Freight scheduling method for hub branch abdominal port system based on intelligent prediction and branch pricing algorithm

Abstract

The invention discloses a hub branch abdominal port system freight scheduling method based on an intelligent prediction and branch pricing algorithm, and relates to the technical field of container liner transportation network scheduling. According to the method, short-term demand prediction is carried out by collecting container loading and unloading demand data of each port and combining an intelligent prediction method machine learning model; based on a three-level port network structure of a central bond port, a branch port and a belly port, a mixed integer linear programming model is constructed, and a ship access port sequence, arrival and departure time, speed configuration and connection transportation coordination are controlled through a genetic algorithm, a simulated annealing algorithm, a branch pricing algorithm and a mixed strategy thereof. A model target of minimizing the total navigation cost and the transportation time is achieved; according to the invention, under a complex transportation network level, through deep fusion of machine learning prediction and a hybrid optimization algorithm, key problems of poor dynamic adaptability, disjunction of prediction and optimization and the like in traditional shipping scheduling are solved, and the transportation efficiency and the energy and environmental performance are improved.

Description

Technical Field

[0001] This invention relates to the field of container liner shipping network scheduling technology, specifically to a freight scheduling method for hub feeder hinterland port systems based on intelligent prediction and branch pricing algorithms. Background Technology

[0002] With the continued growth of global trade, container shipping networks are becoming increasingly complex, and vessel scheduling at multiple port levels has become a key factor affecting transportation efficiency, operating costs, and service quality. Traditional vessel scheduling methods mainly rely on static network models and historical data assumptions, making it difficult to effectively handle dynamic factors such as fluctuations in port demand, adjustments in vessel speed, changes in fuel consumption, and weather effects. This leads to uneven resource allocation, high costs, and insufficient robustness in on-time control. Therefore, researching a scheduling technique based on dynamic prediction, network modeling, and optimization algorithms has become an urgent need to improve the reliability and economy of maritime logistics.

[0003] The multi-level port liner vessel scheduling problem is essentially a large-scale combinatorial optimization problem, exhibiting NP-hard characteristics. Existing research mainly focuses on three aspects: network structure, demand forecasting, and algorithm case size, but methodological limitations still exist. (1) Simplified network modeling: Early studies such as Yue and Mangan (2024) adopted a static reliability framework, focusing on network topology analysis, but did not incorporate dynamic scheduling constraints, resulting in insufficient adaptability of the model in actual operation. Xu et al. (2024) described the global port associations through multi-network theory, providing structural insights, but lacked integration with optimization algorithms and could not handle precise scheduling problems.

[0004] (2) Separation of prediction and optimization: Most methods, such as Tamburini et al. (2023), rely on historical data and static assumptions, which cannot respond to market fluctuations. Wang et al. (2024) developed a multivariate hybrid system for port throughput prediction, which combined ARIMA and LSTM models to achieve an accuracy of MAPE=7.8%, but the prediction results were decoupled from the scheduling decision and were not used for accurate optimization.

[0005] (3) Algorithm efficiency and scale: Exact algorithms (such as branch pricing B&P) can guarantee the optimal solution, but the computational cost is high; heuristic algorithms (such as genetic algorithm GA and simulated annealing SA) are computationally efficient, but they are prone to getting trapped in local optima. For example, Zhao et al. (2024) used GA to achieve a cost saving of about 5%, but assumed that all ports were directly accessible. The number of ports in the case was small, and it was out of touch with the hub-branch hierarchical structure in real logistics.

