Turbine fuel oil supply optimization method considering navigational speed deviation under emission control area

Abstract

The invention discloses a liner fuel oil supply optimization method considering navigational speed deviation under an emission control area, and the method comprises the steps: constructing a dynamic fuel oil supply model with the minimization of ship operation cost, time window punishment cost, fuel oil supply cost and container inventory cost as a target through analyzing the dynamic influence of the navigational speed deviation on fuel oil consumption; and solving the dynamic fuel oil supply model by adopting an improved genetic algorithm based on a repair operator to obtain a liner fuel oil supply optimization result, thereby realizing systematic optimization of a liner fuel oil supply strategy, remarkably reducing the total operation cost of a ship, improving the fuel oil supply economy and the navigational speed adjustment flexibility, and improving the economic benefit of the ship. And reliable decision support is provided for a liner company to formulate a scientific fuel oil supply strategy under a green shipping background.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ship management, and particularly relates to a liner fuel supply optimization method considering speed deviation under an emission control area. BACKGROUND

[0002] With the increasingly stringent global environmental protection policy and the continuous rise of shipping operation cost, the liner transportation industry is facing severe challenges in formulating fuel supply strategies. Fuel cost accounts for more than 70% of the total operation cost of a ship, and there is a cubic relationship between the fuel consumption of a ship and the speed, which makes the fuel supply strategy a key factor affecting the economic benefit of a liner company. Under the emission control area (ECA) policy implemented by the International Maritime Organization (IMO), ships must use high-priced low-sulfur fuel in specific areas, which significantly increases the operation cost. At the same time, the speed deviation caused by uncertain factors such as weather changes and port congestion in actual operation further increases the difficulty of operation management. According to statistics, the reliability of the ship period of the global liner transportation is only about 47%, and the speed deviation not only affects the punctuality of the ship to the port, but also causes additional fuel consumption and delay cost, which seriously restricts the operation efficiency and service quality of the liner company.

[0003] Under this background, the traditional fuel supply strategy often relies on static assumptions and fixed refueling schemes, and it is difficult to effectively cope with the coordinated optimization problem of ECA policy constraints, dynamic speed fluctuations and port time window requirements. The existing methods mostly focus on a single cost dimension, lack of consideration of fuel inventory level, speed deviation adaptive adjustment and multi-port refueling linkage, resulting in problems such as fuel cost overruns, low reliability of arrival at the port, and high risk of violation in actual operation of the liner company. How to solve the problem of fuel cost control and supply decision caused by actual speed fluctuation of the ship under the constraint of ECA policy to reduce the total operation cost of the ship is a technical problem to be solved. SUMMARY

[0004] The present application proposes a liner fuel supply optimization method considering speed deviation under an emission control area. The technical means adopted by the present application are as follows: A liner fuel supply optimization method considering speed deviation under an emission control area, comprising the following steps: Step 1: based on the fixed cost of each cycle of each ship in the liner route and the number of ships configured on the liner route, a total operation cost expression of all ships on the liner route is established; Step 2: based on the planned port time window of the ship in each leg of the liner route, the ship's stay time at each port, the ship's departure time from the port, and the unit time penalty cost of the ship when delayed at each port, a total time penalty cost expression of the ship is established; Step 3: Based on the ship's actual speed outside the ECA and the actual speed inside the ECA on each leg of the journey, the fuel consumption rate function of the liner on each leg of the journey, the fixed cost of refueling at each port, the amount of fuel refueled at each port, and the unit fuel price at each port, establish an expression for the ship's total fuel supply cost. Step 4: Based on the inventory cost per unit container per unit time of the ship in each segment, the container transport volume of the ship in each segment, the sailing distance of the ship outside the ECA in each segment, the sailing distance of the ship inside the ECA in each segment, the actual sailing speed of the ship outside the ECA in each segment, and the actual sailing speed of the ship inside the ECA in each segment, establish the expression for the total container inventory cost of the ship. Step 5: Establish a dynamic fuel replenishment model based on the expressions for the total operating cost of all ships, the total time penalty cost of ships, the total fuel replenishment cost of ships, and the total container inventory cost of ships. Step 6: The improved genetic algorithm based on the repair operator is used to optimize the dynamic fuel replenishment model and obtain the optimized fuel replenishment results for liner ships.

[0005] Furthermore, the objective function of the dynamic fuel replenishment model is: (1) The constraints of the dynamic fuel replenishment model are: (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) In this equation, (2) represents the actual speed of the ship; and (3) represents the time constraint range of the ship, i.e., the time from which the ship arrives at its destination. Hong Kong time is from The time of departure from the port plus the ship's time The sailing time of the segment; Equation (4) represents the time the ship spends in the segment. The carbon emissions of the port should not exceed the carbon emission limits set by the ECA for that segment of the voyage; Equation (5) indicates that the ship's carbon emissions in the port should not exceed the limits set by the ECA for that segment of the voyage. The sulfur emissions at the port should not exceed the ECA's limit on sulfur emissions for that segment of the voyage; Equations (6) and (7) represent limits related to fuel capacity, the former indicating the limits for the ship's fuel capacity. The fuel ordering point at a port must not exceed the port's maximum fuel refueling level, which indicates the level at which a vessel is... The maximum refueling level in the port shall not exceed the maximum capacity of the fuel tank; Equations (8) and (9) indicate that the speed of the vessel outside / inside the ECA shall not exceed the speed at which the vessel is in the port. The speed range of the segment; Equation (10) indicates the speed range of the ship due to the existence of the time window. The port must meet time constraints; Equation (11) represents the influence of internal and external uncertainties encountered by the ship during navigation, which will cause the speed to deviate, and the speed limit after the deviation; Equation (12) represents the ship's speed during navigation. Speed ​​limits for the segment; Equation (13) indicates the speed limit of the vessel in the segment. The relationship between the planned speed of the segment and the planned speed outside / inside the ECA; Equation (14) indicates that the amount of fuel added to the ship must not be negative; Equation (15) indicates that the number of ships assigned to the route must meet the positive integer limit; Equation (16) is a 0-1 decision variable constraint; The dynamic fuel replenishment model includes the following set: , Indicates the assembly point at the port of call; The parameters in the dynamic fuel replenishment model include: Indicates that the ship is scheduled to be in port. i The time window range, in hours; Indicates that the ship is Planned sailing time for a segment of the voyage, in hours; Indicates the arrival / departure of a ship Hong Kong time, in hours; This indicates the maximum capacity of a ship's fuel tanks, in tons. Indicates that the ship is Fuel ordering points in Hong Kong, unit: tons; Indicates that the ship is Maximum fuel level at Hong Kong, unit: tons; Indicates that the ship is The range of speeds along a route, in knots; Indicates carbon emission factor / sulfur emission factor; express Carbon / sulfur emission limits within the ECA segment, in tons; Represents a 0-1 coefficient, when the ship is... If the flight segment is outside the ECA, then ,otherwise ; This represents the total operating cost of all vessels, in US dollars. This represents the total time penalty cost for all vessels, in US dollars. This represents the total fuel replenishment cost for all vessels, in US dollars. This represents the total container inventory cost for all vessels, in US dollars. Ships in Planned speed on a segment of the voyage, in knots; Ships in Extreme speed deviation on a flight segment, in knots; The decision variables in the dynamic fuel replenishment model include: Represents a 0-1 variable; if the ship is... If the fuel is in Hong Kong, the value is 1; otherwise, it is 0. Indicates that the ship is Hong Kong refueling volume, unit: tons; Indicates that the ship is Actual speed outside / inside the ECA on the route segment, in knots; This indicates the number of ships deployed on the route, in units of: vessels.

