Fleet route allocation optimization method and system

Abstract

The invention provides a fleet route allocation optimization method and system, and the method comprises the steps: firstly obtaining ship data of each ship in a fleet and route data of each route, and taking the minimization of the total usage amount of biofuel of the fleet in a planned period and the minimization of the total economic loss caused by not meeting the maximum deployment number of the routes as targets; the method comprises the following steps: respectively establishing a first objective function and a second objective function under a plurality of constraint conditions which are established by taking a ship total number limit and a fuel consumption limit which are deployed in each ship route every year, a ship route change total number limit of a fleet in any year, and a CII grade standard limit of each ship as constraints; and constructing a multi-objective optimization mathematical model based on the first objective function and the second objective function, calculating the multi-objective optimization mathematical model by adopting a non-dominated sorting genetic algorithm to obtain a Pareto optimal solution set, and selecting a final fleet route allocation scheme according to the Pareto optimal solution set. And dual minimization of the total usage amount and the total economic loss of the biofuel is realized.

Description

Technical Field

[0001] This invention relates to the field of shipping management technology, specifically to a method and system for optimizing fleet route allocation. Background Technology

[0002] With increasing global concern about climate change, the International Maritime Organization (IMO) implemented the Operating Carbon Intensity Regulations (CII Regulations) in 2023. According to the CII Regulations, internationally operating vessels are classified into five categories: A, B, C, D, and E. A vessel cannot be rated D for three consecutive years or E in any year. If a vessel is rated D for three consecutive years or E in any year, it is deemed non-compliant and must take measures to upgrade its CII rating to C. Furthermore, according to the CII Regulations, the baseline for vessel rating decreases each year. This means that if a vessel maintains its current operating conditions without implementing any operational emission reduction measures, it will also be reclassified as E. Therefore, operating vessels need to use clean energy or implement energy-saving technological upgrades to avoid non-compliance.

[0003] In liner shipping companies, fleet scheduling is a complex process and a practical engineering problem. For example... Figure 1 As shown, a shipping company owns a total of V ships, which can be allocated to R routes, with allocation taking place annually. Ultimately, as... Figure 2 As shown, each route will be allocated V vessels. However, the number of vessels allocated to each route and the specific vessels allocated will vary each year. Vessels of the same type can be deployed to multiple routes. However, the port distances and planned speeds between routes differ, resulting in varying fuel consumption effects when deployed on different routes. Furthermore, each route has maximum and minimum requirements for the number of vessels deployed. For example, deploying fewer vessels to a particular route may lead to a sustained decline in overall service quality. Therefore, ensuring that routes meet maximum deployment requirements while minimizing economic impact is a critical issue.

[0004] Furthermore, even when deploying similar vessels to the same route, fuel consumption can vary due to differences in their fuel efficiency. For example, a refurbished vessel may exhibit better fuel economy compared to others. Therefore, deploying vessels to different routes has varying impacts, especially when considering the operational restrictions imposed by the International Maritime Organization's Carbon Intensity Index (CII) regulations. To meet annual CII requirements, the entire fleet operation must consider both vessels with poor and good fuel economy to ensure compliance and provide a solid foundation for subsequent fleet operations.

[0005] To improve CII (Carbon Intake Index) levels annually, biofuels can be used to reduce carbon emissions. However, biofuels are more expensive than conventional fuels. Therefore, minimizing the use of biofuels in the fleet has become an important objective.

[0006] In summary, most existing fleet scheduling and optimization methods focus on traditional economic objectives (such as cost minimization and profit maximization) or only consider static energy efficiency constraints, failing to systematically incorporate multiple factors into a unified optimization framework, including dynamic compliance requirements of CII regulations, the degradation of individual vessel fuel consumption performance and the effects of maintenance improvements, and the cost differences between biofuels and conventional fuels. This limitation makes it difficult for existing methods to support shipping companies in developing optimal fleet allocation schemes that balance compliance, economy, and operational feasibility under CII regulations. Therefore, there is an urgent need to develop a new optimization method to address the aforementioned complex decision-making problems involving multiple objectives and constraints. Summary of the Invention

[0007] To address the shortcomings of current fleet route optimization methods, such as the lack of consideration for CII regulations and the impact of changes in vessel fuel consumption performance, this invention provides a fleet route allocation optimization method. By considering the compliant layout of the fleet over the next few years under CII regulations, this method achieves a fleet route allocation scheme that minimizes CII compliance, biofuel usage, and economic losses, effectively reducing operating costs. This invention also relates to a fleet route allocation optimization system.

[0008] The technical solution of the present invention is as follows:

[0009] A method for optimizing fleet route allocation, characterized by comprising the following steps:

[0010] Data acquisition steps: Acquire ship data for each vessel in the fleet and route data for each route. The ship data includes the biofuel value required by the vessel in a given year; the route data includes the maximum number of vessels deployed on each route, the number of vessels deployed on each route in a given year, and the economic loss per vessel due to deploying one less vessel on a route.

[0011] The steps for establishing a multi-objective optimization mathematical model are as follows: The objectives are to minimize the total biofuel consumption of the fleet during the planning period and to minimize the total economic loss caused by failure to meet the maximum deployment number on routes. Under multiple constraints, including the annual deployment limit for each route, fuel consumption limits, the total number of route changes for the fleet in any year, and the CII rating compliance limit for each vessel, a first objective function is established based on the biofuel required by the vessel in a given year. A second objective function is established based on the maximum number of vessels deployed on the route, the number of vessels deployed on the route in a given year, and the economic loss per vessel. A multi-objective optimization mathematical model is then constructed based on the first and second objective functions.

[0012] Initial parent population construction steps: Construct an initial parent population consisting of multiple individuals, each individual representing an annual fleet route allocation scheme; the annual fleet route allocation scheme includes: randomly assigning ships that meet the minimum ship deployment number requirement for each route until all routes have reached the minimum ship deployment number requirement; then randomly assigning the remaining unassigned ships to routes that have not yet reached the maximum ship deployment number requirement until all remaining unassigned ships have been assigned.

[0013] Objective function value calculation steps: Calculate the first objective function value and the second objective function value corresponding to each individual in the initial parent population according to the first objective function and the second objective function respectively; and perform fast non-dominated sorting on all individuals in the initial parent population based on the calculated first objective function value and the second objective function value, thereby dividing the initial parent population into multiple first non-dominated levels arranged from high to low;

[0014] Temporary population generation steps: Based on the first non-dominated level and using the selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm, process the current parent population to generate the offspring population, merge the current parent population with the offspring population to form a temporary population; and calculate the first objective function value and the second objective function value corresponding to each individual in the temporary population.

[0015] Non-dominated sorting and crowding distance calculation steps: Based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, perform fast non-dominated sorting on all individuals in the temporary population, and then divide the temporary population into multiple second non-dominated levels arranged from high to low; then, based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, calculate the crowding distance of each individual in the same non-dominated level;

[0016] New parent population generation steps: Based on the second non-dominant level and crowding distance, and using preset screening rules, a predetermined number of individuals are selected from the temporary population to form a new parent population.