[0006] To address the aforementioned shortcomings, this invention studies multi-level port liner scheduling within a complex transportation network hierarchy, enabling dynamic prediction of port containers and optimization of scheduling routes, thus providing shipping companies with scientific decision-making technical support. Summary of the Invention

[0007] The purpose of this invention is to provide a freight scheduling method for hub feeder hinterland port systems based on intelligent prediction and branch pricing algorithms, so as to solve the problems existing in the prior art mentioned in the background art above.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A freight scheduling method for hub feeder hinterland port systems based on intelligent prediction and branch pricing algorithms includes the following steps: S1: Construct a three-tiered transportation network model including hub ports, feeder ports, and hinterland ports, and define the port topology, transportation relationships, and cargo flow. S2: Based on historical loading and unloading volume data, a dynamic demand forecasting model for ports is constructed to predict the container demand of each port in the future period. Based on the predicted demand, candidate scheduling schemes for main routes and connecting routes are generated, and a comprehensive optimization model including voyage time windows, fuel consumption, loading and unloading operation time and cost is established. S3: A method combining branch pricing algorithm and heuristic algorithm of design column generation architecture is used to solve the comprehensive optimization model and obtain the optimal route scheduling scheme that meets transportation needs and minimizes total cost.

[0009] Preferably, in step S1, the three-layer transportation network model includes a set of hub ports. Ω Feeder ports collection H and inland ports C Ships K They are divided into two types: mainline vessels and feeder vessels; Mainline vessels depart from the hub port, passing through feeder ports with loading needs along the way to complete loading and unloading services, and return to the hub port earliest. At the same time, feeder vessels depart from the hinterland port, transporting the hinterland port's cargo to the feeder port with loading and unloading needs. The transport routes are carried out simultaneously, but feeder vessels must arrive at the feeder port before the mainline vessels arrive.

[0010] Preferably, in step S2, the port dynamic demand forecasting model uses a machine learning long short-term memory network (LSTM) forecasting model for forecasting. The LSTM forecasting model processes the input data through a gating mechanism, including historical throughput, weather indicators, and economic indices.

[0011] Preferably, in step S2, the objective included in the comprehensive optimization model is:

[0012]

[0013]

[0014]

[0015] in Let be the decision variable, representing the ship. From the port sailing to the port The overall objective function is composed of connect, This indicates whether the goods' origin point involves connecting transport; 1 indicates yes, 0 indicates no. Indicates a ship K From the port sailing to the port Fixed costs, This represents the fixed costs of cargo transported via feeder vessels at the point of origin. The cost structure is divided into two main parts: trunk line costs and feeder connection costs, including the operating expenses of various types of vessels used on trunk and feeder routes, as well as container handling fees. ,exist middle, and These respectively indicate that the ship is in port. The unloading volume and loading volume, This represents the cost per unit of loading and unloading volume; Indicates a ship The dynamic costs during the voyage, among which, Indicates fuel consumption cost, The cost of vessel leasing is related to the type of vessel being leased and the total duration of the voyage. Representing environmental emission costs, the comprehensive optimization model achieves a balance between energy economy, transportation efficiency, and environmental benefits by minimizing the weighted sum of these three components. Fixed costs are determined by... Each component is defined to have clear operational and economic significance, and the complete mathematical expression of the integrated optimization model is as follows: ; in, The multiplicative amplification factor representing the effect of sea state and weather on fuel consumption. The value range is 0.5-0.7. The value ranges from 0.3 to 0.5. The exact value depends on the scheduling scale. If complex multi-port operations are involved, the parameter weight is close to 1.

[0016] Preferably, in step S2, the effect of ship speed on fuel consumption satisfies a functional relationship: ,in, Represents the basic fuel consumption coefficient; The speed-power ratio, representing the control energy consumption curve, reflects the sharp increase in fuel consumption at high speeds.

[0017] Preferably, in step S2, the comprehensive optimization model includes: Ensure that every vessel departs from and ultimately returns to the same hub port. Ensure that any vessel entering a feeder port departs from that feeder port; Ensure that each cargo originating from is assigned to exactly one feeder port. Ensure that the total volume of cargo from the point of origin to the port does not exceed the vessel's capacity; Ensure the ship At feeder ports After loading and unloading operations are completed, the remaining capacity must meet the needs of the next feeder port. The loading and unloading needs; Ensure that vessels proceed to feeder ports in sequence and return to the hub port before the latest permitted return time; Ensure that vessels carry out feeder port transport in sequence and return to the hub port before the latest permitted return time; Ensure that feeder vessels deliver cargo from the point of origin to the feeder port before the main vessel arrives; Restricted vessels In feeder ports The berthing time is such that it falls within the port's transport time window.