[0006] Furthermore, the total operating cost of all the aforementioned vessels The expression is: (17) in, This represents the weekly fixed cost per vessel, in US dollars. The ships sail for 168 hours per week, and the number of ships deployed on the route is [number missing]. Calculated using formula (18): (18) in, Indicates that the ship is Port stay time, in hours; ship stay time at port. Planned sailing time on the voyage segment Calculated using formula (19): (19) in, Indicates that the ship is Planned sailing time outside the ECA segment, in hours; Indicates that the ship is Planned sailing time within the ECA segment, in hours; Ships in Planned sailing time outside ECA segment Calculated using formula (20): (20) Ships in Planned sailing time within the ECA segment Calculated using formula (21): (twenty one) in, Indicates that the ship is Distance traveled outside the ECA (Electronic Control Area) during a voyage, in nautical miles; Indicates that the ship is Distance within the ECA segment of a voyage, in nautical miles; Indicates that the ship is Planned speed outside the ECA segment, in knots; Indicates that the ship is Planned speed within the ECA segment, in knots.

[0007] Furthermore, the total time penalty cost of the vessel The expression is: (twenty two) in, Indicates that the ship is Penalty cost per unit time when delays occur in Hong Kong, in US dollars; Indicates that the ship is scheduled to... Latest time in Hong Kong, unit: hour; Ship departs Hong Kong time Calculated using formula (23): (twenty three) in, Indicates that the ship is scheduled to... The earliest time in Hong Kong, in hours.

[0008] Furthermore, the total fuel refueling cost of the vessel The expression is: (twenty four) in, Indicates that the ship is Port fuel supply costs, in US dollars; Ships in Port fuel supply costs Calculated using formula (25): (25) in, Indicates that the ship is Fixed cost for refueling in Hong Kong, unit: US dollars per refueling; Indicates that the ship is Fuel price per unit at Hong Kong refueling site, in US dollars per ton; Ships in Hong Kong's fuel consumption Calculated using formula (26): (26) in, Indicates the arrival of the ship Fuel inventory levels at port, in tons; The value of is calculated by formula (27): (27) in, Represents an arbitrarily large positive number; This indicates the worst-case fuel consumption of a liner on a specific voyage segment; Indicates the ship has left. Fuel inventory levels at port, in tons; Fuel consumption of a ship under worst-case conditions in a specific voyage segment Calculated using formula (28): (28) in, Indicates that the ship is Extreme speed deviation on a flight segment, in knots; Ships in Total fuel consumption during the voyage segment Calculated using formula (29): (29) in, Indicates that the ship is Fuel consumption outside the ECA segment on the flight segment; Indicates that the ship is Fuel consumption within the ECA segment of the flight; Ships in Fuel consumption outside ECA on flight segment Calculated using formula (30): (30) Ships in Fuel consumption within the ECA segment Calculated using formula (31): (31) in, Indicates that the ship is Fuel consumption rate function outside ECA on the flight segment; Indicates that the ship is Fuel consumption rate function within the ECA segment of the flight; Ships in Fuel consumption rate function outside ECA on flight segment Calculated using formula (32): (32) Ships in Fuel consumption rate function within the ECA segment Calculated using formula (33): (33) in, This is the fuel consumption coefficient; Ships in Total fuel consumption during the voyage segment Ships leaving Fuel inventory levels at Hong Kong time Ship arrival Fuel inventory levels at Hong Kong time And the ship's fuel consumption under worst-case conditions in a specific voyage. The relationship is: (34) (35).

[0009] Furthermore, the total container inventory cost for all vessels expression: (36) in, Indicates that the ship is Inventory cost per container per unit time on a shipping segment, in US dollars per hour; Indicates that the ship is Container volume transported on a shipping segment, in TEUs.

[0010] Furthermore, the improved genetic algorithm based on the repair operator optimizes the solution of the dynamic fuel replenishment model, including the following steps: Step 600: Input the relevant parameter values ​​for population size, crossover probability, mutation probability, maximum number of iterations, maximum sailing speed, and minimum sailing speed, and perform the encoding operation to randomly generate the initial population; Step 601: Check each individual in the initial population in turn to determine whether it meets the existence requirements of ECA and the speed requirements of ECA emission limits. If it meets the requirements, proceed to the next step. If it does not meet the requirements, repair the individual. Step 602: Calculate the fitness of each individual in the repaired initial population to obtain the fitness value of each individual. The fitness calculation formula is: (37) in, Indicates the first The fitness value of each individual This represents the total operating cost corresponding to that individual; Step 603: After the fitness value calculation is completed, select the individual with the highest fitness value in the current population as the current optimal individual, and record this current individual as... Output the fitness of the current individual. ; Step 604, Initial Iteration Count ; Step 605: Determine the current generation number of the population. With maximum number of iterations The relationship, when the conditions are met If the condition is not met, proceed to step 606; if the condition is not met... Then proceed to step 613; Step 606: Perform selection, crossover, and mutation operations sequentially on the current population to obtain new population individuals; Step 607: Update and merge the newly obtained individuals in the population to form a new population; Step 608: Check each individual in the new population in turn to determine whether it meets the existence requirements of ECA and the speed requirements of ECA emission limits. If it meets the requirements, proceed to the next step. If it does not meet the requirements, repair the individual. Step 609: Calculate the fitness of each individual in the repaired new population, obtain the fitness value of each individual, and record the best individual in the new population as... and output the fitness of the individual. ; Step 610: Determine the fitness of the new population. Is the fitness of the previous population less than that of the previous population? If yes, proceed to step 611; otherwise, proceed to step 612. Step 611: After performing a variable neighborhood perturbation on the current population, return to step 607; Step 612: Update the current best individual to And update the iteration count: Then return to the judgment operation step 605; Step 613: Output the currently determined optimal individual. Then, perform decoding operations to obtain the optimal solution obtained by the current algorithm.

[0011] Furthermore, the initial population individuals are encoded using a three-layer coding method. The first layer of coding represents the speed outside the ECA, the second layer of coding represents the speed inside the ECA, and the third layer of coding represents whether refueling is required. The length of the chromosome represents the number of ports on the specified liner route. Repairing individuals within a population involves the following steps: Step 6010: Check each entity in turn to determine whether the first layer code and the second layer code meet the existence requirements of the emission control area. If both meet the requirements, proceed to step 6012; otherwise, proceed to step 6011. Step 6011: If the first layer code or the second layer code does not meet the requirements, perform layer-by-layer code replacement; the replacement process is as follows: if the first layer code should not contain a speed outside the ECA, then replace the gene with 0; if the first layer code should not be 0 but is actually 0, then randomly select a gene that meets the requirements of the flight segment for replacement; if the second layer code does not meet the requirements, then randomly select a gene that meets the requirements of the emission control area to replace the original gene. Step 6012: Check each individual in turn to determine whether the second-level code meets the restrictive requirements of the emission control area, that is, whether it meets the carbon emission limit and sulfur emission limit. If both are met, proceed to step 6014; otherwise, proceed to step 6013. Step 6013: Randomly select a gene that represents the carbon and sulfur emission limits for an emission control zone and replace the original gene; Step 6014: Replace the original chromosome with the repaired chromosome and reintroduce it into the population to form an initial population that meets the constraints.

[0012] Further, step 606 includes the following steps: Step 6060: Adopt an elite preservation strategy for the current population, and divide the current population according to its fitness value. Sort and retain the top fitness values. Individuals; a tournament selection strategy is used for the current population, with each selection... Individuals are grouped into groups, and the individual with the highest fitness in the group is added to a new population. This process is repeated until the individual with the highest fitness is found. Individuals; a new individual generation strategy is adopted for the current population to randomly generate individuals. The new individuals; combine the elite-retained individuals, the tournament-selected individuals, and the newly generated individuals to form the population after the selection operation; Step 6061: Perform crossover operation on the population after the selection operation until the number of offspring individuals reaches the set requirement of the population size to obtain the population after crossover operation. Step 6062: Traverse all individuals in the population after the crossover operation. For the currently selected individual, randomly generate a random number in the interval [0, 1]. If the random number is less than the given mutation rate, then perform a uniform mutation operation on the chromosome to cause it to mutate. The mutation position is randomly determined, thereby obtaining a new population after the selection operation, crossover operation and mutation operation.