[0017] The optimal solution set calculation steps are as follows: Based on the new parent population, the temporary population generation step, the non-dominated sorting and crowding distance calculation step, and the new parent population generation step are repeatedly executed until the preset number of iterations is reached. The individual with the smallest objective function value in the new parent population at the preset number of iterations is taken as the Pareto optimal solution set of the multi-objective optimization mathematical model. According to the Pareto optimal solution set, the final fleet route allocation scheme is selected. This scheme achieves the dual minimization of total biofuel consumption and total economic loss under the premise of satisfying all the above constraints.

[0018] Preferably, in the step of establishing the multi-objective optimization mathematical model, the multiple constraints include a first constraint and a second constraint established with the limit on the total number of ships deployed on each route per year as a constraint; a third, fourth, and fifth constraint established with the limit on fuel consumption as a constraint; a sixth constraint established with the limit on the total number of route changes of the fleet in any year as a constraint; and a seventh, eighth, and ninth constraint established with the limit on the carbon intensity index level compliance of each ship as a constraint.

[0019] Preferably, the data acquisition step further acquires CII regulatory data, which includes the target CII value of the vessel in a given year, the actual CII value of the vessel in a given year, and the required CII value of the vessel in a given year; based on the required CII value, the boundary values ​​for the vessel to reach CII level C and the boundary values ​​for the vessel to reach CII level D in a given year are calculated respectively; the vessel data also includes the total fuel consumption required by the vessel in a given year, the conventional fuel required by the vessel in a given year, the biofuel consumption of the vessel in a given year, the deadweight tonnage of the vessel, and the total annual sailing distance of the vessel; the route data also includes the minimum number of vessels deployed on each route and the maximum number of route changes allowed for the fleet;

[0020] In the step of establishing the multi-objective optimization mathematical model, the first constraint is constructed based on the maximum number of ships deployed on the route and the number of ships deployed on the route in a certain year. The second constraint is constructed based on the minimum number of ships deployed on the route and the number of ships deployed on the route in a certain year, so as to ensure that the number of ships deployed on each route in each year is not less than the minimum number of ships deployed on the route and not greater than the maximum number of ships deployed on the route.

[0021] The third constraint is constructed based on the total fuel consumption required by the ship in a certain year, the biofuel required by the ship in a certain year, and the conventional fuel required by the ship in a certain year. The fourth constraint is constructed based on the biofuel required by the ship in a certain year, and the fifth constraint is constructed based on the conventional fuel required by the ship in a certain year, to ensure that the total fuel consumption of the ship is the sum of the biofuel consumption and the conventional fuel consumption, and that both the biofuel consumption and the conventional fuel consumption are non-negative numbers.

[0022] The sixth constraint is constructed based on the ship's biofuel consumption in a certain year and the maximum number of route changes allowed for the fleet, to ensure that the total number of route changes for the fleet during the planning period does not exceed the preset maximum number of allowed changes.

[0023] The seventh constraint is constructed based on the target CII value of the ship in a given year and the actual CII value of the ship in a given year. The eighth constraint is constructed based on the actual CII value of the ship in a given year, the boundary value for the ship to reach CII level C in a given year, the target CII value of the ship in a given year, and the boundary value for the ship to reach CII level D in a given year. The ninth constraint is constructed based on the actual CII value of the ship in a given year, the target CII value of the ship in a given year, the biofuel value required by the ship in a given year, the total fuel consumption value required by the ship in a given year, the deadweight tonnage of the ship, and the total annual sailing distance of the ship, to ensure that the CII level of any ship in any single year shall not be level E, and that the CII level shall not be level D for three consecutive years.

[0024] Preferably, in the new parent population generation step, the screening rules include: selecting all individuals in the non-dominated hierarchy in descending order of non-dominated hierarchy; when selecting all individuals in a certain non-dominated hierarchy would cause the total number to exceed the predetermined number, then selecting individuals in that non-dominated hierarchy in descending order of their crowding distance, until the total number of selected individuals reaches the predetermined number.

[0025] Preferably, in the initial parent population construction step, each individual is encoded using an integer encoding method, and the encoding length is equal to the total number of ships in the fleet.

[0026] A fleet route allocation optimization system, characterized by comprising, in sequence, a data acquisition module, a multi-objective optimization mathematical model establishment module, an initial parent population construction module, an objective function value calculation module, a temporary population generation module, a non-dominated sorting and crowding distance calculation module, a new parent population generation module, and an optimal solution set calculation module.

[0027] The data acquisition module acquires ship data for each vessel in the fleet and route data for each route. The ship data includes the biofuel value required by the vessel in a given year. The route data includes the maximum number of vessels deployed on each route, the number of vessels deployed on each route in a given year, and the economic loss per vessel due to deploying one less vessel on a route.

[0028] The multi-objective optimization mathematical model building module aims to minimize the total biofuel consumption of the fleet during the planning period and minimize the total economic loss caused by failure to meet the maximum deployment number of routes. Under multiple constraints, including the annual limit on the total number of ships deployed on each route, fuel consumption limits, the limit on the total number of route changes of the fleet in any year, and the CII level compliance limit for each ship, a first objective function is established based on the biofuel value required by the ship in a certain year, and a second objective function is established based on the maximum number of ships deployed on the route, the number of ships deployed on the route in a certain year, and the economic loss of each ship. A multi-objective optimization mathematical model is constructed based on the first objective function and the second objective function.

[0029] The initial parent population construction module constructs an initial parent population composed of multiple individuals, each individual representing an annual fleet route allocation scheme. The annual fleet route allocation scheme includes: randomly assigning ships that meet the minimum ship deployment requirement for each route until all routes meet the minimum ship deployment requirement; then randomly assigning the remaining unassigned ships to routes that have not yet met the maximum ship deployment requirement until all remaining unassigned ships have been assigned.

[0030] The objective function value calculation module calculates the first objective function value and the second objective function value corresponding to each individual in the initial parent population according to the first objective function and the second objective function respectively; and performs fast non-dominated sorting on all individuals in the initial parent population based on the calculated first objective function value and the second objective function value, thereby dividing the initial parent population into multiple first non-dominated levels arranged from high to low;

[0031] The temporary population generation module processes the current parent population according to the first non-dominated level and uses selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm to generate a child population, merges the current parent population with the child population to form a temporary population, and calculates the first objective function value and the second objective function value corresponding to each individual in the temporary population.

[0032] The non-dominated sorting and crowding distance calculation module performs a fast non-dominated sorting on all individuals in the temporary population based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, thereby dividing the temporary population into multiple second non-dominated levels arranged from high to low; and then calculates the crowding distance of each individual in the same non-dominated level based on the first objective function value and the second objective function value corresponding to each individual in the temporary population.

[0033] The new parent population generation module selects a predetermined number of individuals from the temporary population to form a new parent population based on the second non-dominant level and crowding distance, and using preset screening rules.

[0034] The optimal solution set calculation module, based on the new parent population, repeatedly executes the temporary population generation module, the non-dominated sorting and crowding distance calculation module, and the new parent population generation module until a preset number of iterations is reached. The individual with the smallest objective function value in the new parent population at the preset number of iterations is taken as the Pareto optimal solution set of the multi-objective optimization mathematical model. Based on the Pareto optimal solution set, the final fleet route allocation scheme is selected. This scheme achieves the dual minimization of total biofuel consumption and total economic loss while satisfying all the aforementioned constraints.

