Green port core resource collaborative scheduling method and system based on machine learning-column generation algorithm

Abstract

The method comprises the following steps: generating an initial feasible column and initializing a feasible column pool; the feasible column is used to represent a feasible scheduling scheme of a ship; a limited master problem is established and solved to obtain a dual variable; a pricing sub-problem is solved based on the dual variable to generate an improved column; the improved column is added to the column pool, and the limited master problem is solved again to update the dual variable; the column pool is expanded, and the combinations of feasible berths, berthing times and departure times for each ship are supplemented; the feasible schemes obtained by supplementing are added to the optional set of the master problem; in the integer master problem, the shore crane allocation scheme pre-generated in the column generation stage is not fixed, and the number of shore cranes used by each ship at each time step is taken as a non-negative integer variable to be re-optimized under global constraints, so that different ships can realize peak-shaving adjustment of the number of shore cranes in overlapping time periods; the integer master problem is solved, and a scheduling result is output.

Description

Technical Field

[0001] This invention relates to the field of efficient and low-carbon scheduling optimization technology for green port resources, specifically to a collaborative scheduling method and system for core green port resources based on machine learning-column generation algorithms. Background Technology

[0002] In port loading and unloading operations, berths and quay cranes are key resources affecting vessel dwell time and port operational efficiency. Berth allocation determines a vessel's spatial berthing position, while quay crane allocation determines the processing time for a vessel during berthing. Allocating more quay cranes to a vessel allows it to complete its operations earlier, but reduces the number of quay cranes available for other vessels during the same period, thus increasing their processing time. Conversely, delaying a vessel's operations to alleviate quay crane congestion increases its waiting time, potentially incurring berthing and departure delay costs. Therefore, berth and quay crane allocation cannot be decided in isolation but should be jointly optimized.

[0003] Under carbon policies, port scheduling also needs to consider the energy consumption and carbon emissions of ships while in port. Traditional fuel oil ships, shore power ships, and LNG ships have different energy consumption rates and emission factors during berthing; the electricity used by quay cranes also generates indirect carbon emissions. Carbon tax policies directly convert emissions into costs, while carbon trading policies need to determine whether total emissions exceed the quota and calculate the carbon trading cost for the excess. Therefore, the port scheduling problem expands from a simple operational cost optimization to a complex combined optimization problem involving operational efficiency, resource conflicts, and carbon emission costs.

[0004] Directly establishing a mixed-integer programming model can effectively express berth selection, berthing and departure times, quay crane allocation, and carbon emission accounting. However, as the number of ships, berths, and time steps increases, the number of binary and integer variables in the model grows rapidly. The coupling with berth sequencing constraints, quay crane capacity constraints, and carbon emission cost calculation makes it difficult for the solver to converge stably within a reasonable time. Although ordinary heuristic methods are computationally faster, they tend to overlook quay crane time-shifting and carbon emission cost calculation, making it difficult to guarantee solution quality. Summary of the Invention

[0005] The purpose of this invention is to provide a collaborative scheduling method and system for core resources of green ports based on machine learning-column generation algorithms. This addresses the problems of low solution efficiency in large-scale berth and quay crane joint scheduling models, difficulty in expressing cross-ship peak shifting using fixed quay crane allocation schemes, and the large computational burden of column generation due to a large number of candidate columns. This invention separates the feasible scheduling schemes for each vessel from the constraints of shared cross-ship resources, improving solution efficiency while maintaining solution quality, and effectively coordinating quay crane resources to ensure a balanced allocation across different time periods.

[0006] To achieve the above objectives, this invention provides a collaborative scheduling method for core resources of green ports based on machine learning-column generation algorithms, the technical solution of which is as follows:

[0007] The first aspect is a collaborative scheduling method for core resources of green ports based on machine learning-column generation algorithms, which includes the following steps:

[0008] S1. Obtain port system parameters and construct a low-carbon collaborative scheduling model for port berths and quay cranes;

[0009] S2. Generate an initial feasible column and initialize the feasible column pool; a feasible column is used to represent a feasible scheduling scheme for a ship;

[0010] S3. Establish and solve the restricted master problem to obtain the dual variables;

[0011] S4. Solve the pricing subproblem based on dual variables and generate an improved column;

[0012] S5. After adding the improved column to the column pool, resolve the restricted master problem and update the dual variables. If no column with a test number less than the preset negative threshold is found in any of the pricing subproblems for all ships, then the column generation is determined to be converged.

[0013] S6. Expand the column pool and supplement each ship with feasible combinations of berths, berthing times and departure times; add the supplemented feasible solutions to the optional set of the main problem; in the integer main problem, do not fix the quay crane allocation scheme pre-generated in the column generation stage, and re-optimize the number of quay cranes used by each ship at each time step as a non-negative integer variable under global constraints, so that different ships can achieve staggered adjustment of the number of quay cranes in overlapping time periods.

[0014] S7. Solve the integer master problem and output the scheduling result.

[0015] As a preferred option, in the low-carbon collaborative scheduling model for port berths and quay cranes in S1:

[0016] Key decisions include: berthing location, berthing time, actual start time of operations, departure time, and the number of quay cranes used by the vessel at each time.

[0017] The overall objective is to minimize total port costs; total port costs consist of waiting costs, delay costs, overdue penalty costs, carbon tax costs, and carbon trading costs.

[0018] Model constraints include: ships must berth upon arrival at the port; each ship can only select one berth; the same berth can be occupied by at most one ship at the same time; and the total number of port quay cranes used at any given time cannot exceed the preset total. When the vessel is within the processing time range, the number of quay cranes meets the preset lower and upper limits; when the vessel is not within the processing time range, the number of quay cranes is 0; and the cumulative amount of quay crane work completed by each vessel is not less than its workload.

[0019] As a preferred option, in S2, the feasible columns include the vessel number, berth number, berthing time, actual operation start time, departure time, quay crane allocation scheme, column cost, and corresponding carbon emissions; S2 includes generating a virtual column for each vessel to ensure the initial feasibility of the constrained main problem; the virtual column does not occupy berth and quay crane resources, and its target value is set to be higher than the value of the real column.