[0018] Preferably, in step S3: Combining heuristic algorithms, genetic algorithms, and simulated annealing algorithms are used to generate initial feasible route and speed allocation schemes. The main problem is constructed with ship type and route column as the decision objects. The shortest path strategy is used to construct sub-problems, and new route columns that reduce costs are continuously introduced through a column generation mechanism. The integer variables are solved based on the set branching strategy until the globally optimal scheduling scheme is obtained. The main problem uses a set-covering model to describe the set of feasible routes; the subproblems use a shortest path pricing model to generate cost-reducing columns; a branching mechanism is triggered when nodes are infeasible or variables conflict to ensure integer feasibility; the initial solution is first obtained using the GA and SA algorithms, followed by a hybrid branch pricing algorithm; finally, based on numerical experiments, the three algorithms, as well as the solver Gurobi and its combinations, are compared and analyzed to evaluate their performance differences in solution quality and computational efficiency.

[0019] Preferably, in step S3, the output results include: the main route access order, the connecting route access order, the speed and time of each segment, the fuel consumption of each ship type, the overall route cost under each algorithm, and a visualization of the final solution.

[0020] Compared with the prior art, the beneficial effects of the present invention are: This invention addresses key issues in traditional shipping scheduling, such as poor dynamic adaptability and the disconnect between prediction and optimization, by deeply integrating machine learning prediction and hybrid optimization algorithms within a complex transportation network hierarchy. This results in improved transportation efficiency and enhanced energy and environmental performance, and is applicable to international container liner shipping scheduling. Attached Figure Description

[0021] Figure 1 This is a flowchart of the overall method of the present invention.

[0022] Figure 2 This is a route diagram for container ships in an embodiment of the present invention.

[0023] Figure 3 This is a chromosome coding design diagram for the genetic algorithm in an embodiment of the present invention.

[0024] Figure 4 This is a flowchart of the genetic algorithm in an embodiment of the present invention.

[0025] Figure 5 This is a flowchart of the branch pricing algorithm in an embodiment of the present invention.

[0026] Figure 6 This is a bar chart showing the evaluation index of machine learning prediction accuracy in an embodiment of the present invention.

[0027] Figure 7 This is a parameter table for the ship in an embodiment of the present invention.

[0028] Figure 8 This is a graph showing the relationship between ship speed, time, and fuel consumption in an embodiment of the present invention.

[0029] Figure 9 This is a table showing the results of each algorithm in each case in the embodiments of the present invention.

[0030] Figure 10 This is a time comparison chart of the hybrid algorithm and the precise algorithm used in various cases in the embodiments of the present invention.

[0031] Figure 11 This is a comparison chart of the running time of the exact algorithm and the solver. Detailed Implementation

[0032] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0033] Please see Figure 1-11 The present invention provides the following technical solutions: A freight scheduling method for hub feeder hinterland port systems based on intelligent prediction and branch pricing algorithms includes the following steps: S1: Construct a three-tiered transportation network model including hub ports, feeder ports, and hinterland ports, defining the port topology, transportation relationships, and cargo flow; the three-tiered transportation network model includes a set of hub ports. Ω Feeder ports collection H and inland ports C Ships K They are divided into two types: mainline vessels and feeder vessels.

[0034] Mainline vessels depart from the hub port, passing through feeder ports with loading needs along the way to complete loading and unloading services, and return to the hub port earliest. At the same time, feeder vessels depart from the hinterland port, transporting the hinterland port's cargo to the feeder port with loading and unloading needs. The transport routes are carried out simultaneously, but feeder vessels must arrive at the feeder port before the mainline vessels arrive.