[0035] Preferably, in the multi-objective optimization mathematical model establishment module, the multiple constraints include a first constraint and a second constraint established with the limit on the total number of ships deployed on each route per year as a constraint; a third, fourth, and fifth constraint established with the limit on fuel consumption as a constraint; a sixth constraint established with the limit on the total number of route changes of the fleet in any year as a constraint; and a seventh, eighth, and ninth constraint established with the limit on the carbon intensity index level compliance of each ship as a constraint.

[0036] Preferably, the data acquisition module also acquires CII regulatory data, which includes the target CII value of the vessel in a given year, the actual CII value of the vessel in a given year, and the required CII value of the vessel in a given year; based on the required CII value, the boundary values ​​for the vessel to reach CII level C and the boundary values ​​for the vessel to reach CII level D in a given year are calculated respectively; the vessel data also includes the total fuel consumption required by the vessel in a given year, the conventional fuel required by the vessel in a given year, the biofuel consumption of the vessel in a given year, the deadweight tonnage of the vessel, and the total annual sailing distance of the vessel; the route data also includes the minimum number of vessels deployed on each route and the maximum number of times the fleet is allowed to change routes;

[0037] In the multi-objective optimization mathematical model building module, the first constraint is constructed based on the maximum number of ships deployed on the route and the number of ships deployed on the route in a certain year. The second constraint is constructed based on the minimum number of ships deployed on the route and the number of ships deployed on the route in a certain year, so as to ensure that the number of ships deployed on each route in each year is not less than the minimum number of ships deployed on the route and not greater than the maximum number of ships deployed on the route.

[0038] The third constraint is constructed based on the total fuel consumption required by the ship in a certain year, the biofuel required by the ship in a certain year, and the conventional fuel required by the ship in a certain year. The fourth constraint is constructed based on the biofuel required by the ship in a certain year, and the fifth constraint is constructed based on the conventional fuel required by the ship in a certain year, to ensure that the total fuel consumption of the ship is the sum of the biofuel consumption and the conventional fuel consumption, and that both the biofuel consumption and the conventional fuel consumption are non-negative numbers.

[0039] The sixth constraint is constructed based on the ship's biofuel consumption in a certain year and the maximum number of route changes allowed for the fleet, to ensure that the total number of route changes for the fleet during the planning period does not exceed the preset maximum number of allowed changes.

[0040] The seventh constraint is constructed based on the target CII value of the ship in a given year and the actual CII value of the ship in a given year. The eighth constraint is constructed based on the actual CII value of the ship in a given year, the boundary value for the ship to reach CII level C in a given year, the target CII value of the ship in a given year, and the boundary value for the ship to reach CII level D in a given year. The ninth constraint is constructed based on the actual CII value of the ship in a given year, the target CII value of the ship in a given year, the biofuel value required by the ship in a given year, the total fuel consumption value required by the ship in a given year, the deadweight tonnage of the ship, and the total annual sailing distance of the ship, to ensure that the CII level of any ship in any single year shall not be level E, and that the CII level shall not be level D for three consecutive years.

[0041] Preferably, in the new parent population generation module, the screening rules include: selecting all individuals in the non-dominated hierarchy in descending order of non-dominated hierarchy; when selecting all individuals in a certain non-dominated hierarchy would cause the total number to exceed the predetermined number, then selecting individuals in that non-dominated hierarchy in descending order of their crowding distance, until the total number of selected individuals reaches the predetermined number.

[0042] Preferably, in the initial parent population construction module, each individual is encoded using an integer encoding method, and the encoding length is equal to the total number of ships in the fleet.

[0043] The beneficial effects of this invention are as follows:

[0044] This invention provides a fleet route allocation optimization method. First, it acquires vessel data for each vessel in the fleet and route data for each route. Then, it sets dual objectives: minimizing the total biofuel consumption of the fleet during the planning period and minimizing the total economic loss caused by failure to meet the maximum deployment quantity for each route. Under multiple constraints—including annual limits on the total number of vessels deployed on each route, fuel consumption limits, limits on the total number of route changes in any given year, and CII level compliance limits for each vessel—a first objective function and a second objective function are established. Based on these two objective functions, a multi-objective optimization mathematical model is constructed. This model simultaneously and accurately captures the two conflicting core objectives of "reducing compliance costs (minimizing biofuel consumption)" and "ensuring operational revenue (minimizing economic losses)." Furthermore, it transforms all key business rules, such as CII regulations, route operation restrictions, and fleet scheduling flexibility, into strict mathematical constraints, ensuring that the generated solution conforms to actual operational boundary conditions and improving the model's practicality and feasibility. Then, an initial parent population consisting of multiple individuals is constructed, with each individual representing an annual fleet route allocation scheme. This scheme prioritizes meeting minimum operational requirements before randomly allocating remaining capacity, ensuring that each allocation scheme in the population satisfies the most basic route deployment constraints. This provides an excellent starting point for the evolutionary algorithm, significantly improving its convergence speed and solution quality. The first and second objective function values ​​for each individual in the initial parent population are then calculated. By quantitatively evaluating each feasible scheme in the initial parent population, the corresponding total biofuel consumption (first objective function value) and total economic loss (second objective function value) are accurately calculated, providing an objective and quantitative basis for subsequent algorithmic comparison and selection of individual solutions. Finally, the initial parent population is divided into multiple first non-dominated levels arranged from high to low using non-dominated sorting. The non-dominated sorting classifies solutions according to their quality, identifying the current optimal set of non-dominated solutions (Pareto front). The offspring population is generated based on the first non-dominated level and using selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm. The current parent population is merged with the offspring population to form a temporary population. By simulating genetic operations (selection, crossover, and mutation) in biological evolution, new solutions (offspring) are explored based on the original solutions (parents), thereby expanding the search range and avoiding getting trapped in local optima. Merging the parents and offspring ensures that excellent genes are preserved (elite preservation strategy), providing a richer set of candidate solutions for the next generation of optimization.The temporary population is then divided into multiple second non-dominated levels arranged from high to low using non-dominated sorting. The crowding distance of each individual within the same non-dominated level is calculated. Non-dominated sorting ranks solutions according to their quality, identifying the current optimal set of non-dominated solutions (Pareto front). Crowding distance calculation measures the distribution density of each solution in the target space. The combination of these two methods provides a precise standard for selecting solutions that simultaneously possess both "excellent" and "diverse" characteristics. Then, based on the second non-dominated level and crowding distance, a predetermined number of individuals are selected from the temporary population using pre-defined selection rules to form a new parent population. This elite-style selection process yields a fixed number of individuals. The best solutions form a new generation of population, ensuring that the optimization process steadily converges to a better Pareto front while maintaining population diversity. This comprehensively characterizes the optimal trade-off between the two objectives and avoids premature convergence. Finally, through iterative execution of the above optimization process, the solution is continuously evolved, ultimately outputting a set of optimal solutions covering the Pareto front (Pareto optimal solution set). This solution set provides users with multiple best feasible solutions at different trade-off levels between biofuel usage and economic losses under CII compliance. It supports decision-makers in selecting the final implementation plan based on actual preferences, thereby achieving the dual minimization of total biofuel usage and total economic losses.