[0013] Compared with existing technologies, the liner fuel replenishment optimization method considering speed deviation under emission control areas disclosed in this invention has the following beneficial effects: This invention analyzes the dynamic impact of speed deviation on fuel consumption, constructs a dynamic fuel replenishment model with the objective of minimizing ship operating costs, time window penalty costs, fuel replenishment costs, and container inventory costs, and obtains the liner fuel replenishment optimization results by solving the dynamic fuel replenishment model using an improved genetic algorithm based on the repair operator. This achieves systematic optimization of liner fuel replenishment strategies, which can significantly reduce total ship operating costs, improve fuel replenishment economy and speed adjustment flexibility, and provide reliable decision support for liner companies to formulate scientific fuel replenishment strategies in the context of green shipping. Attached Figure Description

[0014] Figure 1 This is a flowchart of the liner fuel replenishment optimization method considering speed deviation under the emission control area in this application; Figure 2 This is a flowchart illustrating the optimization solution of the dynamic fuel replenishment model using an improved genetic algorithm based on the repair operator in this application. Figure 3The locational relationship between ports and ECAs; Figure 4 This is a schematic diagram of the population individuals in this application; Figure 5 This is a schematic diagram of the repair process of the repair operator in this application; Figure 6 This is a schematic diagram of the cross-operation in this application; Figure 7 This is a schematic diagram of uniform variation in this application. Detailed Implementation

[0015] like Figure 1 As shown, the liner fuel replenishment optimization method considering speed deviation under emission control areas disclosed in this invention includes the following steps: Step 1: Based on the fixed cost of each ship in each cycle on the liner route and the number of ships configured on the liner route, establish an expression for the total operating cost of all ships on the liner route. Step 2: Based on the planned port time window of the vessel in each segment of the liner route, the vessel's stay time in each port, the vessel's departure time, and the unit time penalty cost when the vessel is delayed in each port, establish an expression for the total time penalty cost of the vessel. Step 3: Based on the ship's actual speed outside the ECA and the actual speed inside the ECA on each leg of the journey, the fuel consumption rate function of the liner on each leg of the journey, the fixed cost of refueling at each port, the amount of fuel refueled at each port, and the unit fuel price at each port, establish an expression for the ship's total fuel supply cost. Step 4: Based on the inventory cost per unit container per unit time of the ship in each segment, the container transport volume of the ship in each segment, the sailing distance of the ship outside the ECA in each segment, the sailing distance of the ship inside the ECA in each segment, the actual sailing speed of the ship outside the ECA in each segment, and the actual sailing speed of the ship inside the ECA in each segment, establish the expression for the total container inventory cost of the ship. Step 5: Establish a dynamic fuel replenishment model based on the expressions for the total operating cost of all ships, the total time penalty cost of ships, the total fuel replenishment cost of ships, and the total container inventory cost of ships. Step 6: The improved genetic algorithm based on the repair operator is used to optimize the dynamic fuel replenishment model and obtain the optimized fuel replenishment results for liner ships.

[0016] This invention analyzes the dynamic impact of speed deviation on fuel consumption for liner ships operating in emission control areas, taking into account speed deviation. It constructs a dynamic fuel replenishment model with the objective of minimizing ship operating costs, total time penalty costs, total fuel replenishment costs, and total container inventory costs. This model achieves systematic optimization of liner ship fuel replenishment strategies. The optimized fuel replenishment results are obtained by solving the dynamic fuel replenishment model using an improved genetic algorithm based on a repair operator. This significantly reduces total ship operating costs, improves fuel replenishment economics and speed adjustment flexibility, and provides reliable decision support for liner companies to formulate scientific fuel replenishment strategies in the context of green shipping. Specifically, the liner company's General Manager Zhou's operating costs It can be represented as:

[0017] The first term represents the total operating cost of the vessel, the second term represents the penalty cost incurred when the vessel arrives late, the third term represents the refueling cost incurred due to refueling, and the fourth term represents the inventory cost of containers on the vessel. Optimizing the total operating cost of liner services and formulating refueling strategies is a complex task involving many factors. In order to facilitate the establishment of a dynamic refueling model for the problem studied, this application sets the following assumptions based on actual conditions: (1) The types of vessels configured on the route are the same in actual operation; (2) The liner route has a weekly departure frequency, that is, the vessel calls at a port once a week; (3) The vessel's sailing route is determined, that is, the order of port calls is determined; (4) Only the fuel consumption of the main engine is considered, and the fuel consumption of the auxiliary engine is included in the fixed cost of the vessel.

[0018] The dynamic fuel replenishment model in this application includes an objective function and constraints, wherein... The objective function of the dynamic fuel replenishment model is: (1) The constraints of the dynamic fuel replenishment model are: (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) In this equation, (2) represents the actual speed of the ship; and (3) represents the time constraint range of the ship, i.e., the time from which the ship arrives at its destination. Hong Kong time is from The time of departure from the port plus the ship's time The sailing time of the segment; Equation (4) represents the time the ship spends in the segment. The carbon emissions of the port should not exceed the carbon emission limits set by the ECA for that segment of the voyage; Equation (5) indicates that the ship's carbon emissions in the port should not exceed the limits set by the ECA for that segment of the voyage. The sulfur emissions at the port should not exceed the ECA's limit on sulfur emissions for that segment of the voyage; Equations (6) and (7) represent limits related to fuel capacity, the former indicating the limits for the ship's fuel capacity. The fuel ordering point at a port must not exceed the port's maximum fuel refueling level, which indicates the level at which a vessel is... The maximum refueling level in the port shall not exceed the maximum capacity of the fuel tank; Equations (8) and (9) indicate that the speed of the vessel outside / inside the ECA shall not exceed the speed at which the vessel is in the port. The speed range of the segment; Equation (10) indicates the speed range of the ship due to the existence of the time window. The port must meet time constraints; Equation (11) represents the influence of internal and external uncertainties encountered by the ship during navigation, which will cause the speed to deviate, and the speed limit after the deviation; Equation (12) represents the ship's speed during navigation. Speed ​​limits for the segment; Equation (13) indicates the speed limit of the vessel in the segment. The relationship between the planned speed of the segment and the planned speed outside / inside the ECA; Equation (14) indicates that the amount of fuel added to the ship must not be negative; Equation (15) indicates that the number of ships assigned to the route must meet the positive integer limit; Equation (16) is a 0-1 decision variable constraint; The dynamic fuel replenishment model includes the following set: , Indicates the assembly point at the port of call; The parameters in the dynamic fuel replenishment model include: Indicates that the ship is scheduled to be in port. i The time window range, in hours; Indicates that the ship is Planned sailing time for a segment of the voyage, in hours; Indicates the arrival / departure of a ship Hong Kong time, in hours; This indicates the maximum capacity of a ship's fuel tanks, in tons. Indicates that the ship is Fuel ordering points in Hong Kong, unit: tons; Indicates that the ship is Maximum fuel level at Hong Kong, unit: tons; Indicates that the ship is The range of speeds along a route, in knots; Indicates carbon emission factor / sulfur emission factor; express Carbon / sulfur emission limits within the ECA segment, in tons; Represents a 0-1 coefficient, when the ship is... If the flight segment is outside the ECA, then ,otherwise ; This represents the total operating cost of all vessels, in US dollars. This represents the total time penalty cost for all vessels, in US dollars. This represents the total fuel replenishment cost for all vessels, in US dollars. This represents the total container inventory cost for all vessels, in US dollars. Ships in Planned speed on a segment of the voyage, in knots; Ships in Extreme speed deviation on a flight segment, in knots; The decision variables in the dynamic fuel replenishment model include: Represents a 0-1 variable; if the ship is... If the fuel is in Hong Kong, the value is 1; otherwise, it is 0. Indicates that the ship is Hong Kong refueling volume, unit: tons; Indicates that the ship is Actual speed outside / inside the ECA on the route segment, in knots; This indicates the number of ships deployed on the route, in units of: vessels.