[0020] As a preferred option, in S3, the linear relaxation form of the restricted master problem is expressed as:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] in, For ships Current feasible column pool, Indicates a ship Select column , Indicates a ship The column The corresponding column cost, Indicates the carbon trading price, This indicates the portion exceeding the carbon quota. Represents column Is it in time? berth occupied ; Represents column In time Number of quay cranes used Represents column The corresponding carbon emissions, Indicates the carbon quota;

[0028] After solving the constrained principal problem, the dual variables are obtained, including: the dual variables corresponding to the ship column selection constraint, the dual variables corresponding to the berth occupancy constraint, and the dual variables corresponding to the quay crane capacity constraint.

[0029] As a preferred option, in S4, the task of the pricing sub-problem is to address the ship... Find the column with the minimum test number among all potential feasible columns; candidate column The test number is expressed as:

[0030]

[0031] in, For the purpose of listing costs, Assignment plan for quay cranes, Indicates a ship candidate columns The test number, This represents the dual variable corresponding to the carbon emission constraint. To list the corresponding carbon emissions, For each ship column, select the dual variable corresponding to the constraint. For the dual variable corresponding to the berth occupancy constraint, These are the dual variables corresponding to the capacity constraints of the quay crane;

[0032] As a preferred option, in S4, solving the pricing subproblem includes:

[0033] For each vessel, candidate berths, berthing times, and departure times are enumerated sequentially. For each candidate scheme, it is determined whether it meets the constraints of arrival time, operation time window, upper and lower limits of quay crane quantity, and loading / unloading volume. For candidate schemes that meet the constraints, a greedy allocation method is used to determine the quay crane allocation scheme: First, the unit quay crane cost for each time step within the processed time range is calculated. The unit quay crane cost is jointly determined by the dual variable corresponding to the quay crane capacity constraint, the quay crane carbon tax cost, and the carbon trading cost. The number of quay cranes in each time step is initialized to the lower limit of the vessel's quay crane quantity, and the remaining operation volume is calculated. If the basic allocation has met the workload, the quay crane allocation scheme is obtained directly; otherwise, quay cranes are added in order of increasing unit quay crane cost, up to the upper limit of the vessel's quay crane quantity in each time step, until the loading / unloading volume is met. If the maximum capacity of the operation window still cannot meet the requirements, the candidate scheme is not feasible.

[0034] When the test number of a candidate column is less than the preset negative threshold, the candidate column is added to the candidate set as an improved column; each ship can retain several improved columns in ascending order of test number.

[0035] As a preferred option, S4 also includes a LightGBM helper column filtering step:

[0036] The LightGBM machine learning model is introduced, which takes the feature vector of a candidate column as input and outputs the probability that the candidate column is accepted. The feature vector includes the test number, normalized test number, column cost, scheduling duration, total quay crane usage, maximum quay crane usage, minimum quay crane usage, average quay crane usage, waiting time, delay time, whether it is overdue, whether it is a shore power berth, ship type, ship size, current iteration number, constraint main problem objective value, current number of existing columns of the ship, and normalized carbon emissions.

[0037] If the probability of a candidate column being accepted is higher than a preset threshold, then the candidate column is accepted and added to the column pool; otherwise, it is not added for the time being.

[0038] As a preferred option, the LightGBM auxiliary column filtering process also includes a four-fold protection mechanism:

[0039] Preheating mechanism: No machine learning screening is performed in the first few preheating iterations; all candidate columns that meet the test number condition can be added to the column pool.

[0040] Full pricing supplement mechanism: When no improved columns are added to the column pool after machine learning screening, the screening results are not adopted. The full test number calculation is performed on the candidate solutions. If a new column with a test number less than the preset negative threshold is found, it is added to the column pool.

[0041] Full enumeration verification mechanism: After the column generation termination condition is met, full enumeration verification is performed on all candidate schemes. If a column with a test number less than the preset negative threshold is found, it is added to the column pool and the iteration continues; if no such column is found, the column generation is confirmed to have converged.

[0042] Degeneracy and rollback mechanism: When the LightGBM machine learning model is unavailable, the algorithm automatically degenerates into a baseline column generation method without screening, and all candidate columns that meet the test number condition are directly added to the column pool.

[0043] As a preferred embodiment, S6 includes:

[0044] set up Indicates a ship Select option column , Indicates a ship In time The number of quay cranes used; the integer main problem includes constraints on single-ship selection, berth occupancy, upper and lower limits of quay cranes, loading and unloading demand, total number of quay cranes, and carbon trading cost calculation. Variable values ​​include binary variables and non-negative integer variables; the integer main problem takes the following form:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] in, List of schemes China Shipbuilding The costs of waiting, delays, overdue payments, and carbon tax. This indicates the implementation of a carbon trading policy. Indicates the carbon trading price, Represents column Is it in time? berth occupied , Indicates a ship Total workload; List of selected schemes Decision, list China Shipbuilding In time The value is 1 if it falls within the processing time range, and 0 otherwise. This represents the carbon tax cost generated per unit time by the quay crane; This indicates the carbon emissions of ships.

[0055] Secondly, a green port core resource collaborative scheduling system based on machine learning-column generation algorithms includes:

[0056] The parameter acquisition module is used to acquire port system parameters;

[0057] The model building module is used to build a low-carbon collaborative scheduling model for port berths and quay cranes.

[0058] The column generation module is used to generate initial feasible columns and initialize the column pool. The feasible columns represent a feasible scheduling scheme for a ship. The module establishes and solves the restricted master problem and obtains the dual variables. Based on the dual variables, the module solves the pricing subproblem and generates improved columns. After adding the improved columns to the column pool, the module solves the restricted master problem again and updates the dual variables. If no column with a test number less than a preset negative threshold is found in the pricing subproblems of all ships, the column generation is considered to have converged.

[0059] The integer optimization module is used to expand the column pool and construct the integer master problem, supplementing each ship with feasible combinations of berth, berthing time and departure time; the supplemented feasible solutions are added to the optional set of the master problem; in the integer master problem, the quay crane allocation scheme pre-generated in the column generation stage is not fixed, and the number of quay cranes used by each ship at each time step is used as a non-negative integer variable to re-optimize under global constraints, so that different ships can achieve staggered adjustment of the number of quay cranes in overlapping time periods;

[0060] The results output module is used to solve the integer master problem and output the scheduling results.

