter indicates: when the yard crane completes container handling... After loading and unloading operations, what is the minimum time required to complete the container handling? Loading and unloading tasks. If containers For imported containers For export boxes, or containers For export boxes and containers For imported containers, this parameter includes the yard crane's position over the container. The destination (a specific location in the yard) is moved to the container. The time of origin (a specific location in the yard), and the container loading and unloading operations by the yard crane. Time; if containers and containers If all are export containers, then this includes container cranes from the container. Move from the starting point to the container The starting time, and the container loading and unloading operations at the yard crane. Time; if containers and containers If all are imported containers, then this includes containers transported by yard cranes. The destination moves to the container. The time of the finish line, and the container loading and unloading operations at the yard crane. The time is calculated by dividing the distance by the crane's speed. The time for loading and unloading a container by the crane is taken as an average based on the actual port operations. Specifically, if... , ,but Indicates container loading and unloading at the yard crane Time; if Then let =0.

[0055] Step 6.1.5, using the second variable defined in step 2.2. Add constraints as shown in formula (20) to represent the inequality relationship between the completion times of the two container loading and unloading operations. Specifically, when When =1, container The loading and unloading operation shall be completed no earlier than the container's loading and unloading operation. Loading and unloading operation completion time and The sum of, among which The value is obtained from step five.

[0056] (20)

[0057] Step 6.2, Define the seventh variable The eighth variable Let represent the dual variables of formulas (19) and (20), respectively. Based on the duality theory of linear programming, the dual model of the temporary optimization model A constructed in step 6.1 is derived, denoted as the second optimization model, which includes the objective function (21) and the constraint condition (22). According to the duality theory of linear programming, , Formulas (21) and (22) do not have a clear physical meaning that is directly related to the port scheduling system, and are only used to generate the cutting plane.

[0058] (twenty one)

[0059] st (twenty two)

[0060] in, and Obtained from step 5.

[0061] Step 6.3: Solve the second optimization model constructed in step 6.2 using the mathematical programming solver. There are two cases.

[0062] Step 6.3.1: If the second optimization model finds the optimal solution, denote the optimal objective function value as... Update the upper bound of the cutting plane algorithm model Obtained from the second optimization model and The value is denoted as and And to the set of cutting planes. Add the following cutting plane:

[0063] (twenty three)

[0064] in, Defined by step 2.2, Calculated from step 6.1.2; Let be a sufficiently large constant, taking the value 1e5; Defined by step 2.6; Calculated from step 6.1.4, Defined by step 2.9.

[0065] Step 6.3.2: If the second optimization model cannot find the optimal solution, then the second optimization model is unbounded, and the upper bound of the cutting plane algorithm is not updated. and the lower realm .remember and The seventh variable in Model 2 and the eighth variable The corresponding polar ray values, which are automatically provided by the mathematical programming solver, are then used to define the cut plane set. Add a cutting plane as shown in formula (24).

[0066] (twenty four)

[0067] in, Calculated from step 6.1.2; Let be a sufficiently large constant, taking the value 1e5; Defined by step 2.6; Calculated from step 6.1.4, Defined by step 2.9.

[0068] Step 7: Based on the set defined in Step 1 and the set obtained in Step 5... For each cluster Construct and solve the third optimization model, and apply it to the set of cutting planes. Add a cutting plane. Specifically:

[0069] Step 7.1, using the second variable defined in step 2.2. The fifth variable defined in step 2.6 The sixth variable defined in step 2.9 According to the information obtained in step five Then, construct the third optimization model. Specifically, add the objective function as shown in formula (25), which has the same meaning as formula (18) defined in step 6.1.1. Add constraints as shown in formulas (26) and (27) to represent clusters. Able to utilize all container trucks in the port to achieve clustering Virtual termination task The theoretical fastest completion time. Add constraints as shown in formulas (28)-(37), with the same meaning as formulas (8)-(17) in the second step. Add constraints as shown in formulas (38)-(39), with the same meaning as formulas (19)-(20) in the sixth step.

[0070] (25)

[0071] st (26)

[0072] (27)

[0073] (28)

[0074] (29)

[0075] (30)

[0076] (31)

[0077] (32)

[0078] (33)

[0079] (34)

[0080] (35)

[0081] (36)

[0082] (37)

[0083] (38)

[0084] (39)

[0085] Step 7.2: Solve the third optimization model constructed in step 7.1 using the mathematical programming solver, and denote the optimal objective function value as... To cut plane set Add a cutting plane as shown in formula (40);

[0086] (40)

[0087] in" "Indicates satisfaction" All bridges and cluster , , Similarly, "Indicates satisfaction" All bridges and cluster , , .

[0088] Step 8: Set the cutting planes All cutting planes are added as constraints to the first optimization model constructed in step two. Repeat steps four through eight.

[0089] Step 9, take the result from step 5 , , , This is transformed into a scheduling scheme for port cranes and container trucks. Specifically:

[0090] Step 9.1, according to The value determines whether to include it in the cluster. All the bridges, if =1 indicates a field bridge To be divided into clusters .

[0091] Step 9.2, according to Determine the cluster The number of CIMC cards, A positive number represents a cluster. The middle is divided as follows A container truck.