[0019] In a specific embodiment, the total operating cost of the ship in the dynamic fuel replenishment model disclosed in this invention Total time penalty cost for ships Total fuel supply cost of ships and the total container inventory cost of the ship The calculation process is as follows: Total operating cost of all vessels described in this application The expression is: (17) in, This represents the weekly fixed cost per vessel, in US dollars. The ships sail for 168 hours per week, and the number of ships deployed on the route is [number missing]. Calculated using formula (18): (18) in, Indicates that the ship is Port stay time, in hours; ship stay time at port. Planned sailing time on the voyage segment Calculated using formula (19): (19) in, Indicates that the ship is Planned sailing time outside the ECA segment, in hours; Indicates that the ship is Planned sailing time within the ECA segment, in hours; Ships in Planned sailing time outside ECA segment Calculated using formula (20): (20) Ships in Planned sailing time within the ECA segment Calculated using formula (21): (twenty one) in, Indicates that the ship is Distance traveled outside the ECA (Electronic Control Area) during a voyage, in nautical miles; Indicates that the ship is Distance within the ECA segment of a voyage, in nautical miles; Indicates that the ship is Planned speed outside the ECA segment, in knots; Indicates that the ship is Planned speed within the ECA segment, in knots.

[0020] The total time penalty cost of the vessel The expression is: (twenty two) in, Indicates that the ship is Penalty cost per unit time when delays occur in Hong Kong, in US dollars; Indicates that the ship is scheduled to... Latest time in Hong Kong, unit: hour; Ship departs Hong Kong time Calculated using formula (23): (twenty three) in, Indicates that the ship is scheduled to... The earliest time in Hong Kong, in hours.

[0021] Furthermore, the total fuel refueling cost of the vessel The expression is: (twenty four) in, Indicates that the ship is Port fuel supply costs, in US dollars; Ships in Port fuel supply costs Calculated using formula (25): (25) in, Indicates that the ship is Fixed cost for refueling in Hong Kong, unit: US dollars per refueling; Indicates that the ship is Fuel price per unit at Hong Kong refueling site, in US dollars per ton; Ships in Hong Kong's fuel consumption Calculated using formula (26): (26) in, Indicates the arrival of the ship Fuel inventory levels at port, in tons; The value of is calculated by formula (27): (27) in, Represents an arbitrarily large positive number; This indicates the worst-case fuel consumption of a liner on a specific voyage segment; Indicates the ship has left. Fuel inventory levels at port, in tons; Fuel consumption of a ship under worst-case conditions in a specific voyage segment Calculated using formula (28): (28) in, Indicates that the ship is Extreme speed deviation on a flight segment, in knots; Ships in Total fuel consumption during the voyage segment Calculated using formula (29): (29) in, Indicates that the ship is Fuel consumption outside the ECA segment on the flight segment; Indicates that the ship is Fuel consumption within the ECA segment of the flight; Ships in Fuel consumption outside ECA on flight segment Calculated using formula (30): (30) Ships in Fuel consumption within the ECA segment Calculated using formula (31): (31) in, Indicates that the ship is Fuel consumption rate function outside ECA on the flight segment; Indicates that the ship is Fuel consumption rate function within the ECA segment of the flight; Ships in Fuel consumption rate function outside ECA on flight segment Calculated using formula (32): (32) Ships in Fuel consumption rate function within the ECA segment Calculated using formula (33): (33) in, This is the fuel consumption coefficient; Ships in Total fuel consumption during the voyage segment Ships leaving Fuel inventory levels at Hong Kong time Ship arrival Fuel inventory levels at Hong Kong time And the ship's fuel consumption under worst-case conditions in a specific voyage. The relationship is: (34) (35).

[0022] Total container inventory cost of all ships expression: (36) in, Indicates that the ship is Inventory cost per container per unit time on a shipping segment, in US dollars per hour; Indicates that the ship is Container volume transported on a shipping segment, in TEUs.

[0023] This application establishes a liner fuel replenishment strategy model considering speed deviation under emission control areas. Taking into account the frequent occurrence of speed deviation in actual shipping operations, a time window constraint is incorporated into the model. Furthermore, considering the impact of fuel price fluctuations and the actual fuel inventory on fuel consumption, a dynamic fuel replenishment strategy based on inventory management is proposed, enabling dynamic optimization and real-time response of the fuel replenishment strategy. This method can effectively reduce the total operating cost of liner shipping, improve fuel utilization and arrival reliability, and provide scientific decision support for liner operations in the context of green shipping. Meanwhile, this invention constructs a dynamic correlation model between speed deviation and fuel consumption, enabling accurate prediction and optimization of fuel replenishment costs, effectively reducing additional fuel consumption caused by speed uncertainty. This method achieves integrated optimization of refueling port selection, refueling volume decisions, and speed adjustments, improving the economy and environmental friendliness of replenishment strategies. Furthermore, by incorporating oil price data and demand forecasts, this method establishes a dynamic fuel replenishment adjustment mechanism, allowing ships to flexibly choose refueling times and ports, utilizing low oil price windows to reduce overall replenishment costs and enhance the market adaptability of operational strategies. It quantifies the impact of extreme speed deviations on fuel costs and reliability, providing liner companies with decision-making basis for speed planning and deviation control, ensuring on-time arrival rates while controlling total costs.

[0024] like Figure 2 As shown, this application uses an improved genetic algorithm with a repair operator to optimize the dynamic fuel replenishment model and obtain the optimized fuel replenishment results for liner ships. The specific solution process includes the following steps: Step 600: Input the relevant parameter values ​​for population size, crossover probability, mutation probability, maximum number of iterations, maximum sailing speed, and minimum sailing speed, and perform the encoding operation to randomly generate the initial population; Specifically, this application inputs parameters such as population size, crossover probability, mutation probability, maximum number of iterations, maximum speed, and minimum speed based on the actual problem, and performs encoding operations to randomly generate initial population individuals. This application, considering the characteristics of refueling strategies, selects a real-number encoding method based on ship speed for the encoding operation. Due to the existence of ports and ECA... Figure 3 In addition to the different fuels used, the coding of the same route segment also needs to be considered. In case (1), both ports and the entire route segment are located within the ECA, and the ship needs to use the more expensive MGO fuel when sailing in this section. In case (2), neither port nor the entire route segment is within the ECA, and the ship only needs to use LSFO fuel when sailing in this section. In case (3), only two ports are within the ECA and the route segment is not. In case (4), only one port is within the ECA. Therefore, in these two cases, the ship needs to use MGO fuel within the ECA and LSFO fuel outside the ECA.

[0025] Therefore, in view of the above, this application adopts a multi-layer coding method to encode the ship speed. The length of each chromosome is the number of ports of the specified liner route. The first layer of coding is the ship's speed outside the ECA. The second layer of coding is the ship's speed inside the ECA (if a port does not have an ECA, the speed of the ECA corresponding to that port is recorded as 0). The third layer of coding indicates whether the ship refuels at that port. If it refuels, it is 1; otherwise, it is 0. Figure 4 A chromosome sample is shown.

[0026] Figure 4 The chromosome in the diagram represents the route's passage through five ports of call. The third segment is entirely within the ECA (Extended Cautionary Area). The speeds outside the ECA in each of the other segments are 18 knots, 17 knots, 23 knots, and 22 knots, respectively. Except for the second segment, which does not pass through the ECA, the speeds within the corresponding ECA segments are 16 knots, 15 knots, 18 knots, and 20 knots, respectively. On this route, the ship will refuel at the third and fifth ports of call. Through multiple iterations of the algorithm, the optimal decoding scheme that meets the model constraints is selected, thereby determining the optimal refueling strategy for this route.