[0035] The specific steps are as follows: collect basic data including port loading and unloading data, ship performance parameters, speed and fuel consumption functions, emission factors, and waterway distances; establish a multi-objective optimization scheduling model with the primary objective of minimizing transportation costs and operating time, and the secondary objective of fuel consumption and pollution emission penalties; and set constraints such as flow conservation, capacity limits, upper and lower speed limits, connection time coordination, and port service frequency to ensure that the scheduling plan meets the actual engineering requirements.

[0036] S2: Based on historical loading and unloading volume data, a dynamic demand forecasting model for ports is constructed to predict the container demand of each port in the future period. Based on the predicted demand, candidate scheduling schemes for main routes and connecting routes are generated, and a comprehensive optimization model including voyage time windows, fuel consumption, loading and unloading operation time and cost is established. The port dynamic demand forecasting model employs a Long Short-Term Memory (LSTM) machine learning network for prediction. The LSTM model processes input data, including historical throughput, weather indicators, and economic indices, through a gating mechanism. Its mathematical expression involves input gates, forget gates, candidate states, and output gates. The preprocessing layer primarily performs data normalization and seasonal deduplication to reduce the complexity of the time series data, thereby facilitating the subsequent learning process of the LSTM network.

[0037] First, the time series data is normalized to reduce numerical differences between different series. A commonly used normalization formula is: .in Indicates time The original value, and These represent the minimum and maximum values ​​of the sequence, respectively. This min-maximum scaling maps the data to the range [0, 1], ensuring numerical consistency between features and preventing bias for variables with large values.

[0038] Subsequently, seasonal decomposition is a crucial step in the preprocessing layer. By separating multi-layer seasonal patterns, the difficulty of LSTM learning long sequences can be further reduced. Multi-layer decomposition divides the time series into three distinct independent components: .in These are observed values. This represents the seasonal component that captures cyclical fluctuations. This represents the seasonal component that captures cyclical fluctuations. The trend component represents long-term changes, while the residual component represents noise and irregular variations. By separating these components, LSTM networks can focus on learning the temporal dependencies of the trend and residual parts without being affected by complex seasonal fluctuations, thereby improving prediction accuracy and training efficiency.

[0039] The specific workflow is as follows: Input Gate Forgotten Gate Candidate state Output gate , To evaluate the accuracy and reliability of the demand forecasting model, several standard statistical indicators were used. These indicators quantitatively assessed the deviation between the predicted and actual container throughput values ​​for each port. The selected evaluation indicators included: 、 、 、 。

[0040] The objective of the comprehensive optimization model is:

[0041]

[0042]

[0043]

[0044] This model achieves a balanced coordination between trunk and feeder transportation services. The model's objective is to minimize total transportation costs and transit time within a given time window. Let be the decision variable, representing the ship. From the port sailing to the port The overall objective function is composed of connect, This indicates whether the goods' origin point involves connecting transport; 1 indicates yes, 0 indicates no. Indicates a ship K From the port sailing to the port Fixed costs, This represents the fixed costs of cargo transported via feeder vessels at the point of origin. The cost structure is divided into two main parts: trunk line costs and feeder connection costs, including the operating expenses of various types of vessels used on trunk and feeder routes, as well as container handling fees. ,exist middle, and These respectively indicate that the ship is in port. The unloading volume and loading volume, This represents the cost per unit of loading and unloading volume; Indicates a ship The dynamic costs during the voyage, among which, Indicates fuel consumption cost, The cost of vessel leasing is related to the type of vessel being leased and the total duration of the voyage. Representing environmental emission costs, the comprehensive optimization model achieves a balance between energy economy, transportation efficiency, and environmental benefits by minimizing the weighted sum of these three components. Fixed costs are determined by... Each component is defined to have clear operational and economic significance, and the complete mathematical expression of the integrated optimization model is as follows: ; in, The multiplicative amplification factor representing the effect of sea state and weather on fuel consumption. The value range is 0.5-0.7. The value ranges from 0.3 to 0.5. The exact value depends on the scheduling scale. If complex multi-port operations are involved, the parameter weight is close to 1.

[0045] The effect of ship speed on fuel consumption follows a functional relationship: ,in, Represents the basic fuel consumption coefficient; The speed-power ratio, representing the control energy consumption curve, reflects the sharp increase in fuel consumption at high speeds.