[0061] The green port core resource collaborative scheduling system based on machine learning-column generation algorithm is used to implement the green port core resource collaborative scheduling method and steps based on machine learning-column generation algorithm as described in the first aspect.

[0062] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0063] (1) This invention combines column generation decomposition, quay crane time allocation re-optimization, LightGBM-assisted column screening, and dual policy modeling of carbon tax and carbon trading to form a combinatorial optimization framework for the coordinated scheduling of core resources of green ports. Specifically, column generation decomposition encapsulates the feasible scheduling schemes of each ship into columns and retains cross-ship shared resource constraints such as berth occupancy and quay crane capacity in the constrained master problem, thereby reducing the solution scale of the berth-quay crane joint scheduling model; on this basis, the pricing subproblem generates improved columns with negative test numbers based on the dual variables returned by the constrained master problem, so that the newly added candidate columns can supplement the current resource bottlenecks instead of blindly enumerating all schemes.

[0064] (2) After the column generation converges, this invention does not directly fix the pre-generated quay crane allocation scheme within the column, but instead resets the quay crane time allocation variable during the integer master problem stage. This setting works in synergy with the column generation stage: the column generation stage is mainly responsible for screening candidate scheduling schemes with better berths, berthing times, operation start times, and departure times; the integer master problem stage then re-optimizes the allocation of quay cranes in each time step based on these candidate scheduling schemes, enabling quay crane staggered scheduling between different vessels. Therefore, this invention retains the advantage of column generation in reducing problem size while avoiding the problem that fixed quay crane allocation schemes cannot cover cross-vessel staggered scheduling patterns.

[0065] (3) This invention introduces the LightGBM model to assist in the screening of candidate columns, and uses it in conjunction with the column generation process through preheating, full-quantity pricing supplementation, and full enumeration verification mechanisms. The LightGBM model is used to reduce obviously invalid candidate columns from entering the column pool, thereby reducing the size of the limiting main problem; the preheating mechanism is used to avoid false screening due to insufficient early samples; the full-quantity pricing supplementation and full enumeration verification mechanisms are used to correct for possible omissions of valid columns in the screening results. The above mechanisms work together to enable machine learning screening to improve the efficiency of column generation, while avoiding the destruction of the validity and stability of the column generation results due to false screening.

[0066] (4) This invention integrates carbon tax costs and carbon trading costs into the scheduling objective, and works in conjunction with the constraints of berth, quay crane, and ship time windows. The carbon cost item affects the calculation of candidate column costs and test numbers, enabling the pricing subproblem to consider both operating costs and carbon emission costs when generating improved columns; the integer main problem further re-coordinates quay crane resources under the conditions of satisfying berth occupancy, quay crane capacity, and loading / unloading requirements. Thus, this invention can improve solution efficiency while forming a collaborative scheduling scheme that takes into account port operation efficiency, quay crane resource utilization, and low-carbon emission requirements. Attached Figure Description

[0067] Figure 1 This is a flowchart of the method provided in Embodiment 1 of the present invention.

[0068] Figure 2 This is a diagram showing the convergence process of column generation upper and lower bounds obtained from the calculation of 30 ship cases in Embodiment 1 of the present invention. Detailed Implementation

[0069] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention.

[0070] To achieve the above objectives, this invention first establishes a mathematical model for the low-carbon collaborative scheduling of berths and quay cranes. Then, using the Dantzig-Wolfe decomposition approach, it encapsulates the internal constraints of a single vessel into columns, while retaining the cross-vessel coupling constraints such as those between berths and quay cranes within the main problem. After linear relaxation convergence, this invention does not directly fix the quay crane allocation scheme in the columns, but instead resets the quay crane usage variables in each time period within the main problem, thereby achieving global coordination of quay crane resources. Furthermore, this invention can utilize machine learning to screen candidate columns, but balances column screening efficiency and result validity through preheating, full-quantity pricing supplementation, and full enumeration verification mechanisms.

[0071] Example 1:

[0072] Combination Figure 1As shown, this invention provides a collaborative scheduling method for core resources of green ports based on machine learning-column generation algorithm, including the following steps: parameter input, model construction, column generation iteration, LightGBM-assisted screening and verification, main problem solving, and result output.

[0073] Step S1: Obtain port system parameters; construct a low-carbon collaborative scheduling model for port berths and quay cranes;

[0074] Step S11: Obtain port system parameters

[0075] In this embodiment, the port system parameters acquired include the vessel set, berth set, time set, total number of available quay cranes Q, vessel arrival time, loading and unloading volume, expected departure time, latest departure time, lower limit and upper limit of permitted quay cranes. For each berth, a shore power capacity flag is acquired, indicating whether the berth has shore power capacity; simultaneously, the test time for vessels connecting to shore power, carbon tax rate, carbon allowance, carbon trading price, and various carbon emission factors are acquired.

[0076] Step S12: Construct a low-carbon collaborative scheduling model for port berths and quay cranes. The main decisions in the model include: berthing location, berthing time, actual operation start time, departure time, and the number of quay cranes used by the vessel at each time. For shore-powered vessels, when berthed at a berth with shore power capability, the actual operation start time needs to be increased from the berthing time to include the testing time for connecting the vessel to shore power; otherwise, the actual operation start time is equal to the berthing time.

[0077] The overall objective is to minimize the total port cost. Its form can be expressed as:

[0078]

[0079] Among them, the total port cost Due to waiting costs Delay costs Overdue penalty costs Carbon tax costs Carbon trading cost composition ; and These indicate whether a carbon tax policy and a carbon trading policy will be implemented. =1 indicates that a carbon tax policy has been implemented. =1 indicates that the carbon trading policy is enabled. Specifically,

[0080]

[0081]

[0082]

[0083] in, , and These are the waiting cost coefficient, the delay cost coefficient, and the overdue penalty cost coefficient, respectively. Ship number, For ships Arrival time For berthing time, For departure time, For the expected departure time, The latest departure time. This is an indicator function.