[0027] Step 601: Check each individual in the initial population in turn to determine whether it meets the existence requirements of ECA and the speed requirements of ECA emission limits. If it meets the requirements, proceed to the next step. If it does not meet the requirements, repair the individual. Specifically, individuals in the initial population are encoded using a three-layer coding method. The first layer of coding represents the speed outside the ECA, the second layer of coding represents the speed inside the ECA, and the third layer of coding represents whether refueling is required. The length of the chromosome represents the number of ports on the specified liner route. Repairing individuals within a population involves the following steps: Step 6010: Check each entity in turn to determine whether the first layer code and the second layer code meet the existence requirements of the emission control area. If both meet the requirements, proceed to step 6012; otherwise, proceed to step 6011. Step 6011: If the first layer code or the second layer code does not meet the requirements, perform layer-by-layer code replacement; the replacement process is as follows: if the first layer code should not contain a speed outside the ECA, then replace the gene with 0; if the first layer code should not be 0 but is actually 0, then randomly select a gene that meets the requirements of the flight segment for replacement; if the second layer code does not meet the requirements, then randomly select a gene that meets the requirements of the emission control area to replace the original gene. Step 6012: Check each individual in turn to determine whether the second-level code meets the restrictive requirements of the emission control area, that is, whether it meets the carbon emission limit and sulfur emission limit. If both are met, proceed to step 6014; otherwise, proceed to step 6013. Step 6013: Randomly select a gene that represents the carbon and sulfur emission limits for an emission control zone and replace the original gene; Step 6014: Replace the original chromosome with the repaired chromosome and reintroduce it into the population to form an initial population that meets the constraints.

[0028] Figure 5 This demonstrates the repair process of the repair operator on inappropriate chromosomes: from Figure 5 As can be seen, in step one, the repair operator detected problems in the first two layers of coding of the chromosome. First, the first repair is initiated, replacing the gene in segment 3 of the first layer of coding with 0, and simultaneously replacing the gene in segment 2 of the second layer of coding with 0, with 24 replaced with 0. Next, in step three, it is found that segment 3 of the second layer of coding does not meet the emission control area's restrictive requirements. Therefore, the second repair is initiated, randomly selecting a velocity gene 15 that corresponds to the emission control area's carbon and sulfur emission limits to replace the original velocity gene 19, making it compliant with the emission control area's requirements.

[0029] Step 602: Calculate the fitness of each individual in the repaired initial population to obtain the fitness value of each individual. The fitness calculation formula is: (37) in, Indicates the first The fitness value of each individual This represents the total operating cost corresponding to that individual; Specifically, in genetic algorithms, fitness represents the degree to which an individual adapts to a specific problem environment; it can also be understood as the individual's quality, and is usually directly related to the problem's objective function. A higher fitness indicates that the individual is of better quality, more adapted to the current problem environment, and therefore more suitable for solving this problem. In this paper, the objective function is the liner company's total weekly operating cost. The smaller the objective function, the higher the quality of the solution represented by that individual, meaning the liner company's total operating cost is minimized. Therefore, there is a negative correlation between total operating cost and the fitness function value; thus, the fitness function in this paper is the reciprocal of the total operating cost. Step 603: After the fitness value calculation is completed, select the individual with the highest fitness value in the current population as the current optimal individual, and record this current individual as... Output the fitness of the current individual. ; Step 604, Initial Iteration Count ; Step 605: Determine the current generation number of the population. With maximum number of iterations The relationship, when the conditions are met If the condition is not met, proceed to step 606; if the condition is not met... Then proceed to step 613; Step 606: Perform selection, crossover, and mutation operations sequentially on the current population to obtain new population individuals; Specifically, step 606 includes the following processes: Step 6060: Adopt an elite preservation strategy for the current population, and divide the current population according to its fitness value. Sort and retain the top fitness values. Individuals; a tournament selection strategy is used for the current population, with each selection... Individuals are grouped into groups, and the individual with the highest fitness in the group is added to a new population. This process is repeated until the individual with the highest fitness is found. Individuals; a new individual generation strategy is adopted for the current population to randomly generate individuals. The selection operator in this application combines a tournament selection strategy and an elite retention strategy. The aim is to select high-performing individuals from the current population to enter a new population so they can act as parents and produce offspring, while simultaneously preserving population diversity. In the tournament selection process, several individuals are randomly selected and their fitness is compared. Individuals with higher fitness are selected and included in the new population. This process is repeated until a certain number is reached. The elite retention strategy retains the individuals with the highest fitness in the original population, ensuring the population evolves towards higher fitness. In this application, the selection operation of the genetic algorithm consists of two parts: a tournament selection strategy and an elite retention strategy. Furthermore, to ensure population diversity, drawing inspiration from multi-population genetic algorithms, a random generation strategy for new individuals is added, providing a second channel for new individual generation in each algorithm iteration.

[0030] Step 6061: Perform crossover operation on the population after the selection operation until the number of offspring individuals reaches the set requirement of the population size to obtain the population after crossover operation. This application employs a single-point crossover method for chromosome crossover. During the execution of the genetic algorithm, two individuals are randomly selected from the population as parents. Simultaneously, a random number is generated within the interval [0, 1]. If this random number is less than a pre-defined crossover rate, the selected chromosome pair will undergo crossover, with the crossover position determined by rolling a random number. The specific operation is as follows: Figure 6 As shown, the chromosomes of two parent individuals are broken at the crossover point, and then gene segments after the breakpoint are exchanged to produce offspring. This crossover operation is repeated until the number of offspring meets the set population size requirement. Figure 6 As can be seen, by randomly selecting a number between 1 and 15, which is 8, the crossover position is the eighth gene, which is the third gene from the left in the second layer of coding. Starting from the crossover position, the two parent chromosomes cross over, exchanging all subsequent genes, thus producing two offspring chromosomes.

[0031] Step 6062: Traverse all individuals in the population after the crossover operation. For the currently selected individual, randomly generate a random number in the interval [0, 1]. If the random number is less than the given mutation rate, then perform a uniform mutation operation on the chromosome to cause it to mutate. The mutation position is randomly determined, thereby obtaining a new population after the selection operation, crossover operation and mutation operation.

[0032] Mutation operations randomly alter an individual's genes with a certain probability, simulating the gene mutation process of biological evolution. They are often placed after crossover to enhance population diversity. This application employs uniform mutation to perform mutation operations on chromosomes. Uniform mutation assigns an independent mutation probability to each gene position in an individual's coding string. When the probability condition is met, that gene position will be replaced by a new gene randomly generated within a given range. This allows for a broad search of the solution space, preventing premature convergence of the population. Figure 7 The process of uniform chromosome mutation is presented. The diagram shows that mutations are triggered at two locations: the third gene in the first layer and the second gene in the second layer. In the first layer, the speed outside the ECA on flight segment 3 changes from 25 to 21; in the second layer, the speed inside the ECA on flight segment 2 changes from 20 to 24; the third layer remains unchanged. All individuals in the population are traversed. For the currently selected individual, a random value is generated within the interval [0, 1]. If the generated random number is greater than or equal to the pre-defined mutation rate, the chromosome remains unchanged; otherwise, if the random number is less than the given mutation rate, the chromosome mutates, and the mutation location is randomly determined. After determining the mutation location, uniform mutation is applied to the chromosome segment, and the mutated individual replaces the original individual.

[0033] Step 607: Update and merge the newly obtained individuals in the population to form a new population; Step 608: Check each individual in the new population in turn to determine whether it meets the existence requirements of ECA and the speed requirements of ECA emission limits. If it meets the requirements, proceed to the next step. If it does not meet the requirements, repair the individual. The specific process is the same as step 601 and will not be described in detail. Step 609: Calculate the fitness of each individual in the repaired new population, obtain the fitness value of each individual, and record the best individual in the new population as... and output the fitness of the individual. ; Step 610: Determine the fitness of the new population. Is the fitness of the previous population less than that of the previous population? If yes, proceed to step 611; otherwise, proceed to step 612. Step 611: After performing a variable neighborhood perturbation on the current population, return to step 607; Specifically, the neighborhood perturbation process involves randomly generating a random number in the interval [0, 1], and selecting different perturbation types based on the magnitude of this random number. When the random number is in [0, 0.5], strategy N1 is selected; when the random number is in [0.5, 0.8], strategy N2 is selected; and when the random number is in [0.8, 1], strategy N3 is selected. The specific strategies and operations are shown in Table 1.

