A robust optimization method for ship scheduling considering uncertainty of port arrival and departure times

Abstract

The application provides a ship scheduling robust optimization method considering the uncertainty of port arrival and departure time. The method comprises the following steps: constructing the uncertainty set of ship port arrival and departure time to realize the accurate description of the robustness of the scheduling scheme; establishing a ship scheduling robust optimization model considering the uncertainty of port arrival and departure time; designing a heuristic algorithm MAVNS based on the memetic algorithm MA and the variable neighborhood search algorithm VNS, and solving the robust optimization model by using the MAVNS to obtain a robust scheduling optimization scheme. The application greatly enriches the current research on uncertain ship scheduling optimization, can provide reliable auxiliary decision for the port department to effectively deal with the fluctuation of ship port arrival and departure time, and the obtained optimization scheduling result has good robustness and economy, and is easy to popularize and apply to related fields.

Description

Technical Field

[0001] This invention relates to the field of ship scheduling technology, and more particularly to a robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times. Background Technology

[0002] With the rapid development of economic globalization, trade liberalization, and green transportation, shipping, as the most internationalized industry, undertakes nearly 90% of world trade, which undoubtedly puts enormous pressure on port and waterway infrastructure. Ship arrival and departure scheduling is one of the most important operational stages in a port, fully utilizing existing resources such as waterways, berths, and anchorages to generate optimal ship traffic scheduling plans, playing a crucial role in waterway navigation efficiency. A key assumption in ship scheduling problems is that all input parameters are deterministic. In reality, these parameters are subject to significant uncertainty due to factors such as severe weather and equipment damage. Ignoring these uncertainties may render the original scheduling plan unreasonable or even infeasible. Therefore, it is essential to consider these uncertainties in advance in ship scheduling problems. This invention primarily focuses on the uncertainty of arrival and departure times in the study of ship scheduling problems.

[0003] Current research on ship scheduling optimization is limited to deterministic environments. Robust optimization problems under uncertain conditions are mostly concentrated in areas such as workshop scheduling, vehicle allocation or route planning, surgical scheduling, flight scheduling, and shipping. Moreover, research on uncertain robust optimization problems in the shipping field mainly focuses on berth allocation or joint scheduling optimization of berth allocation and cranes. There is relatively little research on ship scheduling optimization problems under uncertain conditions. Summary of the Invention

[0004] To address the issue of neglecting the uncertainty of arrival and departure times in the aforementioned ship scheduling optimization problem, this invention proposes a robust optimization method for ship scheduling that takes into account the uncertainty of arrival and departure times. First, a budget uncertainty set is constructed to characterize the uncertainty of arrival and departure times. This ensures the robustness of the obtained scheduling optimization results; that is, as long as the parameters are perturbed within the given uncertainty set, the obtained solutions are feasible. Furthermore, it fills a research gap in ship scheduling optimization problems with uncertainty. Second, a robust optimization model for ship scheduling under the uncertainty of arrival and departure times is established, fully considering the volatility of arrival and departure times, ship navigation continuity, safety, and other constraints, so that the final optimization result satisfies the condition of minimizing the total waiting time under the uncertainty of ship arrival and departure times. Finally, a heuristic algorithm combining a meme algorithm and a variable neighborhood search algorithm is designed for solving the problem.

[0005] The technical means employed in this invention are as follows:

[0006] A robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times includes:

[0007] Construct a set of uncertainties regarding ship arrival and departure times;

[0008] Establish a robust optimization model for ship scheduling that comprehensively considers the uncertainties of port and departure times;

[0009] Based on the meme algorithm MA and the variable neighborhood search algorithm VNS, a heuristic algorithm MAVNS is designed, and the robust optimization model is solved using MAVNS to obtain a robust scheduling optimization scheme.

[0010] Furthermore, the aforementioned set of uncertainties regarding ship arrival and departure times specifically includes:

[0011] Considering the significant fluctuations in the arrival and departure times of vessel i during actual port operations, a budget uncertainty set U is introduced to characterize the uncertainty of arrival and departure times. This set can be represented as:

[0012]

[0013] in, This represents the value when ship i is not delayed; The i ( The i ≥0) indicates deviation The maximum value of ζ; i This represents the control Ta that varies within the uncertain set U. i The uncertainty level parameter of the fluctuation range; Γ represents the adjustable parameter of the conservatism of the control model, and Γ = 0 means that the uncertainty of the arrival and departure times of ships is not considered.