[0092] Step 9.3, according to The value determines the job order of the card sets in each cluster. This indicates a cluster. One of the container trucks first completed the container transport. The loading and unloading operations are then completed for the containers. Loading and unloading operations.

[0093] Step 9.4, according to The value determines the job order of the card sets in each cluster. and This indicates a cluster. Middle Bridge First-hand container Reusable Containers .

[0094] The beneficial effects of this invention are:

[0095] This invention uses the concept of cluster control to obtain the solution by solving Model 1 constructed in the second step. The value represents the clustering strategy for port trucks and yard cranes; [the value is then obtained]. and The value represents the order of container handling by port trucks and yard cranes within each cluster. This invention iteratively solves the first, second, and third optimization models using a cutting plane algorithm, evaluating the efficiency of the current cluster control strategy on a cluster-by-cluster basis, and adding cutting planes to the first optimization model to continuously improve the cluster control strategy until the relative gap between the upper and lower bounds of the cutting plane algorithm is reached. < The optimal cluster control strategy can then be obtained. This invention avoids directly solving the coordinated scheduling optimization problem of all container trucks and yard cranes within the port. On the one hand, it significantly reduces the model size, which is conducive to quickly obtaining a cluster control scheme for port equipment; on the other hand, managing port equipment on a cluster basis reduces the coupling between equipment and facilitates equipment operation and maintenance. Attached Figure Description

[0096] Figure 1 This is a flowchart of the algorithm of the present invention.

[0097] Figure 2 To explain the fifth variable defined in step 2.6 A schematic diagram. Detailed Implementation

[0098] Taking a segment of port operation data as an example, this paper illustrates the specific implementation of the method proposed in this patent.

[0099] A port truck-yard crane cluster control method based on the cutting plane algorithm, such as Figure 1 As shown, the port truck-yard crane cluster control method is an iterative algorithm. In each iteration, three optimization models are solved, and the upper and lower bounds of the cutting plane algorithm are updated. The three optimization models are the first optimization model, the second optimization model, and the third optimization model, respectively. When the upper bound is equal to the lower bound, the cutting plane algorithm obtains the optimal solution, that is, the cluster control strategy for port trucks and yard cranes. Specifically, it includes the following steps:

[0100] The first step is to collect port data, generate truck, yard crane, and container sets based on the port's existing equipment resources, and generate virtual containers and cluster sets based on cluster control strategies.

[0101] The port operation data used includes 4 container trucks, 3 yard cranes, and 10 containers. The port equipment is planned to be divided into 2 clusters. The container truck speed is 6 m / s, the yard crane speed is 1.5 m / s, the average time for a yard crane to complete one container handling cycle is 120 seconds, and the average time for a yard crane to complete one container handling cycle is 150 seconds. The relative coordinates (in meters) of the start and end points of the 10 containers in this operation data segment are shown below. In the fourth column, "Import / Export Type," IN represents an import container, and OUT represents an export container.

[0102]

[0103] Step 1.1: Based on the collected port data, generate a set of existing container trucks for the port. , field bridge assembly Container assembly Each yard bridge Container collection that requires loading and unloading operations ,in .

[0104] In the overall container assembly, each container needs to be transported by truck from its starting point at the yard to its final destination at the quayside, or by truck from its starting point at the quayside to its final destination at the yard; the container assembly middle, This refers to a specific yard crane in the port, and each yard crane needs to complete... The loading and unloading operations of containers in China do not overlap between different yard cranes. Specifically:

[0105] The port currently has a fleet of container trucks. The assembly of field bridges is as follows: The container assembly is as follows: Each yard bridge The containers that require loading and unloading operations are: , , .

[0106] Step 1.2: Generate virtual container nodes to ensure the subsequent model construction, including the virtual starting container. Virtual termination container Generate the set of clusters to be partitioned. Cluster collection Multiple clusters Composition, which will be distributed to each cluster in subsequent steps. A certain number of container trucks and yard bridges are designated in the middle.

[0107] The set of clusters to be partitioned is .

[0108] The second step involves constructing the first optimization model based on the trucks, cranes, containers, container sets, and virtual container and cluster sets created in the first step. The first optimization model is a mixed-integer linear programming model, containing several variables, an objective function, and several constraints. The construction process of the first optimization model is as follows:

[0109] Step 2.1, Define the first variable The value is Set the objective function as follows:

[0110] (1)

[0111] Step 2.2, Define the second variable The value is , indicating containers Clustered During the loading and unloading operations of trucks and yard cranes, the completion time of the container loading and unloading operation is as follows: , Specifically, virtual starting container. Virtual termination container All are in each cluster All equipment loading and unloading operations, .therefore, Represents a cluster The time it takes for all the equipment in the system to complete its work. Add constraints as shown in formula (2) to make the first variable... The total time for all port equipment to complete all operations:

[0112] (2)

[0113] Step 2.3: Assign field bridges to the cluster. Define a third variable. The value can be 0 or 1, if the field bridge Classified as a cluster Then take 1, otherwise take 0, where , Add constraints as shown in formula (3) to indicate that each yard bridge is assigned to a cluster:

[0114] (3)

[0115] Step 2.4, add the constraint shown in formula (4), indicating that at least one field bridge is allocated to each cluster:

[0116] (4)

[0117] Step 2.5: Assign trucks to the cluster. Since all trucks in the port have the same operating capacity, it is only necessary to determine the number of trucks in each cluster. Define the fourth variable. The value is a positive integer, indicating that it has been assigned to a cluster. The number of cluster cards. Add constraints as shown in formula (5) to represent all clusters. The total number of trucks allocated equals the total number of trucks at the port:

[0118] (5)

[0119] Step 2.6, as follows Figure 2 As shown, define the fifth variable. The value can be 0 or 1, if the cluster A certain truck in the middle completed container delivery. Immediately after loading and unloading of containers If the loading and unloading operation is successful, a value of 1 is used; otherwise, a value of 0 is used. In other words, This reflects the sequence of loading and unloading operations on the container trucks. for The precursor mission. for The subsequent task. For example, given a set of containers. , =1 indicates a cluster A container truck inside the container terminal completed its virtual container start operation. Container handling should be carried out immediately after loading and unloading operations. Loading and unloading operations; =1 indicates a cluster A container truck inside the container terminal completed its container handling operations. Virtual termination of container operations immediately after loading and unloading. Loading and unloading operations.

[0120] Add constraints as shown in formulas (6) and (7) to represent clusters. Each truck in the process starts loading and unloading operations from a virtual starting container 0 and ends with a virtual ending container. As the last loading and unloading operation, specifically, the left-hand side of the constraint equation in formula (6) limits the cluster. After the container truck in the middle executed the virtual starting container 0, a total of [number] executions were performed. The subsequent container loading and unloading tasks, namely those assigned to the cluster Each truck in the cluster performs a task; constraint (7) on the left side of the equals sign limits the cluster. The container trucks in the middle perform virtual termination of containers Previously, a total of One front-wheel-drive container loading and unloading task.

[0121] (6)

[0122] (7)

[0123] Step 2.7, add constraints as shown in formulas (8) and (9), indicating that when assigning loading and unloading tasks to container trucks, the set Each container in the system has one and only one preceding task and one succeeding task, thus ensuring that each container is assigned to a single truck.

[0124] (8)

[0125] (9)

[0126] Step 2.8, add constraints as shown in formulas (10) and (11) to limit the cluster. The scope of container loading and unloading operations by internal trucks. Specifically, if... =0, i.e., field bridge Not included in the cluster Then cluster Internal container truck non-loading and unloading operation collection Any container in the cluster is used to ensure that loading and unloading tasks do not overlap between different clusters. To achieve this logic, the summation term on the left side of equation (10) represents the cluster. A certain truck in the area completed container delivery. After the loading and unloading operations, several follow-up tasks need to be performed. Because a container truck can only load and unload one container at a time, the maximum value of this summation term is 1. If =0, the summation term on the left side of formula (10) is 0, that is, in the cluster China, containers There is no follow-up task. Similarly, if =0, formula (11) limits the cluster China Container There is no precursor mission. Therefore, if =0, cluster The container trucks in the middle do not load or unload the containers Any container in the container.

[0127] (10)

[0128] (11)

[0129] Step 2.9, Define the sixth variable The value can be 0 or 1, if the cluster A container bridge in a certain area was completed. Immediately after loading and unloading of containers The value is 1 for loading and unloading operations, and 0 otherwise. This sixth variable has the same meaning as the fifth variable defined in step 2.6. Similar in meaning, but This reflects the sequence of loading and unloading operations on container trucks. The order of loading and unloading operations for the bridge at the site.

[0130] Add constraints as shown in formulas (12) and (13) to represent clusters. Each yard crane in the system originates from a virtual starting container. Loading and unloading operations commenced, and the container was virtually terminated. As the last loading and unloading operation. Specifically, the terms on the right-hand side of the constraint equation in formula (12) Indicates partitioning into a set The total number of field bridges, combined with the terms on the left side of the equation, represents the cluster. The yard crane in the middle executed a total of [number] actions after virtual starting container 0. The subsequent container loading and unloading tasks, namely those assigned to the cluster Each of the field bridges performs a task; the left-hand side of the constraint equation in formula (13) limits the cluster. The yard crane in the middle performs virtual termination of the container Previously, a total of One front-wheel-drive container loading and unloading task.

[0131] (12)

[0132] (13)

[0133] Step 2.10, add constraints as shown in formulas (14) and (15), with meanings similar to formulas (8) and (9) in step 2.7, representing the set when assigning container loading and unloading tasks to the yard crane. Each container in the system has one and only one preceding task and one succeeding task, thus ensuring that each container is assigned to a single yard crane:

[0134] (14)

[0135] (15)

[0136] Step 2.11, add constraints as shown in formulas (16) and (17) to limit the cluster. The scope of container loading and unloading operations at the inner yard crane. Specifically, if... =0, i.e., field bridge Not included in the cluster Then cluster Internal yard bridge non-loading and unloading operation collection This ensures that loading and unloading operations between different clusters do not overlap. To achieve this logic, the summation term on the left side of equation (16) represents the cluster. A container bridge within the area was completed. After the loading and unloading operations, several follow-up tasks are performed. If =0, formula (16) restricts the summation term to 0, that is, in the cluster China, containers There is no follow-up task. Similarly, if =0, formula (17) limits the cluster China Container There is no precursor mission. Therefore, if =0, cluster The yard bridge does not load or unload the assembly Any container in the container.