[0034] Table 1 Disturbance Strategies

[0035] As shown in Table 1, strategy N1 is a single-gene fine-tuning strategy, which involves adding or subtracting one section from a speed gene, or swapping 0 and 1 in a refueling decision; strategy N2 is a same-layer exchange strategy, which involves exchanging two genes in a certain layer to achieve perturbation; strategy N3 is to regenerate the gene values ​​of a certain layer to achieve strong perturbation of the chromosome.

[0036] Step 612: Update the current best individual to And update the iteration count: Then return to the judgment operation step 605; Step 613: Output the currently determined optimal individual. Then, perform decoding operations to obtain the optimal solution obtained by the current algorithm.

[0037] This application addresses the complexity and nonlinearity of the fuel replenishment strategy problem in liner shipping by designing an improved genetic algorithm based on a repair operator. First, an initial population is generated using a multi-layer chromosome encoding method, and a gene repair operator is designed in conjunction with constraints to ensure the feasibility of the initial solution. Second, multiple selection strategies (tournament selection and elite retention) are employed for individual selection, and a new individual generation strategy is introduced to generate new individuals during algorithm execution, effectively maintaining the richness and diversity of the population's genes. Then, a variable neighborhood perturbation method is introduced; when the population shows no improvement for several consecutive generations, a perturbation strategy is triggered, and perturbation measures of varying intensities are implemented based on different probabilities. Finally, by setting a termination condition, the algorithm is ensured to converge to a relatively optimal solution within a reasonable time, providing an effective solution method for subsequent numerical examples and result analysis.

[0038] Example Experiments and Result Analysis The following calculations use actual shipping routes operated by liner companies as the basic scenario. On the one hand, real data related to these routes is collected through various channels; on the other hand, supplementary data is randomly generated according to reasonable rules to construct a complete dataset. Through calculation and analysis of this example, the applicability and effectiveness of the constructed model in handling practical problems are tested, thereby evaluating whether the model can accurately reflect the real situation and provide reliable support for decision-making. For the model of minimizing the total operating cost of liner companies under emission control area conditions, a calculation example analysis is conducted based on the CV5 container liner route of China COSCO Shipping Corporation Limited in the near-sea case, and on the FAL2 container liner route of China COSCO Shipping Corporation Limited in the ocean-going case.

[0039] Example 1: Analysis of Near-Ocean Shipping Routes Example 1 uses COSCO Shipping Container Lines Co., Ltd. as an example. In the near-sea route case study, the Southeast Asia and South Asia route CV5 is selected. This route has three ports of call (each port of call is counted as one port of call), in the following order: Shanghai Port, Xiamen Port, Saigon Port, and Shanghai Port again, for a total of three segments. Shanghai Port and Xiamen Port are both located within the ECA area. To fully verify the applicability of the model constructed in this paper in real shipping scenarios, an in-depth survey of actual shipping conditions and a systematic study of relevant literature were conducted. Data was selected and used, including both fixed data obtained based on actual conditions and data randomly generated according to certain rules.

[0040] The liner company allocates vessels of the same type with a capacity of 10,000 TEU each to operate on this specific route according to a pre-established timetable. The weekly operating cost per vessel is US$150,000. This paper sets the daily fuel consumption coefficient for the vessels based on existing literature data. It is 0.004. The value is 3.3, and the minimum and maximum speeds for vessels on this route are 15 knots and 25 knots, respectively. The relevant parameters for the ports of call on the CV5 route are shown in Table 2. Table 2. CV5 Route Related Data

[0041] Table 2 shows that the data for the CV5 route includes the distance (nautical miles), fuel price (USD / ton), earliest arrival time (hours), latest arrival time (hours), and port dwell time (hours) for each segment. The route distance is sourced from the official website of a liner company, the fuel price is based on international oil prices, and the time information is randomly generated based on actual demand and port loading / unloading efficiency. Additionally, this paper, referencing existing literature, summarizes the values ​​of other parameters in the model in Table 3. Table 3 Model-related parameters

[0042] As shown in Table 3, the specific parameters of the model in this application include the initial inventory level of ship fuel (tons), the maximum fuel capacity of the ship (tons), the maximum container loading capacity of the ship (tons), the inventory cost per unit container (USD / TEU / hour), the extreme value of ship speed deviation (knots), the fixed cost of ship refueling (USD / time), the unit time penalty cost of ship delay (USD / hour), as well as carbon emission factors and sulfur emission factors.

[0043] This application employs multiple methods to solve the model. All software runs on a Windows 11 system, and the computer hardware configuration is an AMD Ryzen 7 5800H CPU 3.20 GHz and 16GB RAM.

[0044] Analysis results of near-ocean shipping routes: For the CV5 route, this application uses both the commercial Gurobi software and the improved genetic algorithm with the repair operator disclosed in this application to solve the problem simultaneously. The algorithm code is written in MATLAB, version R2018b, and the Gurobi solver version is 10.0.3.

[0045] After multiple experiments, the genetic algorithm was tested with 2000 iterations, a population size of 500, a crossover probability of 0.7, a mutation probability of 0.01, and a tournament selection of 4 individuals. The results were compared in five aspects: solution time (seconds), total operating cost (USD ten thousand), number of vessels, average vessel speed (knots), and fuel consumption (tons). Specific results are shown in Table 4. Table 4 Comparison of CV5 route calculation results

[0046] As shown in Table 4, for near-sea routes like CV5, the time taken by the two methods is similar, both taking only a few seconds to produce results quickly. Regarding total operating costs, the improved genetic algorithm calculates $2.411 million, only $0.9 million higher than the Gurobi solver's result of $2.410 million, a deviation of only 0.04%, indicating negligible discrepancies. The two methods yield identical results for vessel deployment and refueling, not affecting vessel configuration. Furthermore, the average speed calculated by both methods for each port is almost identical. Overall, in small-scale near-sea applications, the results of the two methods are nearly identical, demonstrating the effectiveness of the improved genetic algorithm presented in this paper.

[0047] Example 2: Analysis of Ocean Shipping Routes For ocean shipping routes, this paper uses COSCO Shipping Container Lines' Asia-Europe route FAL2 as an example for analysis. The algorithm code is still written in MATLAB, version R2018b. Based on a pre-determined timetable with the port, the liner company allocated a series of vessels of the same type, each with a capacity of 10,000 TEU, to operate on the FAL2 route. Relevant parameters for this route are shown in Table 5. The route distance is from the official website of COSCO Shipping Corporation Limited, fuel prices are based on international oil prices, and time information is randomly generated based on actual demand and port loading / unloading efficiency. The vessel parameters for ocean shipping routes in this example are consistent with those for near-ocean shipping routes.

[0048] Table 5. Data related to the FAL2 route

[0049] As shown in Table 5, the FAL2 route has twelve ports of call, namely: Tianjin New Port, Dalian Port, Qingdao Port, Shanghai Port, Ningbo Port, Singapore Port, Piraeus Port, Rotterdam Port, Hamburg Port, Antwerp Port, Rotterdam Port, Shanghai Port, and Tianjin New Port, totaling 12 segments. The relevant parameters for each port of call include the distance (nautical miles), fuel price (USD / ton), earliest arrival time (hours), latest arrival time (hours), and port dwell time (hours) for each segment.