[0014] Furthermore, the establishment of a robust optimization model for ship scheduling that comprehensively considers the uncertainties of port and departure times specifically includes:

[0015] A deterministic ship scheduling optimization model is established with the objective function of minimizing the total ship waiting time, and it is represented by MILP-D.

[0016] The deterministic ship scheduling optimization model is transformed into a robust ship scheduling optimization model that comprehensively considers the uncertainty of port and departure times.

[0017] Furthermore, the establishment of a deterministic ship scheduling optimization model with the objective function of minimizing total ship waiting time, and represented by MILP-D, specifically includes:

[0018] The objective function is defined as follows:

[0019]

[0020] Set the constraints as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] In this formula, formula (1) indicates that the objective function is to minimize the total waiting time of ships; formula (2) ensures that ships entering and leaving the port adjust their scheduling application time according to the tidal window, and at the same time ensures that the time for ships entering the port to sail to the channel exit is less than the end time of the tidal window; formula (3) ensures that the start scheduling time is greater than or equal to the time for requesting scheduling or re-requesting scheduling; formulas (4), (5), and (6) ensure the navigation continuity of ships entering the port, and at the same time determine the time for ships to sail to the channel entrance, the channel exit, and the berth; formulas (7) and (8) ensure the navigation continuity of ships leaving the port, and at the same time determine the time for ships to sail to the channel exit and the channel entrance; formulas (9) and (10) ensure that ships in the same direction should maintain a certain safe distance in the same direction; formulas (11) and (12) ensure that ships in opposite directions should maintain a certain safe distance in opposite directions; formulas (13), (14), and (15) represent the binary decision variable value constraints; in the above formulas, V represents the ship set; V in Indicates the assembly of ships entering the port; V out Indicates the assembly of departing vessels; d1 id1 represents the distance from the anchorage to the channel entrance; d2 represents the distance from the channel entrance to the channel exit, which is the distance within the channel; d3 represents the distance from the anchorage to the channel entrance. i Indicates the distance of vessel i from the channel exit to the berth; v i T represents the average speed of ship i; si Indicates the start time when vessel i needs to enter or leave the port with the tide; T ei This indicates the end time at which vessel i needs to enter or leave the port with the tide; Ta i c1 represents the time when vessel i requests scheduling, i.e., the estimated arrival and departure times of the vessel; c2 represents the safe distance between vessels traveling in the same direction at the channel entrance or exit; c3 represents the safe distance between vessels traveling in opposite directions at the channel entrance or exit; M represents a large positive integer; Ts i Indicates the start time of scheduling for ship i; R ij Representing binary variables, for inbound ships, if ship j is scheduled after ship i, it is 1; otherwise, it is 0. ij Representing binary variables, for departing ships, the value is 1 if ship j is scheduled after ship i, and 0 otherwise; IO i This represents a binary variable; it is 1 when ship i enters the port and 0 when it leaves the port.

[0036] Furthermore, the transformation of the deterministic ship scheduling optimization model into a robust ship scheduling optimization model that comprehensively considers the uncertainty of port and departure times includes:

[0037] Using the constructed set of uncertainties for ship arrival and departure times, formulas (1) and (3) are transformed into formulas (16) and (17) as follows. At this time, the model includes the uncertain parameters for ship arrival and departure times.

[0038]

[0039]

[0040] Based on the idea of ​​robust optimization, that is, considering the optimal result in the worst case, formulas (16) and (17) are further transformed into formulas (18) and (19), as follows:

[0041]

[0042]

[0043] To transform equations (18) and (19) into convex optimization problems solvable in polynomial time, an auxiliary variable π is introduced. i And w, through duality theory, in the above equation After transformation, its dual expression is obtained as follows:

[0044]

[0045]

[0046]

[0047] Therefore, formula (18) is equivalent to formula (23), with additional constraints (21) and (22). Formula (19) is equivalent to formula (24), with additional constraints (21) and (22). Formulas (23) and (24) are as follows:

[0048]

[0049]

[0050] Furthermore, based on the meme algorithm MA and the variable neighborhood search algorithm VNS, a heuristic algorithm MAVNS is designed, and the robust optimization model is solved using MAVNS to obtain a robust scheduling optimization scheme, including:

[0051] Chromosomes with two layers of coding are generated based on the number of ships and their direction of entry and exit from the port.