[0137] (16)

[0138] (17)

[0139] The third step is to define the lower bound of the cutting plane algorithm. and the Upper Realm This is used in the fourth step to determine whether the cutting plane algorithm has found the optimal solution, i.e., the optimal cluster partitioning scheme. The upper and lower bounds will be continuously updated in subsequent steps; initially, let... =0, = .

[0140] The fourth step is to calculate the relative difference between the upper and lower bounds. If the difference is less than If the cutting plane algorithm has found the optimal solution and obtained the optimal cluster partitioning scheme, the calculation ends and proceeds to step nine; otherwise, proceed to step five. In this calculation, the relative difference between the upper and lower bounds... =1, proceed to step 5.

[0141] The fifth step involves using a mathematical programming solver to solve the first optimization model constructed in the second step. The first variable is then obtained from the optimal solution of the first optimization model. The value is denoted as Update the lower bound of the cutting plane algorithm. Let the upper bound of the cutting plane algorithm be... Obtain the third variable from the optimal solution of the first optimization model. Fourth variable Fifth variable The sixth variable The values ​​are denoted as follows: , , , ,in =1, =1, =1, =0, the rest are equal to 0. The relevant variable value is 0. =0, used in subsequent steps to construct the second and third optimization models. Define the set of cutting planes. This is used to store the cutting planes generated in steps six and seven. The cutting planes are essentially constraints, expressed as inequalities below. All cutting planes will be added to the first optimization model in step eight.

[0142] Step 6: Based on the set defined in Step 1 and the set obtained in Step 5... , For each cluster Construct and solve the second optimization model, and then apply it to the set of cutting planes. Add a cutting plane. Specifically:

[0143] Step 6.1: Construct a temporary optimization model A, which will be used to derive and establish the second optimization model in step 6.2. The specific steps are as follows.

[0144] Step 6.1.1, use the second variable defined in step 2.2. Set the objective function (18) to minimize the cluster. Internal virtual termination container The time required to complete the assignment;

[0145] (18)

[0146] Step 6.1.2, Calculate parameters This is used to derive the completion time of container loading and unloading operations, where... and Indicates containers, This parameter indicates: when the truck completes container loading... After loading and unloading operations, what is the minimum time required to complete the container handling? Loading and unloading tasks, including trucks unloading containers The loading and unloading task ends at a specific location on the shore or in the yard, and the vehicle then proceeds to the container. The time of origin (a location on the shore or in the yard), the truck's departure from the container From the starting point to the container The time to the destination, and the time for loading and unloading container j by quay crane or yard crane. All travel times are obtained by dividing the distance by the truck speed. The loading and unloading time for a container by quay crane and yard crane is taken as an average based on the actual port operations. In particular, if , ,but This indicates that a quay crane or yard crane is used for loading and unloading containers. Time; if Then let =0.

[0147] Container collection Any container origin or destination and the virtual origin container Virtual termination container The distance between them is set to zero, thus virtually starting the container loading and unloading operations of the quay crane and the yard crane. Virtual termination container The time is set to zero.

[0148] Step 6.1.3, Define Let represent a sufficiently large constant, taking the value 1e5. Use the second variable defined in step 2.2. Add constraints as shown in formula (19) to represent the inequality relationship between the completion times of the two container loading and unloading operations. Specifically, when When =1, container The loading and unloading operation shall be completed no earlier than the container's loading and unloading operation. Loading and unloading operation completion time and The sum of, among which The value is obtained from step five.

[0149] (19)

[0150] Step 6.1.4, Calculate parameters This is used to derive the completion time of container loading and unloading operations, where... and Indicates containers, This parameter indicates: when the yard crane completes container handling... After loading and unloading operations, what is the minimum time required to complete the container handling? Loading and unloading tasks. If containers For imported containers For export boxes, or containers For export boxes and containers For imported containers, this parameter includes the yard crane's position over the container. The destination (a specific location in the yard) is moved to the container. The time of origin (a specific location in the yard), and the container loading and unloading operations by the yard crane. Time; if containers and containers If all are export containers, then this includes container cranes from the container. Move from the starting point to the container The starting time, and the container loading and unloading operations at the yard crane. Time; if containers and containers If all are imported containers, then this includes containers transported by yard cranes. The destination moves to the container. The time of the finish line, and the container loading and unloading operations at the yard crane. The time is calculated by dividing the distance by the crane's speed. The time for loading and unloading a container by the crane is taken as an average based on the actual port operations. Specifically, if... , ,but Indicates container loading and unloading at the yard crane Time; if Then let =0.

[0151] Step 6.1.5, using the second variable defined in step 2.2. Add constraints as shown in formula (20) to represent the inequality relationship between the completion times of the two container loading and unloading operations. Specifically, when When =1, container The loading and unloading operation shall be completed no earlier than the container's loading and unloading operation. Loading and unloading operation completion time and The sum of, among which The value is obtained from step five.