[0050] Based on the data above, to verify the effectiveness of the algorithm designed in this paper, for the Asia-Europe route FAL2, both the traditional genetic algorithm and the improved genetic algorithm based on the repair operator were used to calculate the model. The calculation results are compared in the following six aspects: solution time (seconds), total operating cost (USD ten thousand), number of vessels (ships), vessel speed (knots), average speed (knots), and total refueling volume (tons). The comparison of the results under the two algorithms is shown in Table 6: Table 6 Comparison of results under different algorithms

[0051] As shown in Table 6, compared with the traditional genetic algorithm, the improved genetic algorithm based on the repair operator has little difference in solution time, but a significant difference in total operating cost. The total operating cost of the traditional genetic algorithm is US$5.464 million, while that of the improved genetic algorithm is US$5.319 million, representing a reduction of US$145,000. There is no difference in the number of vessels deployed, but the average speed obtained by the traditional genetic algorithm is 20.3 knots, while that of the improved genetic algorithm is 19.4 knots, a reduction of 0.9 knots. In terms of total refueling, the traditional genetic algorithm requires 7,926 tons, while the improved genetic algorithm requires 6,992 tons, a reduction of 934 tons. Therefore, the improved genetic algorithm solution model designed in this paper can significantly reduce the total operating cost of liner companies, while optimizing vessel speed and significantly reducing total refueling, thereby reducing fuel replenishment costs.

[0052] In addition to comparing the algorithms, this paper also compares the dynamic refueling strategy with the traditional refueling strategy, providing a comparison in the following five aspects: total operating cost (USD ten thousand), fuel replenishment cost (USD ten thousand), number of vessels deployed, average vessel speed (knots), and refueling volume (tons). Table 7 shows the comparison of the results between the two refueling strategies: Table 7 Comparison of results under different fuel replenishment strategies

[0053] As shown in Table 7, within a single operating cycle, the total operating cost of the vessel under the traditional refueling strategy is US$5.467 million, while that under the dynamic refueling strategy is US$5.37 million, a reduction of US$97,000. Regarding fuel replenishment costs, the dynamic refueling strategy also shows a significant reduction, with the traditional strategy costing US$4.233 million and the dynamic strategy costing US$3.766 million, saving US$467,000. In terms of fleet size, both refueling strategies require 5 vessels, indicating that the dynamic refueling strategy optimizes costs without affecting capacity allocation. Regarding average speed, the traditional refueling strategy achieves an average speed of 20.7 knots, while the dynamic refueling strategy achieves 19.9 knots, a reduction of 0.8 knots. Furthermore, compared to the concentrated, one-time refueling of the traditional strategy, the dynamic refueling strategy distributes refueling volume more dispersedly, reflecting its ability to flexibly adjust refueling ports and quantities according to actual needs, thereby improving fuel efficiency. In conclusion, the dynamic refueling strategy achieves cost savings and resource optimization while ensuring vessel operational capacity.

[0054] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing liner fuel replenishment considering speed deviations under emission control areas, characterized in that, Includes the following steps: Step 1: Based on the fixed cost of each ship in each cycle on the liner route and the number of ships configured on the liner route, establish an expression for the total operating cost of all ships on the liner route. Step 2: Based on the planned port time window of the vessel in each segment of the liner route, the vessel's stay time in each port, the vessel's departure time, and the unit time penalty cost when the vessel is delayed in each port, establish an expression for the total time penalty cost of the vessel. Step 3: Based on the ship's actual speed outside the ECA and the actual speed inside the ECA on each leg of the journey, the fuel consumption rate function of the liner on each leg of the journey, the fixed cost of refueling at each port, the amount of fuel refueled at each port, and the unit fuel price at each port, establish an expression for the ship's total fuel supply cost. Step 4: Based on the inventory cost per unit container per unit time of the ship in each segment, the container transport volume of the ship in each segment, the sailing distance of the ship outside the ECA in each segment, the sailing distance of the ship inside the ECA in each segment, the actual sailing speed of the ship outside the ECA in each segment, and the actual sailing speed of the ship inside the ECA in each segment, establish the expression for the total container inventory cost of the ship. Step 5: Establish a dynamic fuel replenishment model based on the expressions for the total operating cost of all ships, the total time penalty cost of ships, the total fuel replenishment cost of ships, and the total container inventory cost of ships. Step 6: The improved genetic algorithm based on the repair operator is used to optimize the dynamic fuel replenishment model and obtain the optimized fuel replenishment results for liner ships.

2. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 1, characterized in that: The objective function of the dynamic fuel replenishment model is: （1） The constraints of the dynamic fuel replenishment model are: （2） （3） （4） （5） （6） （7） （8） （9） （10） （11） （12） （13） （14） （15） （16） In this equation, (2) represents the actual speed of the ship; and (3) represents the time constraint range of the ship, i.e., the time from which the ship arrives at its destination. Hong Kong time is from The time of departure from the port plus the ship's time The sailing time of the segment; Equation (4) represents the time the ship spends in the segment. The carbon emissions of the port should not exceed the carbon emission limits set by the ECA for that segment of the voyage; Equation (5) indicates that the ship's carbon emissions in the port should not exceed the limits set by the ECA for that segment of the voyage. The sulfur emissions at the port should not exceed the ECA's limit on sulfur emissions for that segment of the voyage; Equations (6) and (7) represent limits related to fuel capacity, the former indicating the limits for the ship's fuel capacity. The fuel ordering point at a port must not exceed the port's maximum fuel refueling level, which indicates the level at which a vessel is permitted to refuel. The maximum refueling level in the port shall not exceed the maximum capacity of the fuel tank; Equations (8) and (9) indicate that the speed of the vessel outside / inside the ECA shall not exceed the speed at which the vessel is in the port. The speed range of the segment; Equation (10) indicates the speed range of the ship due to the existence of the time window. The port must meet time constraints; Equation (11) represents the influence of internal and external uncertainties encountered by the ship during navigation, which will cause the speed to deviate, and the speed limit after the deviation; Equation (12) represents the ship's speed during navigation. Speed ​​limits for the segment; Equation (13) indicates the speed limit of the vessel in the segment. The relationship between the planned speed of the segment and the planned speed outside / inside the ECA; Equation (14) indicates that the amount of fuel added to the ship must not be negative; Equation (15) indicates that the number of ships assigned to the route must meet the positive integer limit; Equation (16) is a 0-1 decision variable constraint; The dynamic fuel replenishment model includes the following set: , Indicates the port of call for assembly; The parameters in the dynamic fuel replenishment model include: Indicates that the ship is scheduled to be in port. The time window range, in hours; Indicates that the ship is Planned sailing time for a segment of the voyage, in hours; Indicates the arrival / departure of a ship Hong Kong time, in hours; This indicates the maximum capacity of a ship's fuel tanks, in tons. Indicates that the ship is Fuel ordering points in Hong Kong, unit: tons; Indicates that the ship is Maximum fuel level at Hong Kong, unit: tons; Indicates that the ship is The range of speeds along a route, in knots; Indicates carbon emission factor / sulfur emission factor; express Carbon / sulfur emission limits within the ECA segment, in tons; Represents a 0-1 coefficient, when the ship is... If the flight segment is outside the ECA, then ,otherwise ; This represents the total operating cost of all vessels, in US dollars. This represents the total time penalty cost for all vessels, in US dollars. This represents the total fuel replenishment cost for all vessels, in US dollars. This represents the total container inventory cost for all vessels, in US dollars. Ships in Planned speed on a segment of the voyage, in knots; Ships in Extreme speed deviation on a flight segment, in knots; The decision variables in the dynamic fuel replenishment model include: Represents a 0-1 variable; if the ship is... If the fuel is in Hong Kong, the value is 1; otherwise, it is 0. Indicates that the ship is Hong Kong refueling volume, unit: tons; Indicates that the ship is Actual speed outside / inside the ECA on the route segment, in knots; This indicates the number of ships deployed on the route, in units of: vessels.

3. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 2, characterized in that: The total operating cost of all the vessels The expression is: （17） in, This represents the weekly fixed cost per vessel, in US dollars. The ships sail for 168 hours per week, and the number of ships deployed on the route is [number missing]. Calculated using formula (18): （18） in, Indicates that the ship is Port stay time, in hours; ship stay at Planned sailing time on the voyage segment Calculated using formula (19): （19） in, Indicates that the ship is Planned sailing time outside the ECA segment, in hours; Indicates that the ship is Planned sailing time within the ECA segment, in hours; Ships in Planned sailing time outside ECA segment Calculated using formula (20): （20） Ships in Planned sailing time within the ECA segment Calculated using formula (21): （21） in, Indicates that the ship is Distance traveled outside the ECA (Electronic Control Area) during a voyage, in nautical miles; Indicates that the ship is Distance within the ECA segment of a voyage, in nautical miles; Indicates that the ship is Planned speed outside the ECA segment, in knots; Indicates that the ship is Planned speed within the ECA segment, in knots.

4. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 3, characterized in that: The total time penalty cost of the vessel The expression is: （22） in, Indicates that the ship is Penalty cost per unit time when delays occur in Hong Kong, in US dollars; Indicates that the ship is scheduled to... Latest time in Hong Kong, unit: hour; Ship departs Hong Kong time Calculated using formula (23): （23） in, Indicates that the ship is scheduled to... The earliest time in Hong Kong, in hours.

5. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 4, characterized in that: The total fuel replenishment cost of the vessel The expression is: （24） in, Indicates that the ship is Port fuel supply costs, in US dollars; Ships in Port fuel supply costs Calculated using formula (25): （25） in, Indicates that the ship is Fixed cost for refueling in Hong Kong, unit: US dollars per refueling; Indicates that the ship is Fuel price per unit at Hong Kong refueling site, in US dollars per ton; Ships in Hong Kong's fuel consumption Calculated using formula (26): （26） in, Indicates the arrival of the ship Fuel inventory levels at port, in tons; The value of is calculated by formula (27): （27） in, Represents an arbitrarily large positive number; This indicates the worst-case fuel consumption of a liner on a specific voyage segment; Indicates the ship has left. Fuel inventory levels at port, in tons; Fuel consumption of a ship under worst-case conditions in a specific voyage segment Calculated using formula (28): （28） in, Indicates that the ship is Extreme speed deviation on a flight segment, in knots; Ships in Total fuel consumption during the voyage segment Calculated using formula (29): （29） in, Indicates that the ship is Fuel consumption outside the ECA segment on the flight segment; Indicates that the ship is Fuel consumption within the ECA segment of the flight; Ships in Fuel consumption outside ECA on flight segment Calculated using formula (30): （30） Ships in Fuel consumption within the ECA segment Calculated using formula (31): （31） in, Indicates that the ship is Fuel consumption rate function outside ECA on flight segments; Indicates that the ship is Fuel consumption rate function within the ECA segment of the flight; Ships in Fuel consumption rate function outside ECA on flight segment Calculated using formula (32): （32） Ships in Fuel consumption rate function within ECA on flight segment Calculated using formula (33): （33） in, This is the fuel consumption coefficient; Ships in Total fuel consumption during the voyage segment Ships leaving Fuel inventory levels at Hong Kong Ship arrival Fuel inventory levels at Hong Kong And the ship's fuel consumption under worst-case conditions in a specific voyage. The relationship is: （34） （35）。 6. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 5, characterized in that: Total container inventory cost of all ships expression: （36） in, Indicates that the ship is Inventory cost per container per unit time on a shipping segment, in US dollars per hour; Indicates that the ship is Container volume transported on a shipping segment, in TEUs.

7. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 1, characterized in that: The improved genetic algorithm based on the repair operator optimizes the solution of the dynamic fuel replenishment model, including the following steps: Step 600: Input the relevant parameter values ​​for population size, crossover probability, mutation probability, maximum number of iterations, maximum sailing speed, and minimum sailing speed, and perform the encoding operation to randomly generate the initial population; Step 601: Check each individual in the initial population in turn to determine whether it meets the existence requirements of ECA and the speed requirements of ECA emission limits. If it meets the requirements, proceed to the next step. If it does not meet the requirements, repair the individual. Step 602: Calculate the fitness of each individual in the repaired initial population to obtain the fitness value of each individual. The fitness calculation formula is: （37） in, Indicates the first The fitness value of each individual This represents the total operating cost corresponding to that individual; Step 603: After the fitness value calculation is completed, select the individual with the highest fitness value in the current population as the current optimal individual, and record this current individual as... Output the fitness of the current individual. ; Step 604, Initial Iteration Count ; Step 605: Determine the current generation number of the population. With maximum number of iterations The relationship, when the conditions are met If the condition is not met, proceed to step 606; if the condition is not met... Then proceed to step 613; Step 606: Perform selection, crossover, and mutation operations sequentially on the current population to obtain new population individuals; Step 607: Update and merge the newly obtained individuals in the population to form a new population; Step 608: Check each individual in the new population in turn to determine whether it meets the existence requirements of ECA and the speed requirements of ECA emission limits. If it meets the requirements, proceed to the next step. If it does not meet the requirements, repair the individual. Step 609: Calculate the fitness of each individual in the repaired new population, obtain the fitness value of each individual, and record the best individual in the new population as... and output the fitness of the individual. ; Step 610: Determine the fitness of the new population. Is the fitness of the previous population less than that of the previous population? If yes, proceed to step 611; otherwise, proceed to step 612. Step 611: After performing a variable neighborhood perturbation on the current population, return to step 607; Step 612: Update the current best individual to And update the iteration count: Then return to the judgment operation step 605; Step 613: Output the currently determined optimal individual. Then, perform decoding operations to obtain the optimal solution obtained by the current algorithm.

8. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 7, characterized in that: Individuals in the initial population are coded using a three-layer coding method. The first layer of coding represents the speed outside the ECA, the second layer represents the speed inside the ECA, and the third layer represents whether refueling is required. The length of the chromosome represents the number of ports on the specified liner route. Repairing individuals within a population involves the following steps: Step 6010: Check each entity in turn to determine whether the first layer code and the second layer code meet the existence requirements of the emission control area. If both meet the requirements, proceed to step 6012; otherwise, proceed to step 6011. Step 6011: If the first layer code or the second layer code does not meet the requirements, perform layer-by-layer code replacement; the replacement process is as follows: if the first layer code should not contain a speed outside the ECA, then replace the gene with 0; if the first layer code should not be 0 but is actually 0, then randomly select a gene that meets the requirements of the flight segment for replacement; if the second layer code does not meet the requirements, then randomly select a gene that meets the requirements of the emission control area to replace the original gene. Step 6012: Check each individual in turn to determine whether the second-level code meets the restrictive requirements of the emission control area, that is, whether it meets the carbon emission limit and sulfur emission limit. If both are met, proceed to step 6014; otherwise, proceed to step 6013. Step 6013: Randomly select a gene that represents the carbon and sulfur emission limits for an emission control zone and replace the original gene; Step 6014: Replace the original chromosome with the repaired chromosome and reintroduce it into the population to form an initial population that meets the constraints.

9. The liner fuel replenishment optimization method considering speed deviation under emission control areas according to claim 7, characterized in that: Step 606 includes the following steps: Step 6060: Adopt an elite preservation strategy for the current population, and divide the current population according to its fitness value. Sort and retain the top fitness values. Individuals; a tournament selection strategy is used for the current population, with each selection... Individuals are grouped into groups, and the individual with the highest fitness in the group is added to a new population. This process is repeated until the individual with the highest fitness is found. Individuals; a new individual generation strategy is adopted for the current population to randomly generate individuals. The new individuals; combine the elite-retained individuals, the tournament-selected individuals, and the newly generated individuals to form the population after the selection operation; Step 6061: Perform crossover operation on the population after the selection operation until the number of offspring individuals reaches the set requirement of the population size to obtain the population after crossover operation. Step 6062: Traverse all individuals in the population after the crossover operation. For the currently selected individual, randomly generate a random number in the interval [0, 1]. If the random number is less than the given mutation rate, then perform a uniform mutation operation on the chromosome to cause it to mutate. The mutation position is randomly determined, thereby obtaining a new population after the selection operation, crossover operation and mutation operation.

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