[0052] Calculate the target function value for each chromosome;

[0053] Based on the requirements for vessel traffic organization in one-way waterways, a fitness function is defined;

[0054] A roulette wheel selection strategy is used to select chromosome individuals, and the ship scheduling sequence is optimized by combining crossover and mutation operators;

[0055] Based on the coding structure of chromosomes, three neighborhood operators are designed, and the optimal solution for each retained objective value is searched using a variable neighborhood algorithm to find the optimal solution.

[0056] Repair operators are used to repair the generated illegal chromosomes;

[0057] Repeat the above steps until the maximum number of iterations is met, then output the optimal feasible solution.

[0058] Furthermore, the three neighborhood operators in the design include: the 2-opt operator, the Swap operator, and the Insert operator, wherein:

[0059] The 2-opt operator randomly selects two gene positions in the ship scheduling sequence of the chromosome and reverses the gene order between these two points;

[0060] The Swap operator randomly selects two gene positions in the ship scheduling sequence of the chromosome for exchange;

[0061] The Insert operator randomly selects two gene positions in the ship scheduling sequence of the chromosome and inserts the gene at the later position into the gene position at the earlier position.

[0062] Compared with the prior art, the present invention has the following advantages:

[0063] 1. The robust optimization method for ship scheduling provided by this invention takes into account the uncertainty of arrival and departure times. It studies a novel ship scheduling problem under the uncertainty of arrival and departure times, and fills the theoretical gap in the current research on uncertain ship scheduling.

[0064] 2. The robust optimization method for ship scheduling provided by this invention, which comprehensively considers the uncertainty of port and departure times, can not only provide reliable auxiliary decision-making for port scheduling departments to effectively cope with fluctuations in ship arrival and departure times, but also the optimized scheduling results have good robustness and economy.

[0065] Based on the above reasons, this invention can be widely applied in fields such as ship scheduling. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

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

[0068] Figure 2 Convergence curves of MAVNS, MA, and GA algorithms when the number of ships V = 23 and 36 are provided for embodiments of the present invention. Detailed Implementation

[0069] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0072] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0073] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0074] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0075] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0076] like Figure 1 As shown, this invention provides a robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times, including:

[0077] S1. Construct the set of uncertainties for ship arrival and departure times;

[0078] S2. Establish a robust optimization model for ship scheduling that comprehensively considers the uncertainties of port and departure times;

[0079] S3. Based on the meme algorithm MA and the variable neighborhood search algorithm VNS, a heuristic algorithm MAVNS is designed, and the robust optimization model is solved using MAVNS to obtain a robust scheduling optimization scheme.

[0080] In a specific implementation, as a preferred embodiment of the present invention, step S1, which involves constructing the uncertainty set of the ship's arrival and departure times, specifically includes:

[0081] Considering the significant fluctuations in the arrival and departure times of vessel i during actual port operations, a budget uncertainty set U is introduced to characterize the uncertainty of arrival and departure times. This set can be represented as:

[0082]

[0083] in, This represents the value when ship i is not delayed; The i ( Thei ≥0) indicates deviation The maximum value of ζ; i This represents the control Ta that varies within the uncertain set U. i The uncertainty level parameter of the fluctuation range; Γ represents the adjustable parameter of the conservatism of the control model, and Γ = 0 means that the uncertainty of the arrival and departure times of ships is not considered.

[0084] In a specific implementation, as a preferred embodiment of the present invention, step S2, which involves establishing a robust optimization model for ship scheduling that comprehensively considers the uncertainties of port and departure times, specifically includes:

[0085] S21. Establish a deterministic ship scheduling optimization model with the objective function of minimizing the total waiting time of ships, and represent it using MILP-D;

[0086] S22. Transform the deterministic ship scheduling optimization model into a robust ship scheduling optimization model that comprehensively considers the uncertainty of port and departure times.