[0084] Carbon emissions from ships are determined by ship type and port stay duration. For conventional ships, emissions per unit time during port stay can be calculated by multiplying the fuel consumption rate by the fuel emission factor. For shore power ships, emissions during shore power service periods are calculated using the electricity emission factor. For LNG carriers, emissions are calculated using the LNG consumption rate and the LNG emission factor. Carbon emissions from quay cranes are determined by the quay crane's electricity consumption per unit time, the quay crane's electricity emission factor, and the number of quay cranes used in each time period, and can be expressed as:

[0085]

[0086] in, Carbon emissions generated from quay crane operations. This represents the carbon emission coefficient per unit time for a single quay crane. For ships In time The number of quay cranes used. Total carbon emissions are calculated by adding the carbon emissions from ships and the carbon emissions from quay cranes. If a carbon tax policy is implemented, the carbon tax cost is calculated based on the total carbon emissions and the carbon tax rate; if a carbon trading policy is implemented, the carbon trading cost is calculated based on the difference between the total carbon emissions and the carbon allowance: when the total carbon emissions are higher than the carbon allowance, the carbon trading cost is positive; when the total carbon emissions are lower than the carbon allowance, the carbon trading cost is negative, representing the revenue from the remaining carbon allowance.

[0087] Model constraints include the following categories. First, the ship must berth upon arrival at the port, i.e. Second, each vessel can only choose one berth. Third, at most one vessel can occupy the same berth at any given time; that is, for any berth... and time The number of vessels occupying the berth at any given time shall not exceed one. Fourth, the total number of port quay cranes used at any given time shall not exceed [a certain limit]. ,Right now Fifth, the vessel is within the processing timeframe. , When the number of quay cranes meets the requirements... ( and These are the lower and upper limits for the use of quay cranes, respectively; when not within the processing time range... Sixth, the cumulative amount of quay crane work completed by each vessel shall not be less than its total workload, i.e. .

[0088] Step S2: Generate initial rowable columns and initialize the column pool.

[0089] In this embodiment, a column represents a feasible scheduling scheme for a ship. Column It can be represented as:

[0090]

[0091] in, Number the ship Berth numbering For berthing time, This is the actual start time of the operation. For departure time, This is a quay crane allocation scheme used to calculate the test number during the column generation phase. For the purpose of listing costs, The corresponding carbon emissions are listed.

[0092] When generating the initial feasible sequence, first determine the berthing time candidates based on the ship's arrival time, and then determine the departure time candidates based on the loading and unloading volume and the upper and lower limits of the quay cranes; then determine whether the berth has shore power capability and whether the ship is a shore power ship to determine the actual start time of the operation; finally, construct a quay crane allocation scheme that meets the requirements of the upper and lower limits of the quay cranes and the volume of operations for the time range to be processed, and calculate the waiting cost, delay cost, overdue penalty cost and carbon emission cost.

[0093] To ensure the feasibility of the constrained master problem in the initial stage of column generation, a high-cost virtual column can be set for each vessel. This virtual column does not occupy berth or quay crane resources, and its target value is set to be significantly higher than the column cost of the real columns. Specifically, this target value should be significantly higher than the sum of the waiting costs, delay costs, overdue penalty costs, and carbon emission costs that the real columns may incur. This ensures that the virtual column is only used to maintain the initial feasibility of the constrained master problem and will not be preferentially selected when a real feasible column exists. When there are enough real columns to form a feasible solution, the virtual column will not be ultimately selected; when the initial columns are insufficient, the virtual column is used to maintain the solvability of the linear relaxation of the master problem.

[0094] Step S3: Establish and solve the restricted master problem

[0095] In this embodiment, let For ships Current column pool, Indicates a ship Select column The constrained principal problem aims to select a feasible column for each vessel in the current column pool and minimize the total cost corresponding to the current column pool while satisfying constraints on berth occupancy, quay crane capacity, and carbon quotas. Here, we first solve its linear relaxation form, which temporarily allows column selection variables. The values ​​are continuously taken in the range [0,1] to obtain the dual variables needed for subsequent pricing subproblems. The linear relaxation form of the restricted master problem can be expressed as:

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] in, Indicates a ship The column The corresponding column cost, Indicates the carbon trading price, This represents the portion exceeding the carbon quota (a non-negative slack variable). Represents column Is it in time? berth occupied ; Represents column In time Number of quay cranes used. Represents column The corresponding carbon emissions, This indicates the carbon quota.

[0103] After solving the restricted master problem, the dual variables are obtained. The linear relaxation model of the restricted master problem under the current column pool is regarded as a linear programming problem. According to the duality theory of linear programming, each type of constraint in the original problem corresponds to a dual variable. After obtaining the optimal solution of the linear relaxation model, the linear programming solver simultaneously provides the dual multipliers of each constraint under the optimal basis, that is, the marginal change in the optimal value of the objective function when the right-hand side of the constraint changes by a unit. Therefore, in this invention, the dual value corresponding to the selection constraint of each ship column is denoted as... The dual value corresponding to the berth-time occupancy constraint is denoted as The dual value corresponding to the capacity constraint of the quay crane is denoted as The dual variables mentioned above represent the marginal impacts of the ship's requirement to select a column, berth-time resource occupancy, and quay crane capacity limitations on the objective value of the current limiting main problem, and are used to calculate the test numbers for candidate columns in subsequent pricing subproblems. Carbon trading costs are included in the test number calculation as part of the column costs.

[0104] Step S4: Solve the pricing subproblem and generate the improved column.

[0105] In this embodiment, each ship corresponds to a pricing subproblem. The task of the pricing subproblem is to price the ships... Find the column with the minimum test number among all potential feasible columns. Candidate column The test number can be expressed as:

[0106]

[0107] in, Indicates a ship candidate columns The test number, This represents the dual variable corresponding to the carbon emission constraint. Since quay crane capacity constraints and berth occupancy constraints are usually in the form of less than or equal to, their dual variable can be understood as the resource scarcity level in the minimization problem; carbon emissions are included in the column cost through carbon tax costs and carbon trading costs. Here, "resource penalty" specifically refers to the berth occupancy dual term and quay crane capacity dual term superimposed in the test number when the candidate column occupies berth and quay crane resources. Therefore, the above formula can also be equivalently understood as: the original cost of the candidate column minus the dual contribution corresponding to the ship column selection constraint, plus the dual cost brought about by occupying scarce quay cranes and scarce berths.