[0045] This invention achieves scientific, refined, and intelligent fleet annual scheduling decisions by constructing a multi-objective optimization model integrating carbon intensity management, capacity allocation, and economic cost control, combined with an efficient solution mechanism based on a non-dominated sorting genetic algorithm. It has the following significant technical effects:

[0046] 1) Comprehensive assurance of IMO CII compliance and mitigation of regulatory risks: By using the "CII rating compliance limit for each vessel" as a hard constraint, the optimization process avoids generating scheduling schemes that could result in vessels being rated D for three consecutive years or E in any year. Simultaneously, by introducing the "biofuel value required by a vessel in a given year" as an emission reduction measure, the system dynamically responds to the increasingly stringent CII baseline requirements, ensuring that the fleet continuously meets the IMO's carbon intensity compliance requirements without relying on excessive technological upgrades, effectively mitigating port state control (PSC) inspection risks, corporate carbon credit losses, and market access restrictions. 2) Achieving the optimal trade-off between environmental goals and economic costs: This invention innovatively constructs a dual-objective optimization framework: on the one hand, minimizing the total biofuel usage to reduce the high operating costs associated with low-carbon fuels; on the other hand, minimizing economic losses due to failure to meet the maximum deployment quantity on routes, ensuring transportation service capacity. By generating Pareto optimal solution sets, this invention supports decision-makers in making flexible choices based on corporate strategic preferences (such as "green priority" or "economic priority"), achieving a scientific balance between carbon emission reduction and economic benefits, and avoiding the resource waste caused by the "one-size-fits-all" emission reduction approach in traditional methods. 3) Enhancing the precision and personalization of fleet scheduling: This invention fully considers the performance differences between individual ships (such as improved energy efficiency after maintenance and fuel consumption degradation due to ship age), and differentiates the carbon intensity performance and fuel demand of each ship in the model to achieve precise scheduling based on the specific ship. High-efficiency ships are prioritized for deployment on high-carbon-intensity routes, while low-energy-consumption ships are used for critical capacity support, fully leveraging the potential of existing assets and improving overall operational efficiency. 4) Enhancing the feasibility and stability of scheduling schemes: By setting realistic constraints such as "upper and lower limits on the number of ships deployed on each route" and "limits on the total number of route changes per year," this invention ensures that the generated scheduling schemes meet the actual requirements of port unloading capacity, schedule density, and management coordination. This avoids operational chaos and increased management costs caused by frequent route adjustments, and improves the continuity and executability of fleet operations. 5) Improving the convergence efficiency and solution set quality of the optimization algorithm: A non-dominated sorting genetic algorithm (NSGA-II) combined with a feasible solution-first initial parent population construction strategy is adopted to ensure that the initial solution meets key constraints such as minimum capacity guarantee, significantly improving the algorithm's convergence speed. Through non-dominated sorting and congestion distance mechanisms, a uniformly distributed and highly diverse Pareto front solution set is generated, providing rich and high-quality candidate solutions for decision-making. In summary, this invention, for the first time, incorporates multiple factors such as CII compliance constraints, individual ship performance differences, biofuel costs, and capacity economic losses into a unified fleet scheduling optimization framework, solving key technical problems in existing technologies such as the separation of environmental and economic goals, infeasibility of scheduling schemes, and lack of forward-looking compliance management. The proposed method has strong practicality, high scalability, and good engineering applicability, and can be widely applied to fleet management practices of various shipping companies, including liner shipping and dry bulk shipping, with significant economic, environmental, and social benefits.

[0047] Furthermore, the selection rules include: selecting all individuals in the non-dominated levels layer by layer in descending order of non-dominated levels; when selecting all individuals in a certain non-dominated level would cause the total number to exceed the predetermined number, then individuals in that non-dominated level are selected in descending order of their crowding distance until the total number of selected individuals reaches the predetermined number. Through the mechanism of "selecting layer by layer in descending order of non-dominated levels", the individuals with the best performance on the Pareto front (i.e., the first non-dominated level) are preferentially retained, ensuring that the best scheduling scheme is not lost in each generation of evolution. This achieves efficient retention of high-quality, highly diverse solutions (elite retention), significantly improving the speed and stability of the algorithm's convergence to the global optimum.

[0048] Furthermore, each individual is encoded using an integer encoding method, with the encoding length equal to the total number of ships in the fleet. Integer encoding transforms a complex annual fleet route allocation scheme into a fixed-length array, allowing the abstract scheduling decision to be directly processed by the genetic algorithm. The encoding length being equal to the total number of ships in the fleet ensures that the scheduling assignment of each ship is fully covered, avoiding ship omissions or duplicate assignments, thus improving the interpretability and engineering feasibility of the model solution.

[0049] This invention also relates to a fleet route allocation optimization system, which corresponds to the aforementioned fleet route allocation optimization method. This system can be understood as a system that implements the aforementioned fleet route allocation optimization method, comprising a data acquisition module, a multi-objective optimization mathematical model establishment module, an initial parent population construction module, an objective function value calculation module, a temporary population generation module, a non-dominated sorting and congestion distance calculation module, a new parent population generation module, and an optimal solution set calculation module, all connected sequentially. These modules work collaboratively, using the International Maritime Organization (IMO) CII regulatory compliance requirements as the core constraint, and optimizing them within a unified framework of the operational economic objectives of liner shipping. By establishing a bi-objective mathematical model and using an improved NSGA-II algorithm for solving it, a series of Pareto optimal solutions that achieve the best trade-off between biofuel usage (compliance costs) and economic losses due to insufficient capacity deployment can be automatically generated. This enables shipping companies to scientifically select the fleet scheduling strategy with the lowest total operating cost while strictly complying with CII regulations and avoiding compliance risks. Simultaneously considering the annual decline of the CII baseline, the degradation of ship fuel efficiency over time, and the need for maintenance improvements, this invention optimizes the allocation scheme for the planning period over multiple years. This not only meets the compliance requirements of the current year but also lays a solid foundation for operations in subsequent years, significantly enhancing the foresight and strategic value of decision-making and helping companies maintain initiative throughout the regulatory transition period. Furthermore, addressing the high-dimensional, discrete, and complex constraints of the problem, the improved NSGA-II algorithm, through fast non-dominated sorting and crowding calculation, efficiently handles two conflicting objectives and uniformly explores and converges to the global Pareto front in the solution space. This overcomes the high computational complexity or difficulty in convergence that traditional mathematical programming methods may face when solving such large-scale combinatorial optimization problems, providing a high-quality solution set within a reasonable timeframe. This invention provides a systematic and automated decision support tool for solving the core operational challenges faced by shipping companies under CII regulations. It effectively resolves the dilemma between "compliance" and "profitability," helping shipping companies achieve a balance between environmental and economic benefits in the new context of green transformation. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the fleet layout.

[0051] Figure 2 This is a diagram showing the fleet layout each year.

[0052] Figure 3 This is a flowchart of the fleet route allocation optimization method of the present invention.

[0053] Figure 4 This is a schematic diagram of the boundary lines for the grade division of this invention.