[0152] (20)

[0153] Step 6.2, Define the seventh variable The eighth variable Let represent the dual variables of formulas (19) and (20), respectively. Based on the duality theory of linear programming, the dual model of the temporary optimization model A constructed in step 6.1 is derived, denoted as the second optimization model, which includes the objective function (21) and the constraint condition (22). According to the duality theory of linear programming, , Formulas (21) and (22) do not have a clear physical meaning that is directly related to the port scheduling system, and are only used to generate the cutting plane.

[0154] (twenty one)

[0155] st (twenty two)

[0156] in, and Obtained from step 5.

[0157] Step 6.3: Solve the second optimization model constructed in step 6.2 using the mathematical programming solver. There are two cases.

[0158] Step 6.3.1: If the second optimization model finds the optimal solution, denote the optimal objective function value as... Update the upper bound of the cutting plane algorithm model Obtained from the second optimization model and The value is denoted as and And to the set of cutting planes. Add the following cutting plane:

[0159] (twenty three)

[0160] in, Defined by step 2.2, Calculated from step 6.1.2; Let be a sufficiently large constant, taking the value 1e5; Defined by step 2.6; Calculated from step 6.1.4, Defined by step 2.9.

[0161] Step 6.3.2: If the second optimization model cannot find the optimal solution, then the second optimization model is unbounded, and the upper bound of the cutting plane algorithm is not updated. and the lower realm .remember and The seventh variable in Model 2 and the eighth variable The corresponding polar ray values, which are automatically provided by the mathematical programming solver, are then used to define the cut plane set. Add a cutting plane as shown in formula (24).

[0162] (twenty four)

[0163] in, Calculated from step 6.1.2; Let be a sufficiently large constant, taking the value 1e5; Defined by step 2.6; Calculated from step 6.1.4, Defined by step 2.9.

[0164] In this solution, the model is unbounded, and the polar ray values ​​are obtained: =1, =1, =1, set of cutting planes Add the following cutting plane:

[0165]

[0166] Step 7: Based on the set defined in Step 1 and the set obtained in Step 5... For each cluster Construct and solve the third optimization model, and apply it to the set of cutting planes. Add a cutting plane. Specifically:

[0167] Step 7.1, using the second variable defined in step 2.2. The fifth variable defined in step 2.6 The sixth variable defined in step 2.9 According to the information obtained in step five Then, construct the third optimization model. Specifically, add the objective function as shown in formula (25), which has the same meaning as formula (18) defined in step 6.1.1. Add constraints as shown in formulas (26) and (27) to represent clusters. Able to utilize all container trucks in the port to achieve clustering Virtual termination task The theoretical fastest completion time. Add constraints as shown in formulas (28)-(37), with the same meaning as formulas (8)-(17) in the second step. Add constraints as shown in formulas (38)-(39), with the same meaning as formulas (19)-(20) in the sixth step.

[0168] (25)

[0169] st (26)

[0170] (27)

[0171] (28)

[0172] (29)

[0173] (30)

[0174] (31)

[0175] (32)

[0176] (33)

[0177] (34)

[0178] (35)

[0179] (36)

[0180] (37)

[0181] (38)

[0182] (39)

[0183] Step 7.2: Solve the third optimization model constructed in step 7.1 using the mathematical programming solver, and denote the optimal objective function value as... To cut plane set Add a cutting plane as shown in formula (40);

[0184] (40)

[0185] in" "Indicates satisfaction" All bridges and cluster , , Similarly, "Indicates satisfaction" All bridges and cluster , , .

[0186] The optimal objective function value obtained in this solution is: To cut plane set Add the following cutting plane

[0187]

[0188] Step 8: Set the cutting planes All cutting planes are added as constraints to the first optimization model constructed in step two. Repeat steps four through eight.

[0189] Step 9, take the result from step 5 , , , This is transformed into a scheduling scheme for port cranes and container trucks. Specifically:

[0190] Step 9.1, according to The value determines whether to include it in the cluster. All the bridges, if =1 indicates a field bridge To be divided into clusters .

[0191] Step 9.2, according to Determine the cluster The number of CIMC cards, A positive number represents a cluster. The middle is divided as follows A container truck.

[0192] Step 9.3, according to The value determines the job order of the card sets in each cluster. This indicates a cluster. One of the container trucks first completed the container transport. The loading and unloading operations are then completed for the containers. Loading and unloading operations.

[0193] Step 9.4, according to The value determines the job order of the card sets in each cluster. and This indicates a cluster. Middle Bridge First-hand container Reusable Containers .

[0194] In the fourth step Then proceed to step nine. Because... =1, =1, =1, Yard Bridge , To be divided into clusters , Yard Bridge To be divided into clusters After executing steps 9.1-9.4, the scheduling scheme is as follows:

[0195]

[0196] Cluster Includes yard bridge and Among them, the yard bridge The order of container handling is as follows - - , Yard Bridge The order of container handling is as follows - - Two container trucks were allocated in total. The order of container handling is as follows - - trucks The order of container handling is as follows - - Cluster Includes yard bridge The order of their container operations is as follows - - - Two container trucks were allocated in total. The order of tasks is as follows - trucks The order of tasks is as follows - .