[0087] In a specific implementation, as a preferred embodiment of the present invention, step S21 specifically includes:

[0088] S211. Establish the objective function as follows:

[0089]

[0090] S212. Set the constraints as follows:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] In this formula, formula (1) indicates that the objective function is to minimize the total waiting time of ships; formula (2) ensures that ships entering and leaving the port adjust their scheduling application time according to the tidal window, and at the same time ensures that the time for ships entering the port to sail to the channel exit is less than the end time of the tidal window; formula (3) ensures that the start scheduling time is greater than or equal to the time for requesting scheduling or re-requesting scheduling; formulas (4), (5), and (6) ensure the navigation continuity of ships entering the port, and at the same time determine the time for ships to sail to the channel entrance, the channel exit, and the berth; formulas (7) and (8) ensure the navigation continuity of ships leaving the port, and at the same time determine the time for ships to sail to the channel exit and the channel entrance; formulas (9) and (10) ensure that ships in the same direction should maintain a certain safe distance in the same direction; formulas (11) and (12) ensure that ships in opposite directions should maintain a certain safe distance in opposite directions; formulas (13), (14), and (15) represent the binary decision variable value constraints; in the above formulas, V represents the ship set; V in Indicates the assembly of ships entering the port; V out Indicates the assembly of departing vessels; d1 i d1 represents the distance from the anchorage to the channel entrance; d2 represents the distance from the channel entrance to the channel exit, which is the distance within the channel; d3 represents the distance from the anchorage to the channel entrance. i Indicates the distance of vessel i from the channel exit to the berth; v i T represents the average speed of ship i; si Indicates the start time when vessel i needs to enter or leave the port with the tide; T ei This indicates the end time at which vessel i needs to enter or leave the port with the tide; Ta i c1 represents the time when vessel i requests scheduling, i.e., the estimated arrival and departure times of the vessel; c2 represents the safe distance between vessels traveling in the same direction at the channel entrance or exit; c3 represents the safe distance between vessels traveling in opposite directions at the channel entrance or exit; M represents a large positive integer; Ts i Indicates the start time of scheduling for ship i; R ij Representing binary variables, for inbound ships, if ship j is scheduled after ship i, it is 1; otherwise, it is 0. ij Representing binary variables, for departing ships, the value is 1 if ship j is scheduled after ship i, and 0 otherwise; IO i This represents a binary variable; it is 1 when ship i enters the port and 0 when it leaves the port.

[0106] In a specific implementation, as a preferred embodiment of the present invention, step S22 specifically includes:

[0107] S221. Using the constructed set of uncertainties for ship arrival and departure times, formulas (1) and (3) are transformed into the following formulas (16) and (17). At this time, the model includes the uncertain parameters for ship arrival and departure times.

[0108]

[0109]

[0110] S222. Based on the idea of ​​robust optimization, that is, considering the best result in the worst case, formulas (16) and (17) are further transformed into formulas (18) and (19), as follows:

[0111]

[0112]

[0113] S223. To transform formulas (18) and (19) into convex optimization problems solvable in polynomial time, an auxiliary variable π is introduced. i And w, through duality theory, in the above equation After transformation, its dual expression is obtained as follows:

[0114]

[0115]

[0116]

[0117] Therefore, formula (18) is equivalent to formula (23), with additional constraints (21) and (22). Formula (19) is equivalent to formula (24), with additional constraints (21) and (22). Formulas (23) and (24) are as follows:

[0118]

[0119]

[0120] In a specific implementation, as a preferred embodiment of the present invention, in step S3, based on the meme algorithm MA and the variable neighborhood search algorithm VNS, a heuristic algorithm MAVNS is designed, and the robust optimization model is solved using MAVNS to obtain a robust scheduling optimization scheme, including:

[0121] S31. Generate a chromosome with two layers of coding based on the number of ships and their direction of entry and exit from the port;

[0122] S32. Calculate the objective function value for each chromosome;

[0123] S33. Based on the requirements for vessel traffic organization in one-way waterways, set a fitness function;

[0124] S34. A roulette wheel selection strategy is used to select chromosome individuals, and the ship scheduling sequence is optimized by combining crossover and mutation operators;

[0125] S35. Based on the coding structure of chromosomes, design three neighborhood operators, and use a variable neighborhood algorithm to search for the optimal solution for each retained target value.

[0126] S36. Repair the generated illegal chromosomes using a repair operator;

[0127] S37. Repeat the above steps until the maximum number of iterations is met, then output the optimal feasible solution.

[0128] In a specific implementation, as a preferred embodiment of the present invention, the three neighborhood operators designed in step S35 include: the 2-opt operator, the Swap operator, and the Insert operator, wherein:

[0129] The 2-opt operator randomly selects two gene positions in the ship scheduling sequence of the chromosome and reverses the gene order between these two points;

[0130] The Swap operator randomly selects two gene positions in the ship scheduling sequence of the chromosome for exchange;

[0131] The Insert operator randomly selects two gene positions in the ship scheduling sequence of the chromosome and inserts the gene at the later position into the gene position at the earlier position.