[0046] The comprehensive optimization model includes: Ensure that every vessel departs from and ultimately returns to the same hub port. Ensure that any vessel entering a feeder port departs from that feeder port; Ensure that each cargo originating from is assigned to exactly one feeder port. Ensure that the total volume of cargo from the point of origin to the port does not exceed the vessel's capacity; Ensure the ship At feeder ports After loading and unloading operations are completed, the remaining capacity must meet the needs of the next feeder port. The loading and unloading needs; Ensure that vessels proceed to feeder ports in sequence and return to the hub port before the latest permitted return time; Ensure that vessels carry out feeder port transport in sequence and return to the hub port before the latest permitted return time; Ensure that feeder vessels deliver cargo from the point of origin to the feeder port before the main vessel arrives; Restricted vessels In feeder ports The berthing time is such that it falls within the port's transport time window.

[0047] S3: A method combining branch pricing algorithm and heuristic algorithm of design column generation architecture is used to solve the comprehensive optimization model (MILP) to obtain the optimal route scheduling scheme that meets transportation demand and minimizes total cost.

[0048] To efficiently solve the MILP model, this invention proposes a hybrid algorithm that combines heuristic algorithms with genetic and simulated annealing algorithms to generate initial feasible route and speed allocation schemes. It constructs a main problem with ship type and route column as decision objects, uses the shortest path strategy to construct subproblems, and continuously introduces new route columns that reduce costs through a column generation mechanism. Based on the set branching strategy, it solves the integer variables until the globally optimal scheduling scheme is obtained. The main problem uses a set-covering model to describe the set of feasible routes; the subproblems use a shortest path pricing model to generate cost-reducing columns; a branching mechanism is triggered when nodes are infeasible or variables conflict to ensure integer feasibility; the initial solution is first obtained using the GA and SA algorithms, followed by a hybrid branch pricing algorithm; finally, based on numerical experiments, the three algorithms, as well as the solver Gurobi and its combinations, are compared and analyzed to evaluate their performance differences in solution quality and computational efficiency.

[0049] The specific steps are as follows: First, a genetic algorithm is used to solve for the initial solution. In the chromosome encoding process of the genetic algorithm (GA), a hybrid random generation strategy is adopted to encode the entire route planning (including trunk and branch line operations) into a chromosome structure that can be processed by the genetic algorithm. For the main route, each chromosome encodes a point-to-point port sequence, where each gene represents the visiting order of a port node (ranging from 5 to 15), strictly following the principle of starting and ending at the hub port. Intermediate nodes include branch ports and some unvisited cargo source points, which together constitute the backbone of trunk line transportation. For example, [1, 3, 4, 5, 1] ​​indicates that the main route starts from hub port 1, traverses port 3, port 4, port 5 in sequence, and finally returns to hub port 1.

[0050] Subsequently, the fitness function is calculated. In the process of calculating the fitness function, the randomly generated genes are first decoded to obtain the number of services of each ship type on the route. Once the number of ships deployed on the route is determined, the number of chartered ships can be determined. Using the calculation formula in the model, the cost and carbon emissions are calculated based on the known ship speed and port visit order. At the same time, the value that can be brought to the shipping company by efficiently transporting containers can be calculated based on the number of containers transported at each port, thus obtaining the fitness value of the gene. In terms of selection operations, the roulette wheel selection method is used to design the selection operator for the genetic algorithm. Roulette wheel selection is one of the commonly used selection operations in genetic algorithms. It normalizes the fitness value of an individual into a selection probability and creates a mechanism similar to a roulette wheel to select individuals. Individuals with higher fitness values ​​have a greater probability of being selected during the selection process, thus having a greater chance of being retained to the next generation. Roulette wheel selection is relatively simple and easy to implement, and can effectively retain excellent individuals and promote the evolution of the population. The fitness value of each individual is calculated because the fitness value reflects the individual's quality. The fitness values ​​of all individuals are normalized so that their sum is 1. The purpose of normalization is to convert the fitness value into a selection probability, for example, using... Indicates the first The fitness function values ​​of each chromosome individual, among which The range should not exceed the maximum population size. ,Right now The following formula can be used to express this. The probability that a chromosome is selected to be passed on to the next generation: Create a roulette wheel with a length equal to the number of individuals in the population. The size of the roulette area occupied by each individual is proportional to its fitness value. During the selection process, several selection operations are performed. Each time an individual is selected, a random number between 0 and 1 is randomly generated. Then, the individual is selected based on the roulette area where the random number is located. The larger the roulette area, the greater the probability of the individual being selected. Finally, the operation is repeated until a sufficient number of individuals are selected.