[0197] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A port tractor- yard bridge cluster control method based on a cutting plane algorithm, characterized in that, The port tractor-bridge cluster control method is an iterative algorithm, three optimization models are solved in each iteration, and the upper and lower bounds of the cut plane algorithm are updated, wherein the three optimization models are a first optimization model, a second optimization model and a third optimization model; when the upper bound is equal to the lower bound, the cut plane algorithm obtains an optimal solution, that is, the cluster control strategy of the port tractor and the bridge is obtained; The method comprises the following steps: Step 1, collecting port data, generating a container set according to the existing equipment resources of the port, and generating a virtual container set and a cluster set according to the cluster control strategy; Secondly, according to the container truck, the yard crane, the container, the container set and the virtual container and the cluster set created in the first step, a first optimization model is constructed; the first optimization model is a mixed integer linear programming model, including a plurality of variables, a target function and a plurality of constraint conditions; the plurality of variables include a first variable , a second variable , a third variable , a fourth variable , a fifth variable , and a sixth variable . Third step, define the lower bound of the cut plane algorithm and the upper bound , which are used to determine whether the cut plane algorithm has found the optimal solution, i.e. the optimal clustering scheme, in the fourth step; the upper and lower bounds will be updated in the subsequent steps, and initially let = 0, = ; Step 4, calculate the relative gap between the upper and lower bounds If the gap is less than , the optimal solution is obtained by the cut-plane algorithm, and the optimal clustering scheme is obtained, and the calculation is ended and enters Step 9; otherwise, Step 5 is entered. In the fifth step, the first optimization model built in the second step is solved by a mathematical programming solver; the value of the first variable is obtained from the optimal solution of the first optimization model, denoted as ;​ Lower bound of the update cut plane algorithm Upper bound of the cut plane algorithm Obtain the values of the third variable , the fourth variable , the fifth variable , the sixth variable from the optimal solution of the first optimization model, respectively denoted as , , , which are used to construct the second optimization model, the third optimization model in the subsequent steps; define a set of cut planes , which is used to store the cut planes generated in the sixth step and the seventh step; all cut planes will be added to the first optimization model in the eighth step; Step 6: For each cluster defined in step 1, construct and solve a second optimization model and add a cut to the set of cuts , , and for each cluster , construct, solve a second optimization model, and add a cut to the set of cuts . Step 7: according to the set defined in step 1 and the set obtained in step 5 , for each cluster , construct, solve the third optimization model, and add the cut plane to the set of cut planes ; Step 8. Add all the cut planes to the first optimization model built in Step 2 in a constraint form; repeat Steps 4-8. Step 8. Add all the cut planes to the first optimization model built in Step 2 in a constraint form; repeat Steps 4-8. In the ninth step, the scheduling scheme of the port yard bridge and the truck is converted from the fifth step. , , 、 converted into a scheduling scheme of a port yard bridge and a truck.

2. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 1, wherein, The first step is specifically: Step 1.1, generating a set of existing trucks in the port based on the collected port data , a set of yard cranes , a set of containers as a whole , each yard crane , a set of containers that need to be handled , wherein ; Each container in the container set needs to be transported by a truck from a starting point in a yard to an ending point at a shore, or from a starting point at the shore to an ending point in the yard , Each container in the container set needs to be transported by a truck from a starting point in a yard to an ending point at a shore, or from a starting point at the shore to an ending point in the yard , Each container in the container set needs to be transported by a truck from a starting point in a yard to an ending point at a shore, or from a starting point at the shore to an ending point in the yard Step 1.2, generating virtual container nodes for ensuring subsequent model construction, including a virtual start container , a virtual end container ; generating a set of clusters to be partitioned , the set of clusters consists of multiple clusters , and a certain number of container trucks and yard cranes will be partitioned into each cluster in the subsequent steps.

3. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 2, wherein, In the second step, the first optimization model is constructed as follows: Step 2.1, define first variable , with value ; set objective function to: （1）； Step 2.2, define the second variable , takes the value , represents the container is clustered in the container truck, the container truck unloading operation time, wherein , ; specifically, the virtual starting container , the virtual end container are all loaded and unloaded by all devices in each cluster , ; then represent the time when all devices in the cluster complete the operation; Add the constraint condition as shown in formula (2) to make the first variable Total time of all equipment in the port to complete all operations: （2）； Step 2.3, dividing the bridge into the cluster; Define the third variable , which takes the value 0 or 1, and takes the value 1 if the field bridge is divided into a cluster , otherwise takes 0, wherein , ; add a constraint as shown in equation (3) to represent that each field bridge is divided into a cluster: （3）； Step 2.4, adding constraints as shown in formula (4) to represent that at least one bridge is divided into each cluster: （4）； Step 2.5: Assign trucks to the cluster; since all trucks in the port have the same operating capacity, it is only necessary to determine the number of trucks in each cluster; define the fourth variable. The value is a positive integer, indicating that it has been assigned to a cluster. The number of cluster cards; add constraints as shown in formula (5) to represent all clusters The total number of trucks allocated equals the total number of trucks at the port: （5）； Step 2.6, define the fifth variable , which takes the value 0 or 1, if the container handling of a certain container truck in the cluster is completed immediately after the container handling of a certain container truck in the cluster , which takes the value 1 if the container handling of a certain container truck in the cluster is completed immediately after the container handling of a certain container truck in the cluster , which takes the value 0 if the container handling of a certain container truck in the cluster is completed immediately after the container handling of a certain container truck in the cluster ; the fifth variable embodies the sequence of the container handling of the container trucks, the predecessor task of the container handling of the container truck , and the successor task of the container handling of the container truck ; the fifth variable is used to determine the sequence of the container handling of the container trucks. Add the constraints as shown in equation (6) and equation (7) to represent that each truck in the cluster starts from the virtual start container 0 and ends at the virtual end container as the last task of the loading and unloading operation. Specifically, the terms on the left-hand side of the constraint equality in formula (6) limit the cluster. After the container truck in the middle executes the virtual starting container 0, it executes a total of The subsequent container loading and unloading tasks, namely those assigned to the cluster Each truck in the cluster performs a task; the left-hand side of the constraint in formula (7) limits the cluster. The container trucks in the middle perform virtual termination of containers Previously executed One front-wheel container loading and unloading task; （6）； （7）； Step 2.7, add constraints as shown in equation (8), equation (9) to represent that each container in set has and only has one predecessor task and one successor task, so as to ensure that each container is assigned to one truck: （8）； （9）； Step 2.8, add constraints as shown in formula (10), formula (11) to limit the cluster The scope of the container truck loading and unloading operation; in particular, if =0, i.e. the bridge is not divided into clusters , then the cluster The container truck does not load and unload any container in the set , to ensure that the loading and unloading tasks of different clusters do not cross each other; if =0, the summation term on the left side of formula (10) is 0, i.e. in the cluster , the container has no subsequent task; if =0, formula (11) limits the container in the cluster has no predecessor task; then if =0, the container truck in the cluster does not load and unload any container in the set ; （10）； （11）； Step 2.9, Define the sixth variable The value can be 0 or 1, if the cluster A container bridge in a certain area was completed. Immediately after loading and unloading of containers For loading and unloading operations, a value of 1 is used; otherwise, a value of 0 is used. This reflects the sequence of loading and unloading operations on container trucks. The order of loading and unloading operations for the bridge at the site; Add constraints as shown in formulas (12) and (13) to represent clusters. Each yard crane in the system originates from a virtual starting container. Loading and unloading operations commenced, and the container was virtually terminated. As the last loading and unloading operation; specifically, the terms on the right side of the constraint equation in formula (12) Indicates partitioning into a set The total number of field bridges, combined with the terms on the left side of the equation, represents the cluster. The yard crane in the middle executed a total of [number] actions after virtual starting container 0. The subsequent container loading and unloading tasks, namely those assigned to the cluster Each of the field bridges performs a task; the left-hand side of the constraint equation in formula (13) limits the cluster. The yard crane in the middle performs virtual termination of the container Previously, a total of One front-wheel container loading and unloading task; （12）； （13）； Step 2.10, add constraints as shown in formula (14), formula (15), which have the same meaning as formula (8), formula (9) in step 2.7, which means that when the spreader assigns the container handling task, each container in set has and only has one predecessor task and one successor task, which ensures that each container is assigned to a spreader: （14）； （15）； Step 2.11, add constraints as shown in equation (16), equation (17) to limit the cluster The scope of the container handling task of the yard bridge in the cluster; in particular, if =0, the yard bridge is not divided into the cluster , then the yard bridge in the cluster does not handle any container in the container handling task set , ensuring that the container handling tasks in different clusters do not cross; if =0, equation (16) limits the sum term to 0, i.e. in the cluster , the container has no subsequent task; if =0, equation (17) limits the container in the cluster to have no predecessor task; then if =0, the yard bridge in the cluster does not handle any container in the container handling set . （16）； （17）。 4. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 3, wherein, The sixth step is specifically: Step 6.1, constructing a temporary optimization model A for deriving the second optimization model in step 6.2; Step 6.2, define the seventh variable , the eighth variable , respectively, denote the dual variables of equations (19) and (20), the dual model of the temporary optimization model A constructed in step 6.1 is derived according to the linear programming dual theory, denoted as the second optimization model; Step 6.3, solving the second optimization model constructed in step 6.2 by a mathematical programming solver.

5. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 4, wherein, The step 6.1 is specifically: Step 6.1.1, using the second variable defined in step 2.2 ; setting an objective function (18) to minimize the completion time of the jobs within the virtual termination container ​ （18）； Step 6.1.2, calculation of parameters , for deriving the completion time of a container handling task, wherein and represent a container, ; the parameters represent: how long does it take for the truck to complete the container handling task after it has finished the container handling task, including the time for the truck to travel from the end point of the container handling task to the start point of the container handling task, the time for the truck to travel from the start point of the container to the end point of the container, and the time for the container j to be handled by the quay crane or the yard crane; all travel times are obtained by dividing the distance by the truck travel speed, and the time for a quay crane or a yard crane to handle a container is an average value according to the actual operation of the port; if , , then represents the time for the container j to be handled by the quay crane or the yard crane; if , then =0; Container collection Any container origin or destination and the virtual origin container Virtual termination container The distance between them is set to zero, thus virtually starting the container loading and unloading operations of the quay crane and the yard crane. Virtual termination container The time is set to zero; Step 6.1.3, Define Represents a large constant; use the second variable defined in step 2.