[0054] Figure 5 This is a flowchart of the NSGA II algorithm of this invention. Detailed Implementation

[0055] The present invention will now be described with reference to the accompanying drawings.

[0056] This invention relates to a method for optimizing fleet route allocation, the flowchart of which is shown below. Figure 3 As shown, the steps are as follows:

[0057] I. Data Acquisition Steps: Acquire vessel data for each vessel in the fleet, route data for each route, and CII regulatory data. Vessel data includes the vessel's required biofuel value, total fuel consumption, conventional fuel requirement, biofuel usage, deadweight tonnage, and total annual sailing distance for a given year. Route data includes the maximum number of vessels deployed on each route, the number of vessels deployed on each route in a given year, the economic loss per vessel due to missing a vessel on a route, the minimum number of vessels deployed on each route, and the maximum number of route changes allowed for the fleet. CII regulatory data includes the vessel's target CII value, actual CII value, and required CII value for a given year.

[0058] The acquired data can be expressed using corresponding symbols, the explanations of which are as follows:

[0059]

[0060] The actual CII value of ship v in year k is calculated using the following formula:

[0061]

[0062] In the above formula, This represents the actual CII value of ship v in year k; This represents the biofuel value required by ship v in year k; Indicates the carbon coefficient of biofuel; This represents the conventional fuel required by ship v in year k; Indicates the carbon coefficient of conventional fuels; Indicates the deadweight tonnage of the ship v; This represents the total annual sailing distance of vessel v.

[0063] The formula for calculating the required CII value of ship v in year k (i.e., the CII value that ship v needs to achieve in year k) is as follows:

[0064]

[0065] According to CII regulations, the annual reduction factor (The annual reduction factor in the CII regulations) is listed in Table 1.

[0066] Table 1

[0067]

[0068] In addition, under the CII regulations, the carbon intensity rating of ships is divided into five levels, from excellent to unqualified, marked as A, B, C, D and E respectively. Figure 4 The boundary lines defining these grade divisions are shown. Based on the CII target value (CIIreq), the five grade intervals are divided by the boundary distances of d1, d2, d3, and d4. A corresponds to the interval with the lowest carbon intensity, and E corresponds to the non-compliant interval with the highest carbon intensity.

[0069] For ship operations, the CII regulations stipulate that a ship may not be rated E in any year, or be rated D for three consecutive years. Therefore, based on the required CII value (i.e., the CII value that ship v needs to achieve in year k), the boundary values ​​for achieving a CII rating of C in year k are calculated. (i.e., the CII value of ship v at the boundary between class C and D), and the boundary value at which a ship reaches class D in a certain year. (That is, the CII value of ship v at the boundary between class D and class E), calculated according to the following formula:

[0070]

[0071]

[0072] In the above formula, To obtain the required CII value (i.e., the CII value that ship v needs to reach in year k); These are the boundary parameters for grades C and D in the CII regulations; These are the boundary parameters for levels D and E in the CII regulations.

[0073] II. Steps for establishing a multi-objective optimization mathematical model: The objectives are to minimize the total biofuel consumption of the fleet during the planning period and to minimize the total economic loss caused by failure to meet the maximum deployment number of routes. Under multiple constraints, including the annual limit on the total number of ships deployed on each route, fuel consumption limits, the limit on the total number of route changes of the fleet in any year, and the CII level compliance limit for each ship, a first objective function is established based on the biofuel value required by the ships in a certain year. A second objective function is established based on the maximum number of ships deployed on the route, the number of ships deployed on the route in a certain year, and the economic loss of each ship. A multi-objective optimization mathematical model is then constructed based on the first and second objective functions.

[0074] Specifically, using biofuels to upgrade CII ratings can effectively prevent non-compliance. Considering the overall requirements for route changes, the number of route changes cannot exceed the prescribed threshold. Furthermore, the total number of vessels deployed on each route annually must not exceed the maximum planned deployment number, nor fall below the minimum planned deployment number. However, failure to meet the maximum deployment requirements may result in certain economic losses. Two objectives are set first: minimizing the total biofuel consumption of the fleet during the planning period is the primary objective; minimizing the total economic losses caused by failing to meet the maximum deployment number on each route is the secondary objective.

[0075] Then, under multiple constraints—including the annual deployment limit for each route, fuel consumption limits, the limit on the total number of route changes for the fleet in any given year, and the CII rating compliance limit for each vessel—a first objective function is established based on the biofuel required by the vessel in a given year. First objective function The aim is to minimize the total biofuel consumption of all vessels in the fleet throughout the entire planning period (e.g., the next 3 or 5 years), expressed as follows:

[0076]

[0077] In the above formula, Indicates a ship exist The annual biofuel value required; Represents a set of years; Indicates a collection of ships.

[0078] Then, a second objective function is established based on the maximum number of ships deployed on the route, the number of ships deployed on the route in a certain year, and the economic loss per ship. Second objective function The aim is to minimize the cumulative total economic loss caused by the failure of the actual number of vessels deployed on all routes to reach their respective maximum deployment numbers throughout the entire planning period, expressed by the following formula:

[0079]

[0080] In the above formula, This indicates the maximum number of ships that can be deployed on route r; This represents the number of ships deployed on route r in year k; This represents the economic loss per ship resulting from deploying one less ship on route r. This represents a set of flight routes.

[0081] Finally, a multi-objective optimization mathematical model is constructed based on the first and second objective functions. To solve the fleet allocation problem, the following formula is used:

[0082]

[0083] Several constraints include a first and a second constraint based on the total number of vessels deployed annually on each route, ensuring that the number of vessels deployed on each route in any given year is neither less than the minimum deployment number nor greater than the maximum deployment number. A third, fourth, and fifth constraint based on fuel consumption limits ensure that the total fuel consumption of vessels is the sum of biofuel and conventional fuel consumption, and that both biofuel and conventional fuel consumption are non-negative. A sixth constraint based on the total number of route changes the fleet can make in any given year ensures that the total number of route changes the fleet can make during the planning period does not exceed the preset maximum allowed number of changes. Finally, a seventh, eighth, and ninth constraint based on the carbon intensity index (CII) compliance limit for each vessel ensures that no vessel's CII rating is E in any single year, and that no vessel can have a CII rating of D for three consecutive years.

[0084] The first constraint is based on the maximum number of ships deployed on route r. And the number of ships deployed on route r in year k. The construction is as follows:

[0085]

[0086] The second constraint is based on the minimum number of ships deployed on route r. And the number of ships deployed on route r in year k. The construction is as follows:

[0087]

[0088] The third constraint is based on the total fuel consumption required by ship v in year k. The biofuel value required by ship v in year k And the conventional fuel value required by ship v in year k. The construction is as follows:

[0089]

[0090] This formula defines a ship's total fuel consumption as the sum of conventional fuel and biofuel usage.

[0091] The fourth constraint is based on the biofuel value required by ship v in year k. The construction is as follows:

[0092]

[0093] The fifth constraint is based on the conventional fuel required by ship v in year k. The construction is as follows:

[0094]

[0095] The fourth and fifth constraints limit the total number of route changes a vessel can make within the specified limits.