[0132] Example

[0133] This embodiment uses a comprehensive port area as an example to illustrate the robust optimization model for ship scheduling and the hybrid heuristic algorithm proposed in this invention. The channel of this comprehensive port area is a narrow, one-way channel for 200,000-ton vessels, with a total length of 31 nautical miles.

[0134] To test the effectiveness of the proposed algorithm in solving the robust optimization model of ship scheduling, this section designs a comparative experiment with different numbers of ships, setting Γ=3 and ζ=1. The First-Come, First-Served (FCFS) strategy and the proposed algorithm (MAVNS) are compared in terms of total ship waiting time, optimal gap, and CPU running time. All examples are generated based on actual ship entry and exit data from a comprehensive port area. Each example is solved ten times, and the average value is taken. Table 1 records the solution results of the robust optimization model of ship scheduling using MAVNS and FCFS. As can be seen from Table 1, for all examples, although the FCFS strategy is faster, its total waiting time is much higher than that of the MAVNS method, with an average gap of 98.67%. This is because the FCFS method predetermines the ship entry and exit order, making it difficult to arrange a reasonable scheduling order.

[0135] Table 1 compares the proposed algorithm (MAVNS) and the First-Come, First-Served (FCFS) strategy.

[0136]

[0137] To verify the robustness of the proposed model (MILP-R), the MILP-D and MILP-R models were solved using the MAVNS algorithm. Each set of examples was run 10 times and the average value was taken. The calculation results are shown in Table 2. Where F... D-MAVNS and F R-MAVNS This represents the optimal objective value obtained by solving the MILP-D and MILP-R models using MAVNS, respectively, maxTf D and maxTf R Let Γ = 3 and ζ = 1, representing the time when the last ship completes its scheduling, obtained from solving the MILP-D and MILP-R models. Analysis of Table 2 shows that the relative error gap values ​​are all between 0 and 10, indicating that the robust scheduling solution obtained by the MILP-R model suffers some loss in objective function performance to absorb the impact of disturbances in ship arrival and departure times. However, considering the objective function value and the time when the last ship completes its scheduling, compared to the MILP-D model, the optimal solution obtained by the MILP-R model can ensure that the scheduling completion time remains basically unchanged or has minimal delay, thus giving the ship arrival and departure times a flexible characteristic. That is, when arrival and departure times fluctuate within a certain range, it can ensure that the ship scheduling completion time will not be significantly delayed, indicating better robustness of the scheduling solution.

[0138] Table 2. Calculation results of MAVNS algorithm for solving the deterministic ship scheduling model (MILP-D) and the robust ship scheduling model (MILP-R).

[0139]