2. Add constraints as shown in formula (19) to represent the inequality relationship between the completion times of the two container loading and unloading operations; specifically, when When =1, container The loading and unloading operation shall be completed no earlier than the container's loading and unloading operation. Loading and unloading operation completion time and The sum of, among which The value is obtained from step five; （19）； Step 6.1.4, calculation of parameters , for deriving the completion time of a container handling task, wherein and represent containers, ; the parameter represents: how long does it take to complete the handling task of container after the container handling task is completed by the yard crane; if container is an import container, container is an export container, or container is an export container and container is an import container, the parameter includes the time for the yard crane to move from the end point of container to the start point of container , and the time for the yard crane to handle container ; if container and container are both export containers, the parameter includes the time for the yard crane to move from the start point of container to the start point of container , and the time for the yard crane to handle container ; if container and container are both import containers, the parameter includes the time for the yard crane to move from the end point of container to the end point of container , and the time for the yard crane to handle container ; all the travel times are obtained by dividing the distance by the travel speed of the yard crane, and the time for the yard crane to handle one container is an average value according to the actual operation of the port; if , , then represents the time for the yard crane to handle container ; if , then let =0; Step 6.1.5, using the second variable defined in step 2.

2. Add constraints as shown in formula (20) to represent the inequality relationship between the completion times of the two container loading and unloading operations; specifically, when When =1, container The loading and unloading operation shall be completed no earlier than the container's loading and unloading operation. Loading and unloading operation completion time and The sum of, among which The value is obtained from step five; （20）。 6. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 5, wherein, In the step 6.2, the second optimization model comprises an objective function (21) and constraints (22); according to the linear programming dual theory, , , and the formulas (21), (22) do not have explicit, direct physical meanings related to the port scheduling system, and are only used to generate the cutting plane; （21）； s.t. (22); wherein and obtained from the fifth step.

7. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 6, wherein, The step 6.3 is divided into the following two cases: Step 6.3.1, if the second optimization model finds an optimal solution, let the optimal objective function value be , update the upper bound of the cut-plane algorithm model ; from the second optimization model and denoted by and ; and adding the following cutting plane to the set of cutting planes ​ （23）； wherein defined by step 2.2, calculated from step 6.1.2; is a sufficiently large constant, taken as le5; defined by step 2.6; calculated from step 6.1.4, defined by step 2.9; Step 6.3.2, if the second optimization model cannot find an optimal solution, then the second optimization model is unbounded, and the cutting plane algorithm upper bound is not updated and lower bound ; record and the seventh variable and the eighth variable corresponding to the polar ray value, which is automatically given by the mathematical programming solver; and add the cutting plane as shown in equation (24) to the cutting plane set ; （24）； where calculated from step 6.1.2; is a sufficiently large constant, taken as le5; defined from step 2.6; calculated from step 6.1.4, defined from step 2.

9.

8. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 7, wherein, The seventh step is specifically: Step 7.1, using the second variable defined in step 2.2 , the fifth variable defined in step 2.6 , the sixth variable defined in step 2.9 ; according to the fifth step , a third optimization model is constructed; specifically, an objective function as shown in formula (25) is added, which has the same meaning as formula (18) defined in step 6.1.1; constraints as shown in formulas (26) and (27) are added, which represent the cluster can use all the trucks in the port to obtain the theoretical fastest job completion time of the virtual termination task in the cluster ; Adding constraints as shown in formulas (28)-(37), which have the same meaning as formulas (8)-(17) in the second step; Adding constraints as shown in formulas (38)-(39); （25）； s.t. (26); (27);​ （28）； （29）； （30）； （31）； （32）； （33）； （34）； （35）； （36） （37）； （38）； （39）； Step 7.2, solve the third optimization model constructed in Step 7.1 by a mathematical programming solver, and denote the optimal objective function value as add the cutting plane as shown in equation (40) to the cutting plane set ​ （40）； wherein ” denotes all field bridges satisfying , and clusters , , ; similarly, ” denotes all field bridges satisfying , and clusters , , .

9. The port yard truck - yard bridge cluster control method based on the slicing plane algorithm of claim 8, wherein, The ninth step is specifically: Step 9.1, according to The value determines whether to include it in the cluster. All the bridges, if =1 indicates a field bridge To be divided into clusters ; Step 9.2, according to determining the cluster number of trucks in the cluster, is a positive number indicating the cluster is divided as trucks; Step 9.3, determine the job order of the container trucks in each cluster according to the value of If , it means that the container truck in the cluster finishes the loading and unloading of the container first and then finishes the loading and unloading of the container . Step 9.

4. Determine the job order of the container handlers in each cluster according to the values of If and , then it means that the yard cranes in the cluster work on the containers first and then on the containers .

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