[0096] The sixth constraint is based on the biofuel consumption of ship v in year k. And the maximum number of times the fleet is allowed to change its route. The construction is as follows:

[0097]

[0098] This formula limits the total number of route changes a vessel can make within a specified limit.

[0099] The seventh constraint is based on the target CII value of ship v in year k. And the actual CII value of ship v in year k. The construction is as follows:

[0100]

[0101] This formula requires that the CII value of a vessel in a given year must not exceed the specified target value.

[0102] The eighth constraint is based on the ship's actual CII values ​​in year k and year k-1 ( , The boundary values ​​for a ship to reach CII level C in years k, k+1, and k-1. , , ), the target CII value of the ship in year k+1 The boundary values ​​for a ship to reach CII level D in years k, k+1, and k-1 ( , , The structure is as follows:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] This formula, in accordance with CII regulations, specifies the vessel's CII target rating for the following year.

[0110] The ninth constraint is based on the actual CII value of ship v in year k. The target CII value of ship v in year k The biofuel value required by ship v in year k The total fuel consumption required by ship v in year k The deadweight tonnage of ship v and the total annual sailing distance of vessel v The construction is as follows:

[0111]

[0112]

[0113]

[0114] In the above formula, Indicates the carbon coefficient of conventional fuels; This indicates the carbon coefficient of biofuel; the formula stipulates that if a vessel's CII rating exceeds the target rating in a given year, it must use biofuel to reduce its CII value.

[0115] III. Initial Parent Population Construction Steps: Construct an initial parent population consisting of multiple individuals, each representing an annual fleet route allocation scheme; the annual fleet route allocation scheme includes: randomly assigning ships that meet the minimum ship deployment requirements for each route until all routes have reached the minimum ship deployment requirements; then randomly assigning the remaining unassigned ships to routes that have not yet reached the maximum ship deployment requirements until all remaining unassigned ships have been assigned.

[0116] After constructing the multi-objective optimization mathematical model, the non-dominated sorting genetic algorithm (NGSA II algorithm) is used to solve the multi-objective optimization mathematical model to obtain the Pareto optimal solution set. Specifically, as follows... Figure 5As shown, the population is first initialized, i.e., an initial parent population consisting of multiple individuals is constructed (the population contains multiple individual groups, and each individual group consists of multiple individuals, with each individual within an individual group being independent of the others). Each individual represents an annual fleet route allocation scheme, and each individual is encoded using an integer encoding method, with the encoding length equal to the total number of ships in the fleet. In the encoding logic, the entire fleet is treated as an independent individual each year, represented by an array recording the route number assigned to each ship. Specifically, an array with a length equal to the number of ships in the fleet is initialized. Each ship can be assigned to any one of the R routes. For example, assuming the fleet consists of 8 ships (v1, v2…v8) and there are 5 routes (r1, r2…r5) to choose from, each ship is assigned to a corresponding route, as illustrated in Table 2: v1 is assigned to r2, v2 is assigned to r4, and so on. Therefore, the encoding array for this individual will be [2,4,1,3,3,5,1,2]. This indicates that 2 ships were allocated for route 1, 2 ships for route 2, 2 ships for route 3, 1 ship for route 4, and 1 ship for route 5.

[0117] Table 2

[0118]

[0119] The annual fleet route allocation scheme includes: allocating ships to each route that meet its minimum ship deployment requirement until all routes meet the minimum ship deployment requirement; then randomly assigning the remaining unallocated ships to routes that have not yet met the maximum ship deployment requirement until all remaining unallocated ships are allocated. Specifically, the genes in the initialization strategy ensure that the generated initial parent population satisfies all constraints by satisfying the minimum ship requirements for all routes, thus laying a solid foundation for subsequent evolutionary operations. This strategy first satisfies the basic operational needs of each route, and then introduces diversity by randomly allocating the remaining ships, ensuring that the initial parent population covers different regions of the search space. This initialization method combines constraint satisfaction and randomness, effectively exploring potential optimization solutions while meeting actual business needs. Assume there are V ships and R routes, each route has a minimum ship deployment requirement r. min And a maximum number of ships required for deployment r max All routes r min The sum of values ​​is denoted as m (i.e., m = Σr). min ).

[0120] 1) Initial Allocation: Meet the minimum ship deployment requirements for each route, ensuring the minimum ship deployment requirement r for each route is met. minThe requirement is met. Method: Randomly select ships from the fleet and assign them to the route one by one. At each assignment, randomly select a ship whose minimum ship deployment requirement (i.e., the current number of ships) has not yet been met. <r min The route is determined and the vessels are assigned to it. This process continues until the minimum number of vessels required for deployment on all routes is met (r). min All conditions are met. At this point, m ships in the fleet have been allocated, and each route has at least met its minimum ship deployment requirement.

[0121] 2) Secondary Allocation: Allocate the remaining ships by assigning the remaining unallocated ships (Vm) to routes that have not yet reached the maximum ship deployment requirement, until all ships are allocated. Method: Randomly select one ship from the remaining unallocated ships. From the perspective of this ship, randomly select a route (from R routes). Check the number of ships currently allocated to the selected route: If the current number of ships is less than the maximum limit for that route (i.e., the maximum ship deployment requirement r), then... max If the current number of ships has reached the maximum limit (r) for that route, then the ships will be assigned to that route. max If a new vessel is not found on a given route, that route will no longer accept new vessels, and the vessels must be reassigned to another randomly selected route until a route that has not yet reached its maximum vessel deployment requirement is found. Repeat the above steps until all remaining vessels (Vm) are successfully assigned to a route.

[0122] IV. Objective Function Value Calculation Steps: Calculate the first objective function value (total biofuel consumption) and the second objective function value (total economic loss) for each individual in the initial parent population based on the first and second objective functions, while simultaneously satisfying all the aforementioned constraints. Then, based on the calculated first and second objective function values ​​for each individual in the initial parent population, perform a fast non-dominated sort on all individuals in the initial parent population, thereby dividing the initial parent population into multiple first non-dominated levels (frontiers) arranged from high to low. The fast non-dominated sorting involves: firstly, performing a non-dominated sort on all individuals in the population, dividing them into m frontiers F (F1, F2, ..., F...). m The frontier F1 includes all non-dominated individuals, F2 includes the non-dominated individuals remaining after removing F1, and so on.

[0123] V. Temporary Population Generation Steps: Based on the first non-dominated level, the current parent population is processed using selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm to generate a child population. The current parent population is then merged with the child population to form a temporary population. The first objective function value and the second objective function value corresponding to each individual in the temporary population are calculated.

[0124] VI. Non-dominated sorting and crowding distance calculation steps: Based on the first and second objective function values ​​corresponding to each individual in the temporary population, a fast non-dominated sort is performed on all individuals in the temporary population, thereby dividing the temporary population into multiple second non-dominated levels arranged from high to low. Then, based on the first and second objective function values ​​corresponding to each individual in the temporary population, the crowding distance of each individual in the same non-dominated level is calculated. The crowding distance measures the distribution density of an individual in the objective value space. Individuals with larger crowding distances are located in regions where the objective value distribution is sparse, which helps maintain population diversity.