[0108] In the specific solution, for each ship Enumerate candidate berths in sequence berthing time and departure time For each candidate solution, first determine whether it meets the requirements for arrival time, processing time range, testing time for ship connection to shore power, and maximum quay crane handling capacity. If the candidate solution is feasible, calculate its waiting cost, delay cost, overdue penalty cost, ship carbon emissions, and berth occupancy dual terms.

[0109] For the quay crane allocation schemes in the candidate schemes, a greedy allocation method is adopted. First, the unit quay crane cost for each time period within the processing time range is calculated. This cost is jointly formed by the quay crane capacity duality, the quay crane carbon tax cost, and the carbon trading cost. Then, the number of quay cranes at each time period is initialized to the lower limit of the ship-to-quay crane capacity. Next, the remaining workload is calculated. If the basic allocation already meets the workload, the quay crane allocation for the candidate scheme is obtained directly; otherwise, quay cranes are added in order of increasing unit quay crane cost, up to the upper limit of the ship-to-quay crane capacity at each time period, until the loading and unloading workload is met. If the maximum capacity of the operation window still cannot meet the workload, the candidate scheme is not feasible.

[0110] When the test number of a candidate column If the number of positive columns is less than a preset negative threshold, the candidate column is added to the candidate set as an improved column. Each ship can retain a number of improved columns in ascending order of the number of tests to reduce the expansion of the main problem caused by too many columns added in a single round.

[0111] In an optional embodiment, to reduce the number of invalid candidate columns entering the main problem, this invention introduces a LightGBM auxiliary column filtering mechanism. This mechanism does not change the mathematical model or the main problem, but rather, after generating candidate columns from the pricing subproblem, it performs a probabilistic judgment on whether a candidate column is worth adding to the column pool.

[0112] Candidate column features include test number, normalized test number, column cost, scheduling duration, total quay crane usage, maximum quay crane usage, minimum quay crane usage, average quay crane usage, waiting time, delay time, whether overdue, whether it is a shore power berth, vessel type, vessel size, current iteration number, constraint on the main problem objective value, current number of existing vessel columns, vessel column selection constraint duality, and normalized carbon emissions. Training labels can be determined based on whether candidate columns appear in integer solutions or linear relaxation bases.

[0113] The LightGBM candidate column selection model outputs the probability of a candidate column being accepted. If the probability is higher than a threshold, the candidate column is accepted; if the probability is lower than the threshold, it is not added to the main problem. The threshold can be automatically determined based on the recall requirements on the training set, so that the model minimizes the omission of potentially valid columns.

[0114] To reduce the impact of machine learning misjudgments on column generation results, this embodiment sets up the following protection mechanisms: First, no screening is performed in the first few warm-up rounds, and all candidate columns can be added; Second, when no improved columns are added after screening, a full pricing supplement mechanism is triggered, that is, the screening results are temporarily not used, and a complete test number calculation is performed on the candidate schemes. If a new column with a test number less than a preset negative threshold is found, it is added to the column pool; Third, after column generation is completed, a full enumeration verification is performed. If a column with a negative test number is still found, it is added to the column pool and the iteration continues; Fourth, when the machine learning model is unavailable, the algorithm automatically degenerates into the baseline column generation method without screening.

[0115] Step S5: Convergence Determination of Column Generation

[0116] In this embodiment, after adding the improved column obtained in step S4 to the column pool, the restricted master problem is solved again and the dual variables are updated. If at least one ship generates a new negative test number sequence, the next round of column generation continues; if no column with a test number less than a preset negative threshold is found in the pricing subproblems of all ships, it indicates that the linear relaxation of the current restricted master problem has satisfied the column generation convergence condition.

[0117] This convergence condition comes from the duality theory of linear programming: when there are no negative test numbers for any of the potential columns, the linear relaxation solution of the current constrained master problem is the optimal solution of the linear relaxation problem corresponding to the complete set of columns.

[0118] Step S6: Expand the column pool and build the main problem

[0119] After column generation converges, linear relaxation optimality does not necessarily mean that the current column pool contains the scheduling scheme required for the integer solution. Therefore, this embodiment expands the column pool before entering the integer solution stage. The column pool expansion process supplements each ship with feasible combinations of berths, berthing times, and departure times, and adds the supplemented feasible schemes to the optional set of the main problem.

[0120] The integer master problem is used to determine the final vessel scheduling scheme from the expanded feasible set and to re-optimize the number of quay cranes used by each vessel in each time step. The scheme column determines the vessel's berth, berthing time, actual operation start time, and departure time; the quay crane time usage variable represents the actual number of quay cranes allocated to each vessel in each time step. Quay crane upper and lower limit constraints are implemented by associating the quay crane time usage variable with the time range indicator variable corresponding to the selected scheme column: when a vessel in the selected scheme column is within the processing time range in a certain time step, the number of quay cranes for that vessel in that time step must meet the lower and upper limits of the quay crane constraints; when it is not within the processing time range, the number of quay cranes is zero. Through the above settings, the integer master problem no longer fixes the quay crane allocation scheme pre-generated in the column generation stage, but instead, while satisfying the requirements of berth occupancy, quay crane capacity, and loading / unloading operations, it globally coordinates and staggers the allocation of quay crane resources among different vessels. Let... Indicates a ship Select option column , Indicates a ship In time The number of quay cranes used; before listing the model, it should be noted that the main problem includes constraints such as single-ship selection, berth occupancy, upper and lower limits of quay cranes, loading and unloading demand, total number of quay cranes, and carbon trading cost calculation. The variable values ​​include binary variables and non-negative integer variables.

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[0129]

[0130] in, List of schemes China Shipbuilding The costs of waiting, delays, overdue payments, and carbon tax. Indicates a ship Total workload; List of selected schemes Decision, list China Shipbuilding In time The value is 1 if it falls within the processing time range, and 0 otherwise. This represents the carbon tax cost generated per unit time by the quay crane; This indicates the carbon emissions of ships.