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times, characterized in that, include: Construct a set of uncertainties regarding ship arrival and departure times; Establish a robust optimization model for ship scheduling that comprehensively considers the uncertainties of port and departure times, specifically including: A deterministic ship scheduling optimization model is established with the objective function of minimizing total ship waiting time, and denoted by MILP-D. Specifically, it includes: The objective function is defined as follows: Min (1) Set the constraints as follows: (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) In this context, formula (1) represents the objective function as minimizing the total waiting time of ships; formula (2) ensures that ships entering and leaving the port adjust their scheduling application time according to the tidal window, while ensuring that the time for ships entering the port to sail to the channel exit is less than the end time of the tidal window; formula (3) ensures that the start scheduling time is greater than or equal to the time for requesting scheduling or re-requesting scheduling; formulas (4), (5), and (6) ensure the navigation continuity of ships entering the port, while determining the time for ships to sail to the channel entrance, the channel exit, and the berth in sequence; formulas (7) and (8) ensure the navigation continuity of ships leaving the port, while determining the time for ships to sail to the channel exit and the channel entrance in sequence; formulas (9) and (10) ensure that ships in the same direction should maintain a certain safe distance in the same direction; formulas (11) and (12) ensure that ships in opposite directions should maintain a certain safe distance in opposite directions; formulas (13), (14), and (15) represent the binary decision variable value constraints; in the above formulas, Indicates a collection of ships; Indicates the assembly of ships entering the port; Indicates the assembly of departing vessels; Indicates a ship i The distance from the anchorage to the entrance to the channel; This indicates the distance from the entrance to the exit of the waterway, which is the distance of the waterway itself. Indicates a ship i The distance from the channel exit to the berth; Indicates a ship i The average speed of the ship; Indicates a ship i The start time for entering or leaving the port with the tide; Indicates a ship i The end time for those needing to enter or leave the port with the tide; Indicates a ship i The time for requesting dispatch, i.e., the estimated arrival and departure times of the vessel; Indicates the safe distance between vessels traveling in the same direction at the entrance or exit of a waterway; Indicates the safe distance between vessels traveling in opposite directions at the entrance or exit of a waterway; Represents large positive integers; Indicates a ship i Start scheduling time; Representing binary variables, for ships entering the port, the ship j on board i The value is 1 for subsequent scheduling, and 0 otherwise. Representing binary variables, for departing ships, the ship j on board i The value is 1 for subsequent scheduling, and 0 otherwise. Represents a binary variable, ship i The value is 1 for inbound traffic and 0 for outbound traffic; The deterministic ship scheduling optimization model is transformed into a robust ship scheduling optimization model that comprehensively considers the uncertainty of port and departure times, including: Using the constructed set of uncertainties for ship arrival and departure times, formulas (1) and (3) are transformed into formulas (16) and (17) as follows. At this time, the model includes the uncertain parameters for ship arrival and departure times. (16) (17) Based on the idea of ​​robust optimization, that is, considering the optimal result in the worst case, formulas (16) and (17) are further transformed into formulas (18) and (19), as follows: (18) (19) To transform equations (18) and (19) into convex optimization problems solvable in polynomial time, auxiliary variables are introduced. By applying duality theory to the above equation After transformation, its dual expression is obtained as follows: (20) (21) (22) Therefore, formula (18) is equivalent to formula (23), with additional constraints (21) and (22). Formula (19) is equivalent to formula (24), with additional constraints (21) and (22). Formulas (23) and (24) are as follows: (23) (24) Based on the meme algorithm MA and the variable neighborhood search algorithm VNS, a heuristic algorithm MAVNS is designed, and the robust optimization model is solved using MAVNS to obtain a robust scheduling optimization scheme.

2. The robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times as described in claim 1, characterized in that, The set of uncertainties for ship arrival and departure times specifically includes: Considering the ship i Arrival and departure times fluctuate significantly in actual port operations, leading to the introduction of budget uncertainty. To characterize the uncertainty of arrival and departure times, the set can be represented as: in, Indicates a ship i The value when no delay occurs; Indicates deviation The maximum value; Indicates in the uncertain set Internal changes, control Uncertainty level parameter of fluctuation range; An adjustable parameter representing the conservatism of the control model. This indicates that the uncertainty of the arrival and departure times of ships is not taken into account.

3. The robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times as described in claim 1, characterized in that, The heuristic algorithm MAVNS is designed based on the meme algorithm MA and the variable neighborhood search algorithm VNS. The robust optimization model is then solved using MAVNS to obtain a robust scheduling optimization scheme, including: Chromosomes with two layers of coding are generated based on the number of ships and their direction of entry and exit from the port. Calculate the target function value for each chromosome; Based on the requirements for vessel traffic organization in one-way waterways, a fitness function is defined; A roulette wheel selection strategy is used to select chromosome individuals, and the ship scheduling sequence is optimized by combining crossover and mutation operators; Based on the coding structure of chromosomes, three neighborhood operators are designed, and the optimal solution for each retained objective value is searched using a variable neighborhood algorithm to find the optimal solution. Repair operators are used to repair the generated illegal chromosomes; Repeat the above steps until the maximum number of iterations is met, then output the optimal feasible solution.

4. The robust optimization method for ship scheduling that comprehensively considers the uncertainties of port and departure times as described in claim 3, is characterized in that, The three neighborhood operators described in the design include: the 2-opt operator, the Swap operator, and the Insert operator, wherein: The 2-opt operator randomly selects two gene positions in the ship scheduling sequence of the chromosome and reverses the gene order between these two points; The Swap operator randomly selects two gene positions in the ship scheduling sequence of the chromosome for exchange; The Insert operator randomly selects two gene positions in the ship scheduling sequence of the chromosome and inserts the gene at the later position into the gene position at the earlier position.

Images