[0125] The selection, crossover, and mutation operations ensure the diversity and effectiveness of the NSGA-II algorithm. Selection, based on non-dominated sorting and crowding distance, prioritizes high-quality individuals; crossover generates new offspring through partial matching crossover (PMX); and mutation introduces diversity by randomly altering ship assignments. These operations work together to enable the algorithm to effectively explore and mine potential optimal solutions in the search space. Specifically, the selection operation aims to select high-performing individuals from the current population, increasing their probability of passing on their genes to the next generation, thus ensuring population diversity and solution quality. Selection begins with the F1 front, adding individuals sequentially to the selection pool. If the required selection number is not reached after adding all individuals from a front, selection continues to the next front. If some individuals from a front need to be selected, selection is performed from largest to smallest based on crowding distance until the required number is met.

[0126] Crossover operation: By combining the features of two parent individuals, new child individuals are generated, thereby exploring new regions of the solution space. The steps are as follows:

[0127] Step 1: Selecting intersections and copying segments:

[0128] Two crossover points are randomly selected on the chromosomes of two parent individuals to form a crossover segment;

[0129] Chromosomes were selected from two parent individuals, within the range [V] n V m ], where 1≤V n <V m ≤V, where V is the total length of the chromosomes;

[0130] The offspring directly replicate the genes at the corresponding positions in the parent individual in the segments between the crossover points.

[0131] Step 2: Calculate the flight route deployment margin and target quantity:

[0132] Deployment capacity: Represents the remaining number of ships that can be deployed along the route, denoted as r = [r1, r2, ..., rn ], where r i = Maximum deployment quantity for the route - Number of vessels already deployed for the route, where n is the route number. When r i When r ≥ 0, it means that ships can continue to be deployed on this route; when r i When the value is less than 0, it indicates that the number of ships deployed on the route has exceeded the limit and needs to be adjusted to meet the route requirements.

[0133] Compliance Quantity: Represents the minimum number of vessels required to meet the route requirements, denoted as =[ 1, 2,..., n ],in i =Number of vessels already deployed on the route - Minimum number of vessels required for the route. When i When ≥0, it indicates that the number of ships deployed on this route has reached or exceeded the target value; when i A value less than 0 indicates that the number of vessels deployed on that route has not met the target and needs to be forcibly replenished. i =0, to ensure compliance with route requirements.

[0134] Step 3: Gene repair to ensure that the crossovered individuals meet the maximum and minimum deployment requirements of the flight path.

[0135] If r ≥ 0 and If the value is ≥ 0, it means that the deployment of the fleet meets the route requirements and no repair is needed;

[0136] If r exists i <0, but If r ≥ 0, it means that the number of ships deployed on route i has exceeded the maximum limit, but meets the minimum number of ships requirement. In this case, the last |ri| ships on route i are redistributed to routes that have not yet reached the maximum deployment number, so that r ≥ 0;

[0137] If r m <0 and k <0 indicates that the number of ships deployed for route m exceeds the maximum limit, while the number of ships deployed for route k does not meet the limit. In this case, the last |r of route m will be... m | The ships are assigned to route k such that r≥0 and l≥0;

[0138] For example, as shown in Table 3, which illustrates the crossover and gene repair operations of the NSGA II algorithm, assuming a fleet of 8 ships deployed across 5 routes, with a minimum deployment of 1 ship and a maximum deployment of 2 ships per route. The deployment logic for ships 1-8 of Parent 1 is [2, 4, 1, 3, 3, 5, 1, 2], and the deployment logic for ships 1-8 of Parent 2 is [3, 5, 2, 1, 4, 3, 2, 4]. This means that all 5 routes meet the deployment requirements for each route.

[0139] Table 3

[0140]

[0141] ① Selecting and copying intersection points:

[0142] Crossing between vessels number 3 and 6;

[0143] After crossover, we get Proto-child 1 and Proto-child 2. The deployment logic for ships 1-8 of Proto-child 1 is [2, 4, 2, 1, 4, 3, 1, 2], and the deployment logic for ships 1-8 of Proto-child 2 is [3, 5, 1, 3, 3, 5, 2, 4].

[0144] ② Calculate the remaining capacity and target capacity of the flight routes:

[0145] For Sub-1: The deployment margin for routes 1-5 is [0, -1, 1, 0, 2], and the required number of vessels is [0, 0, 0, 0, 1]. Therefore, the number of vessels on route 2 exceeds the maximum limit (deployment margin is -1), while route 5 does not meet the minimum deployment requirement (the required number of vessels is 1).

[0146] For Sub-Generation 2, the available deployment capacity for routes 1-5 is [1, 1, -1, 1, 0], and the required capacity is [0, 0, 0, 0, 0]. Therefore, the number of vessels on route 3 exceeds the maximum limit (deployment capacity is -1), but all routes meet the minimum deployment requirements.

[0147] ③ Gene repair:

[0148] Offspring 1: The last ship deployed on route 2 (ship No. 8) will be reassigned to route 5, corresponding to the offspring 1 code [2, 4, 2, 1, 4, 3, 1, 5], to meet the deployment requirements of the route;

[0149] Offspring 2: The last ship deployed on route 3 (ship 5) will be randomly assigned to one of routes 1, 2 or 4, corresponding to the offspring 2 code [3, 5, 1, 3, 2, 5, 2, 4], to ensure that all routes meet the maximum and minimum deployment requirements.

[0150] Mutation operation: Randomness is introduced to maintain population diversity and prevent the algorithm from prematurely converging to a local optimum. Several individuals in the population are randomly selected for mutation. For each selected individual, the route assignments of several ships are randomly changed. The number of routes is counted; if the route deployment requirements are not met, steps 2 and 3 of the crossover operation are followed to correct the issue, ensuring that the mutated individuals satisfy the constraint that the number of ships on each route does not exceed the maximum limit and also meets the minimum ship number constraint.

[0151] VII. New Parent Population Generation Steps: Based on the second non-dominated level and crowding distance, and using preset screening rules, a predetermined number of individuals are selected from the temporary population to form the new parent population. The screening rules include: selecting all individuals in each non-dominated level in descending order of non-dominated level; if selecting all individuals in a certain non-dominated level would cause the total number to exceed the predetermined number, then individuals in that non-dominated level are selected in descending order of their crowding distance until the total number of selected individuals reaches the predetermined number.

[0152] 8. Optimal Solution Set Calculation Steps: Based on the new parent population, the temporary population generation step, non-dominated sorting and crowding distance calculation step, and new parent population generation step are repeatedly executed until the preset number of iterations is reached (i.e., the current number of iterations (G) > the maximum number of iterations (Gen)). The individual with the smallest objective function value in the new parent population when the preset number of iterations is reached is taken as the Pareto optimal solution set of the multi-objective optimization mathematical model. According to the Pareto optimal solution set, the final fleet route allocation scheme is selected. This scheme achieves the dual minimization of total biofuel consumption and total economic loss under the premise of satisfying all the above constraints.

[0153] This invention also relates to a fleet route allocation optimization system, which corresponds to the aforementioned fleet route allocation optimization method and can be understood as a system for implementing the above method. This system includes, in sequence, a data acquisition module, a multi-objective optimization mathematical model establishment module, an initial parent population construction module, an objective function value calculation module, a temporary population generation module, a non-dominated sorting and crowding distance calculation module, a new parent population generation module, and an optimal solution set calculation module. Specifically,

[0154] The data acquisition module acquires ship data for each vessel in the fleet and route data for each route. The ship data includes the biofuel value required by the vessel in a given year. The route data includes the maximum number of vessels deployed on each route, the number of vessels deployed on each route in a given year, and the economic loss per vessel due to deploying one less vessel on a route.