[0051] The crossover operation uses a sequential crossover method to ensure that offspring do not visit the same port multiple times. For the main path, if parent 1 is [1,2,3,4,5,1] and parent 2 is [1,5,4,2,3,1], then the middle segment is selected: the segment [3,4] in parent 1 is fixed in the same position in the offspring. Then, starting from parent 2, the remaining positions are filled sequentially, skipping the already included [3,4]. The middle part of parent 2 is [5,4,2,3]; after removing [3,4], the remaining [5,2] is filled into the offspring sequentially, finally resulting in [1,5,3,4,2,1].

[0052] A cross-mutation strategy is employed to optimize the port access order. During mutation, only genes corresponding to the same path type (main path or branch path) are considered. Two intermediate ports are randomly selected and their positions are exchanged in the offspring chromosomes. This approach enhances population diversity and helps avoid premature convergence to local optima by preserving the logical structure of each path.

[0053] Furthermore, simulated annealing (SA) is employed as a second heuristic algorithm to solve the model for comparison. In each iteration, the scheduling cost of the current solution is first evaluated, and then the cost difference between the newly generated solution and the current solution is calculated. If the new solution has a lower cost, it is directly adopted as the current state. Otherwise, even if the new solution has a lower cost, it may be accepted with a certain probability, determined by the following formula: .in This represents the current temperature. As the temperature gradually decreases, the tolerance of the simulated annealing algorithm for poor solutions also decreases accordingly. Furthermore, to ensure that only feasible scheduling schemes are considered during the search process, each newly generated solution must undergo constraint verification. If any of the following fundamental constraints are violated, the solution will be considered infeasible and discarded: (1) The total carrying capacity of the vessel must be sufficient to meet all loading and unloading needs on the route; (2) The arrival time of the vessel at each port must conform to its designated service time window; (3) The total flight time must not exceed the predetermined maximum scheduling cycle. Therefore, the feasibility check can be expressed mathematically as follows:

[0054] A scheduling scheme is considered feasible only if it simultaneously satisfies all constraints, including vessel capacity limitations, port service time windows, and total voyage duration thresholds. Otherwise, the scheme will be discarded without a final acceptance decision. Therefore, the final simulated annealing acceptance function is defined as follows:

[0055] Once the initial solution is obtained through a heuristic algorithm, the exact solution algorithm can be applied. Specifically, all integer decision variables are encoded in binary format, which simplifies the branching process. Each path is represented as a variable column and contains the following structured information: (1) Port access order (path); (2) Total travel time; (3) Total transportation cost; (4) Connection cost indicators; (5) Requirements for vessel type, speed, and number of vessels.

[0056] When restricting the final solution of the main problem (RMP) to non-integer values, branch and bound are required. This involves decomposing the problem into several subproblems, solving each subproblem one by one, and finally obtaining an integer solution. The specific branching strategy is as follows: (1) If the solution of the current node is an integer, it means that this is a feasible integer scheduling scheme. Calculate its total cost (target value) and compare it with the current best integer scheme: if it is better, update the best scheme; otherwise, discard it. (2) If the solution is not an integer, further branching is required; (3) If the lower bound of the linear programming solution at the current node is greater than the current best integer solution, it means that a better solution cannot be found from this node and a branch is needed; (4) If the current node violates the constraint (no feasible path), the node is considered infeasible and is discarded.