[0131] The main problem aims to preserve the global coordination capability of quay crane resources. The quay crane allocation scheme in the column generation phase is primarily used to calculate the check number and estimate column costs in the pricing subproblem. The integer solution phase redefines the quay crane time allocation, allowing different vessels to stagger quay crane usage during overlapping periods. For example, if one vessel reduces quay crane usage at certain times, while another increases it during the same time, both vessels can still jointly meet the total quay crane capacity and their respective loading / unloading operation requirements.

[0132] Step S7: Solve the main problem and output the scheduling results.

[0133] After solving the main problem, the system outputs the berth number assigned to each vessel, berthing time, actual operation start time, departure time, and the number of quay cranes at each time within the processing time range. It also outputs the total target cost, waiting cost, delay cost, overdue penalty cost, carbon emissions generated by the vessel, carbon emissions generated by the quay cranes, total carbon emissions, excess carbon allowance, number of column generation iterations, and column pool size.

[0134] Example 2:

[0135] In a specific example, the scheduling cycle is 48 time steps. The port includes several berths and a certain number of quay cranes. Vessels are classified as small, medium, and large. Small vessels can be allocated 1 to 3 quay cranes, medium vessels 2 to 4, and large vessels 3 to 5. Vessel types include conventional ships, shore-powered ships, and LNG carriers. Carbon policy parameters include carbon tax rates, carbon quotas, carbon trading prices, quay crane power emission factors, conventional ship fuel emission factors, shore-powered ship power emission factors, and LNG emission factors.

[0136] After inputting the above data into steps S1 to S7, the system first generates an initial column for each vessel, and then generates more valid columns by alternating between the constrained main problem and the pricing subproblem. Once the column generation converges, the system supplements candidate solutions for each vessel and solves the main problem to obtain the berth arrangement, berthing and departure times, and quay crane time allocation for each vessel.

[0137] Compared to direct mixed-integer programming, the solution process of this invention utilizes a ship-specific decomposition structure. The main problem retains only cross-ship coupling constraints such as berths, quay cranes, and carbon quotas, while intra-ship decisions are generated by pricing subproblems, thus significantly reducing the scale of each main problem solution. Compared to column-integer feasible methods for fixed quay crane allocation schemes, this invention re-optimizes quay crane usage during integer phases, enabling a more comprehensive expression of quay crane staggered scheduling coordination among multiple ships.

[0138] Example 3:

[0139] In the scenario of low-carbon policy sensitivity analysis, the allocation of ship and port resources can be fixed, while the carbon tax rate, carbon quota, carbon trading price, shore power berth ratio, testing time for ships connecting to shore power, and different energy emission factors can be changed. For each parameter change, steps S1 to S7 are re-executed, recording the total cost, total carbon emissions, and scheduling results for each ship type. This allows for analysis of the impact of low-carbon policy parameters on port scheduling schemes, providing a basis for decision-making regarding shore power berth construction, carbon quota setting, and operating cost control.

[0140] Example 4:

[0141] Based on the technical solution of this invention, the following case scenario illustrates the implementation process of this invention in practical application. The specific application implementation scheme is as follows: the scheduling cycle is 48 time steps, the port has a total of 8 berths and 40 quay cranes, and 30 ships arrive at the port. The carbon policy simultaneously implements carbon tax and carbon trading mechanisms. =1, =1).

[0142] Table 1: Ship-Related Parameters

[0143]

[0144] After inputting the above data into steps S1 to S7, the algorithm performs a total of 5 rounds of column generation iterations. When column generation converges, the column pool size is 1566 columns, which expands to a total of 2116 columns. The final target value is $65014.65. Table 2 shows the main parameters and optimal solution results of this example.

[0145] Table 2: Optimal Results of the Example

[0146]

[0147] As shown in Table 2, there are a total of 30 ships, with total waiting costs of $25,600, total delay costs of $25,600, total overdue costs of $7,200, total carbon tax costs of $2,439.05, carbon trading costs of $4,175.60, ship carbon emissions of 316,926.21 kg, and total carbon emissions of 322,199.90 kg (the sum of ship carbon emissions and quay crane carbon emissions). The total objective function value is $65,014.65.

[0148] Table 3 presents the parameter values ​​in the model. As shown in Table 3, this example simultaneously utilizes carbon tax and carbon trading policies. Regarding emission factors, traditional ships have the highest (3.16 kg / time), shore power ships the lowest (0.54 kg / time), and LNG ships are in the middle (2.75 kg / time). Therefore, the model prioritizes shore power ships and LNG ships using quay cranes, thereby reducing total carbon emissions, provided resources permit. The waiting penalty and delay penalty are both $800 / time, and the overdue penalty is $2400 / time. The model achieves an optimal balance between carbon costs and operating costs.

[0149] Table 3: Parameter values ​​in the model

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[0151] like Figure 2 As shown, the proposed method exhibits clear column generation convergence characteristics in the 30 ship case studies. The solid line in the figure represents the upper bound of the current constrained master problem's objective value formation, while the dashed line represents the dual lower bound estimate obtained based on the convergence trend of the pricing subproblem's test number. The curve below gives the relative gap between the upper and lower bounds and the absolute value of the minimum test number. It can be seen that as column generation iterates, the upper bound gradually decreases from 108682.66, while the lower bound gradually increases, aligning with each other in the 5th iteration. Simultaneously, the absolute value of the minimum test number converges to 0, indicating that the current constrained master problem has met the column generation termination condition. The final integer master problem objective value is $65014.65, close to the reference objective value of $65017.98 in the column generation convergence stage, demonstrating that the proposed method can obtain a stable and convergent berth and quay crane coordinated scheduling scheme while ensuring solution efficiency.

[0152] Example 5:

[0153] A green port core resource collaborative scheduling system based on machine learning-column generation algorithms includes:

[0154] The parameter acquisition module is used to acquire port system parameters;

[0155] The model building module is used to build a low-carbon collaborative scheduling model for port berths and quay cranes.

[0156] The column generation module is used to generate initial feasible columns and initialize the column pool. The feasible columns represent a feasible scheduling scheme for a ship. The module establishes and solves the restricted master problem and obtains the dual variables. Based on the dual variables, the module solves the pricing subproblem and generates improved columns. After adding the improved columns to the column pool, the module solves the restricted master problem again and updates the dual variables. If no column with a test number less than a preset negative threshold is found in the pricing subproblems of all ships, the column generation is considered to have converged.