[0057] Example This invention validates its methodology through three case studies: small-scale (15 ports), medium-scale (24 ports), and large-scale (33 ports). Case studies strictly follow the technical methods described in steps 1-3, yielding: the main route access order; the connecting route access order; the speed and time for each segment; fuel consumption for each ship type; the overall route cost under each algorithm; and a visualization of the final solution. Details are as follows: To evaluate the effectiveness of the proposed model and algorithm, an experiment was conducted using a real flight route between China, Japan, and South Korea as the first scenario. Figure 7 It contains information about the vessel, including its speed, rental rate, capacity, fixed costs, and service fees for loading and unloading.

[0058] For further details, please refer to [link / reference]. Figure 3-6 First, machine learning was used to predict the model, followed by genetic algorithm, simulated annealing algorithm and branch-and-bound combined algorithm to solve the model. Then, the accuracy and efficiency of all algorithms were analyzed and evaluated. The evaluation was carried out by setting the number of ports to be traversed to 5-20. In the interval [5,20], all integers are the total number of ports to be traversed, that is, each case needs 16 sets of data for comparison.

[0059] Figure 9-10 Experiments show that, for combinations of small, medium, and large multi-level ports, the combination of simulated annealing and branch-and-price algorithms can reduce total transportation costs by an average of approximately 0.81% to 8.08%, with a maximum improvement of 8.08%, compared to traditional genetic algorithms. Simultaneously, it reduces computation time by approximately 16.86% to 24.7%. Furthermore, to illustrate the effectiveness of the exact algorithm in solving complex problems, the solution time of the exact algorithm is compared with that of the Gurobi solver. Figure 11 As shown, these results ultimately demonstrate the stability of combining precise and heuristic algorithms.

[0060] By comparing the optimal results and running time of the branch-pricing algorithm for each case with the fusion heuristic branch-pricing algorithm, the results show that the fusion algorithm achieves a lower total cost objective in most test cases and demonstrates better solution quality.

[0061] As the number of ports visited and network complexity increase, the overall optimization effect improves: from 0.19% to 1.90% in small-scale cases, from 0.94% to 4.51% in medium-scale cases, and exceeding 8.00% in large-scale scenarios. This indicates that the fusion algorithm is particularly effective for complex route planning problems. The "Time" column represents the CPU runtime (in seconds), measured from the start of algorithm computation. Figure 8 This graph shows the relationship between speed, time, and fuel consumption during the main route and connecting routes.

[0062] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A freight scheduling method for a hub-and-spoke hinterland port system based on intelligent prediction and branch pricing algorithms, characterized in that, Includes the following steps: S1: Construct a three-tiered transportation network model including hub ports, feeder ports, and hinterland ports, and define the port topology, transportation relationships, and cargo flow. S2: Based on historical loading and unloading volume data, a port dynamic demand forecasting model is constructed to predict the container demand of each port in the future period. Based on the predicted demand, candidate scheduling schemes for main routes and connecting routes are generated, and a comprehensive optimization model including voyage time windows, fuel consumption, loading and unloading operation time and cost is established. S3: A method combining branch pricing algorithm and heuristic algorithm of design column generation architecture is used to solve the comprehensive optimization model and obtain the optimal route scheduling scheme that meets transportation needs and minimizes total cost.

2. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 1, characterized in that, In step S1, the three-layer transportation network model includes a set of hub ports. Ω Feeder Port Collection H and inland ports C Ships K They are divided into two types: mainline vessels and feeder vessels; Mainline vessels depart from the hub port, passing through feeder ports with loading needs along the way to complete loading and unloading services, and return to the hub port earliest. At the same time, feeder vessels depart from the hinterland port, transporting the hinterland port's cargo to the feeder port with loading and unloading needs. The transport routes are carried out simultaneously, but feeder vessels must arrive at the feeder port before the mainline vessels arrive.

3. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 1, characterized in that, In step S2, the port dynamic demand forecasting model uses a machine learning long short-term memory network (LSTM) forecasting model for prediction. The LSTM forecasting model processes the input data through a gating mechanism, including historical throughput, weather indicators, and economic indices.

4. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 2, characterized in that, In step S2, the objective included in the comprehensive optimization model is: in, Let be the decision variable, representing the ship. From the port sailing to the port The overall objective function is composed of connect, This indicates whether the goods' origin point involves connecting transport; 1 indicates yes, 0 indicates no. Indicates a ship K From the port sailing to the port Fixed costs, This represents the fixed costs of cargo transported via feeder vessels at the point of origin. The cost structure is divided into two main parts: trunk line costs and feeder connection costs, including the operating expenses of various types of vessels used on trunk and feeder routes, as well as container handling fees. ,exist middle, and These respectively indicate that the ship is in port. The unloading and loading volumes, This represents the cost per unit of loading and unloading volume; Indicates a ship The dynamic costs during the voyage, among which, Indicates fuel consumption cost, The cost of vessel leasing is related to the type of vessel being leased and the total duration of the voyage. Representing environmental emission costs, the comprehensive optimization model achieves a balance between energy economy, transportation efficiency, and environmental benefits by minimizing the weighted sum of these three components. Fixed costs are determined by... Each component is defined to have clear operational and economic significance, and the complete mathematical expression of the integrated optimization model is as follows: ; in, The multiplicative amplification factor representing the effect of sea state and weather on fuel consumption. The value range is 0.5-0.

7. The value ranges from 0.3 to 0.

5. The exact value depends on the scheduling scale. If complex multi-port operations are involved, the parameter weight is close to 1.

5. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 4, characterized in that, In step S2, the effect of ship speed on fuel consumption satisfies a functional relationship: ,in, Represents the basic fuel consumption coefficient; The speed-power ratio, representing the control energy consumption curve, reflects the sharp increase in fuel consumption at high speeds.

6. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 4, characterized in that, In step S2, the comprehensive optimization model includes: Ensure that every vessel departs from and ultimately returns to the same hub port. Ensure that any vessel entering a feeder port departs from that feeder port; Ensure that each cargo originating from is assigned to exactly one feeder port. Ensure that the total volume of cargo from the point of origin to the port does not exceed the vessel's capacity; Ensure the ship At feeder ports After loading and unloading operations are completed, the remaining capacity must meet the needs of the next feeder port. The loading and unloading needs; Ensure that vessels proceed to feeder ports in sequence and return to the hub port before the latest permitted return time; Ensure that vessels carry out feeder port transport in sequence and return to the hub port before the latest permitted return time; Ensure that feeder vessels deliver cargo from the point of origin to the feeder port before the main vessel arrives; Restricted ships In feeder ports The berthing time is such that it falls within the port's transport time window.

7. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 1, characterized in that, In step S3: Combining heuristic algorithms, genetic algorithms, and simulated annealing algorithms are used to generate initial feasible route and speed allocation schemes. The main problem is constructed with ship type and route column as the decision objects. The shortest path strategy is used to construct sub-problems, and new route columns that reduce costs are continuously introduced through a column generation mechanism. The integer variables are solved based on the set branching strategy until the globally optimal scheduling scheme is obtained. The main problem uses a set-covering model to describe the set of feasible routes; the subproblems use a shortest path pricing model to generate cost-reducing columns; a branching mechanism is triggered when nodes are infeasible or variables conflict to ensure integer feasibility; the initial solution is first obtained using the GA and SA algorithms, followed by a hybrid branch pricing algorithm; finally, based on numerical experiments, the three algorithms, as well as the solver Gurobi and its combinations, are compared and analyzed to evaluate their performance differences in solution quality and computational efficiency.

8. The freight scheduling method for a hub feeder hinterland port system based on intelligent prediction and branch pricing algorithm according to claim 1, characterized in that, In step S3, the output results include: the main route access order, the connecting route access order, the speed and time of each segment, the fuel consumption of each ship type, the overall route cost under each algorithm, and a visualization of the final solution.

Images