[0157] The integer optimization module is used to expand the column pool and construct the integer master problem, supplementing each ship with feasible combinations of berth, berthing time and departure time; the supplemented feasible solutions are added to the optional set of the master problem; in the integer master problem, the quay crane allocation scheme pre-generated in the column generation stage is not fixed, and the number of quay cranes used by each ship at each time step is used as a non-negative integer variable to re-optimize under global constraints, so that different ships can achieve staggered adjustment of the number of quay cranes in overlapping time periods;

[0158] The results output module is used to solve the integer master problem and output the scheduling results.

[0159] It should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, or improvements made to the candidate column generation method, pricing sub-problem solving method, main problem and limiting main problem construction method, machine learning model type, carbon emission parameters, cost parameters, and main problem solving settings without departing from the technical concept of the present invention should be included within the protection scope of the present invention.

Claims

1. A collaborative scheduling method for core resources of green ports based on machine learning-column generation algorithm, characterized in that, Includes the following steps: S1. Obtain port system parameters and construct a low-carbon collaborative scheduling model for port berths and quay cranes; S2. Generate the initial rowable columns and initialize the rowable column pool; A feasible column is used to represent a feasible scheduling plan for a ship; S3. Establish and solve the restricted master problem to obtain the dual variables; S4. Solve the pricing subproblem based on dual variables and generate an improved column; the task of the pricing subproblem is to address the pricing issue in shipping... Find the column with the minimum test number among all potential feasible columns; candidate column The test number is expressed as: ； in, For the purpose of listing costs, Assignment plan for quay cranes, Indicates a ship candidate columns The test number, This represents the dual variable corresponding to the carbon emission constraint. To list the corresponding carbon emissions, For each ship column, select the dual variable corresponding to the constraint. For the dual variable corresponding to the berth occupancy constraint, These are the dual variables corresponding to the capacity constraints of the quay crane; Solving the pricing component problem includes: For each vessel, enumerate the candidate berths, berthing times, and departure times in sequence; for each candidate plan, determine whether it meets the constraints of arrival time, operation time window, upper and lower limits of the number of quay cranes, and loading and unloading volume. For candidate schemes that meet the constraints, a greedy allocation method is used to determine the quay crane allocation scheme: First, the unit quay crane cost for each time step within the processing time range is calculated. The unit quay crane cost is jointly determined by the dual variable corresponding to the quay crane capacity constraint, the quay crane carbon tax cost, and the carbon trading cost. The number of quay cranes in each time step is initialized to the lower limit of the ship-to-quay crane limit, and the remaining workload is calculated. If the basic allocation has met the workload, the quay crane allocation scheme is obtained directly. Otherwise, quay cranes are added in order of increasing unit quay crane cost, up to the upper limit of the ship-to-quay crane limit in each time step, until the loading and unloading workload is met. If the maximum capacity of the operation window still cannot meet the requirements, the candidate scheme is not feasible. When the test number of a candidate column is less than a preset negative threshold, the candidate column is added to the candidate set as an improved column; each ship can retain a number of improved columns in ascending order of test number; S4 also includes a LightGBM helper column filtering step: The LightGBM machine learning model is introduced, which takes the feature vector of a candidate column as input and outputs the probability that the candidate column is accepted. The feature vector includes the test number, normalized test number, column cost, scheduling duration, total quay crane usage, maximum quay crane usage, minimum quay crane usage, average quay crane usage, waiting time, delay time, whether it is overdue, whether it is a shore power berth, ship type, ship size, current iteration number, constraint main problem objective value, current number of existing columns of the ship, and normalized carbon emissions. If the probability of a candidate column being accepted is higher than a preset threshold, then the candidate column is accepted and added to the column pool; otherwise, it is not added for the time being. S5. After adding the improved column to the column pool, resolve the restricted master problem and update the dual variables. If no column with a test number less than the preset negative threshold is found in any of the pricing subproblems for all ships, then the column generation is determined to be converged. S6. Expand the column pool and supplement each ship with feasible combinations of berths, berthing times and departure times; add the supplemented feasible solutions to the optional set of the main problem; in the integer main problem, do not fix the quay crane allocation scheme pre-generated in the column generation stage, and re-optimize the number of quay cranes used by each ship at each time step as a non-negative integer variable under global constraints, so that different ships can achieve staggered adjustment of the number of quay cranes in overlapping time periods. S7. Solve the integer master problem and output the scheduling result.

2. The green port core resource collaborative scheduling method based on machine learning-column generation algorithm according to claim 1, characterized in that, In the low-carbon collaborative scheduling model of port berths and quay cranes in S1: Key decisions include: berthing location, berthing time, actual start time of operations, departure time, and the number of quay cranes used by the vessel at each time. The overall objective is to minimize total port costs; total port costs consist of waiting costs, delay costs, overdue penalty costs, carbon tax costs, and carbon trading costs. Model constraints include: ships must berth upon arrival at the port; each ship can only select one berth; the same berth can be occupied by at most one ship at the same time; and the total number of port quay cranes used at any given time cannot exceed the preset total. When the vessel is within the processing time range, the number of quay cranes meets the preset lower and upper limits; when the vessel is not within the processing time range, the number of quay cranes is 0; and the cumulative amount of quay crane work completed by each vessel is not less than its workload.

3. The green port core resource collaborative scheduling method based on machine learning-column generation algorithm according to claim 1, characterized in that, In S2, feasible columns include vessel number, berth number, berthing time, actual operation start time, departure time, quay crane allocation scheme, column cost, and corresponding carbon emissions; S2 includes generating virtual columns for each vessel to ensure the initial feasibility of the constrained main problem; virtual columns do not occupy berth and quay crane resources, and their target values ​​are set higher than the values ​​of real columns.

4. The green port core resource collaborative scheduling method based on machine learning-column generation algorithm according to claim 1, characterized in that, In S3, the linear relaxation form of the restricted principal problem is expressed as: ； ； ； ； ； ； in, For ships Current feasible column pool, Indicates a ship Select column , Indicates a ship The column The corresponding column cost, Indicates the carbon trading price, This indicates the portion exceeding the carbon quota. Represents column Is it in time? berth occupied ; Represents column In time Number of quay cranes used Represents column The corresponding carbon emissions, Indicates the carbon quota; After solving the constrained principal problem, the dual variables are obtained, including: the dual variables corresponding to the ship column selection constraint, the dual variables corresponding to the berth occupancy constraint, and the dual variables corresponding to the quay crane capacity constraint.

5. The green port core resource collaborative scheduling method based on machine learning-column generation algorithm according to claim 1, characterized in that, The LightGBM helper column filtering process also includes four layers of protection: Preheating mechanism: No machine learning screening is performed in the first few preheating iterations; all candidate columns that meet the test number condition can be added to the column pool. Full pricing supplement mechanism: When no improved columns are added to the column pool after machine learning screening, the screening results are not adopted. The full test number calculation is performed on the candidate solutions. If a new column with a test number less than the preset negative threshold is found, it is added to the column pool. Full enumeration verification mechanism: After the column generation termination condition is met, full enumeration verification is performed on all candidate schemes. If a column with a test number less than the preset negative threshold is found, it is added to the column pool and the iteration continues; if no such column is found, the column generation is confirmed to have converged. Degeneracy and rollback mechanism: When the LightGBM machine learning model is unavailable, the algorithm automatically degenerates into a baseline column generation method without screening, and all candidate columns that meet the test number condition are directly added to the column pool.

6. The green port core resource collaborative scheduling method based on machine learning-column generation algorithm according to claim 1, characterized in that, S6 include: set up Indicates a ship Select option column , Indicates a ship In time The number of quay cranes used; the integer main problem includes constraints on single-ship selection, berth occupancy, upper and lower limits of quay cranes, loading and unloading demand, total number of quay cranes, and carbon trading cost calculation. Variable values ​​include binary variables and non-negative integer variables; the integer main problem takes the following form: ； ； ； ； ； ； ； ； ； in, List of schemes China Shipbuilding The costs of waiting, delays, overdue payments, and carbon tax. This indicates the implementation of a carbon trading policy. Indicates the carbon trading price, Represents column Is it in time? berth occupied , Indicates a ship Total workload; List of selected schemes Decision, list China Shipbuilding In time The value is 1 if it falls within the processing time range, and 0 otherwise. This represents the carbon tax cost generated per unit time by the quay crane; This indicates the carbon emissions of ships.

7. A green port core resource collaborative scheduling system based on machine learning-column generation algorithm, characterized in that, include: The parameter acquisition module is used to acquire port system parameters; The model building module is used to build a low-carbon collaborative scheduling model for port berths and quay cranes. The column generation module is used to generate initial rowable columns and initialize the column pool. The feasible column is used to represent a feasible scheduling scheme for a ship; the restricted master problem is established and solved to obtain the dual variables; the pricing subproblem is solved based on the dual variables and an improved column is generated; the improved column is added to the column pool and the restricted master problem is solved again and the dual variables are updated. If no column with a test number less than a preset negative threshold is found in the pricing subproblem of all ships, the column generation is considered converged. The task of pricing sub-problems is in ships Find the column with the minimum test number among all potential feasible columns; candidate column The test number is expressed as: ； in, For the purpose of listing costs, Assignment plan for quay cranes, Indicates a ship candidate columns The test number, This represents the dual variable corresponding to the carbon emission constraint. To list the corresponding carbon emissions, For each ship column, select the dual variable corresponding to the constraint. For the dual variable corresponding to the berth occupancy constraint, These are the dual variables corresponding to the capacity constraints of the quay crane; Solving the pricing component problem includes: For each vessel, enumerate the candidate berths, berthing times, and departure times in sequence; for each candidate plan, determine whether it meets the constraints of arrival time, operation time window, upper and lower limits of the number of quay cranes, and loading and unloading volume. For candidate schemes that meet the constraints, a greedy allocation method is used to determine the quay crane allocation scheme: First, the unit quay crane cost for each time step within the processing time range is calculated. The unit quay crane cost is jointly determined by the dual variable corresponding to the quay crane capacity constraint, the quay crane carbon tax cost, and the carbon trading cost. The number of quay cranes in each time step is initialized to the lower limit of the ship-to-quay crane limit, and the remaining workload is calculated. If the basic allocation has met the workload, the quay crane allocation scheme is obtained directly. Otherwise, quay cranes are added in order of increasing unit quay crane cost, up to the upper limit of the ship-to-quay crane limit in each time step, until the loading and unloading workload is met. If the maximum capacity of the operation window still cannot meet the requirements, the candidate scheme is not feasible. When the test number of a candidate column is less than a preset negative threshold, the candidate column is added to the candidate set as an improved column; each ship can retain a number of improved columns in ascending order of test number; It also includes the LightGBM helper column filtering step: The LightGBM machine learning model is introduced, which takes the feature vector of a candidate column as input and outputs the probability that the candidate column is accepted. The feature vector includes the test number, normalized test number, column cost, scheduling duration, total quay crane usage, maximum quay crane usage, minimum quay crane usage, average quay crane usage, waiting time, delay time, whether it is overdue, whether it is a shore power berth, ship type, ship size, current iteration number, constraint main problem objective value, current number of existing columns of the ship, and normalized carbon emissions. If the probability of a candidate column being accepted is higher than a preset threshold, then the candidate column is accepted and added to the column pool; otherwise, it is not added for the time being. The integer optimization module is used to expand the column pool and construct the integer master problem, supplementing each ship with feasible combinations of berth, berthing time and departure time; the supplemented feasible solutions are added to the optional set of the master problem; in the integer master problem, the quay crane allocation scheme pre-generated in the column generation stage is not fixed, and the number of quay cranes used by each ship at each time step is used as a non-negative integer variable to re-optimize under global constraints, so that different ships can achieve staggered adjustment of the number of quay cranes in overlapping time periods; The results output module is used to solve the integer master problem and output the scheduling results. The green port core resource collaborative scheduling system based on machine learning-column generation algorithm is used to implement the green port core resource collaborative scheduling method and steps based on machine learning-column generation algorithm as described in claim 1.

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