[0155] The multi-objective optimization mathematical model building module aims to minimize the total biofuel consumption of the fleet during the planning period and minimize the total economic loss caused by failure to meet the maximum deployment number of routes. Under multiple constraints, including the annual limit on the total number of ships deployed on each route, fuel consumption limits, the limit on the total number of route changes of the fleet in any year, and the CII level compliance limit for each ship, a first objective function is established based on the biofuel value required by the ship in a certain year, and a second objective function is established based on the maximum number of ships deployed on the route, the number of ships deployed on the route in a certain year, and the economic loss of each ship. A multi-objective optimization mathematical model is constructed based on the first objective function and the second objective function.

[0156] The initial parent population construction module constructs an initial parent population composed of multiple individuals, each individual representing an annual fleet route allocation scheme. The annual fleet route allocation scheme includes: randomly assigning ships that meet the minimum ship deployment requirement for each route until all routes meet the minimum ship deployment requirement; then randomly assigning the remaining unassigned ships to routes that have not yet met the maximum ship deployment requirement until all remaining unassigned ships have been assigned.

[0157] The objective function value calculation module calculates the first objective function value and the second objective function value corresponding to each individual in the initial parent population according to the first objective function and the second objective function respectively; and performs fast non-dominated sorting on all individuals in the initial parent population based on the calculated first objective function value and the second objective function value, thereby dividing the initial parent population into multiple first non-dominated levels arranged from high to low;

[0158] The temporary population generation module processes the current parent population according to the first non-dominated level and uses selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm to generate a child population, merges the current parent population with the child population to form a temporary population, and calculates the first objective function value and the second objective function value corresponding to each individual in the temporary population.

[0159] The non-dominated sorting and crowding distance calculation module performs a fast non-dominated sorting on all individuals in the temporary population based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, thereby dividing the temporary population into multiple second non-dominated levels arranged from high to low; and then calculates the crowding distance of each individual in the same non-dominated level based on the first objective function value and the second objective function value corresponding to each individual in the temporary population.

[0160] The new parent population generation module selects a predetermined number of individuals from the temporary population to form a new parent population based on the second non-dominant level and crowding distance, and using preset screening rules.

[0161] The optimal solution set calculation module, based on the new parent population, repeatedly executes the temporary population generation module, the non-dominated sorting and crowding distance calculation module, and the new parent population generation module until a preset number of iterations is reached. The individual with the smallest objective function value in the new parent population at the preset number of iterations is taken as the Pareto optimal solution set of the multi-objective optimization mathematical model. Based on the Pareto optimal solution set, the final fleet route allocation scheme is selected. This scheme achieves the dual minimization of total biofuel consumption and total economic loss while satisfying all the aforementioned constraints.

[0162] Preferably, in the multi-objective optimization mathematical model establishment module, the multiple constraints include a first constraint and a second constraint established with the limit on the total number of ships deployed on each route per year as a constraint; a third, fourth, and fifth constraint established with the limit on fuel consumption as a constraint; a sixth constraint established with the limit on the total number of route changes of the fleet in any year as a constraint; and a seventh, eighth, and ninth constraint established with the limit on the carbon intensity index level compliance of each ship as a constraint.

[0163] Preferably, the data acquisition module also acquires CII regulatory data, which includes the target CII value of the vessel in a given year, the actual CII value of the vessel in a given year, and the required CII value of the vessel in a given year; based on the required CII value, the boundary values ​​for the vessel to reach CII level C and the boundary values ​​for the vessel to reach CII level D in a given year are calculated respectively; the vessel data also includes the total fuel consumption required by the vessel in a given year, the conventional fuel required by the vessel in a given year, the biofuel consumption of the vessel in a given year, the deadweight tonnage of the vessel, and the total annual sailing distance of the vessel; the route data also includes the minimum number of vessels deployed on each route and the maximum number of times the fleet is allowed to change routes;

[0164] In the multi-objective optimization mathematical model building module, the first constraint is constructed based on the maximum number of ships deployed on the route and the number of ships deployed on the route in a certain year. The second constraint is constructed based on the minimum number of ships deployed on the route and the number of ships deployed on the route in a certain year, so as to ensure that the number of ships deployed on each route in each year is not less than the minimum number of ships deployed on the route and not greater than the maximum number of ships deployed on the route.

[0165] The third constraint is constructed based on the total fuel consumption required by the ship in a certain year, the biofuel required by the ship in a certain year, and the conventional fuel required by the ship in a certain year. The fourth constraint is constructed based on the biofuel required by the ship in a certain year, and the fifth constraint is constructed based on the conventional fuel required by the ship in a certain year, to ensure that the total fuel consumption of the ship is the sum of the biofuel consumption and the conventional fuel consumption, and that both the biofuel consumption and the conventional fuel consumption are non-negative numbers.

[0166] The sixth constraint is constructed based on the ship's biofuel consumption in a certain year and the maximum number of route changes allowed for the fleet, to ensure that the total number of route changes for the fleet during the planning period does not exceed the preset maximum number of allowed changes.

[0167] The seventh constraint is constructed based on the target CII value of the ship in a given year and the actual CII value of the ship in a given year. The eighth constraint is constructed based on the actual CII value of the ship in a given year, the boundary value for the ship to reach CII level C in a given year, the target CII value of the ship in a given year, and the boundary value for the ship to reach CII level D in a given year. The ninth constraint is constructed based on the actual CII value of the ship in a given year, the target CII value of the ship in a given year, the biofuel value required by the ship in a given year, the total fuel consumption value required by the ship in a given year, the deadweight tonnage of the ship, and the total annual sailing distance of the ship, to ensure that the CII level of any ship in any single year shall not be level E, and that the CII level shall not be level D for three consecutive years.

[0168] Preferably, in the new parent population generation module, the screening rules include: selecting all individuals in the non-dominated hierarchy in descending order of non-dominated hierarchy; when selecting all individuals in a certain non-dominated hierarchy would cause the total number to exceed the predetermined number, then selecting individuals in that non-dominated hierarchy in descending order of their crowding distance, until the total number of selected individuals reaches the predetermined number.

[0169] Preferably, in the initial parent population construction module, each individual is encoded using an integer encoding method, and the encoding length is equal to the total number of ships in the fleet.

[0170] This invention provides an objective and scientific method and system for optimizing fleet route allocation. By establishing a bi-objective mathematical model and using an improved NSGA-II algorithm for solution, it can automatically generate a series of Pareto optimal solutions that achieve the best trade-off between biofuel usage (compliance costs) and economic losses caused by insufficient capacity deployment. This enables shipping companies to scientifically select the fleet scheduling strategy with the lowest total operating cost while strictly complying with CII regulations and avoiding compliance risks. It overcomes the difficulties of high computational complexity or poor convergence that traditional mathematical programming methods may face when solving such large-scale combinatorial optimization problems, and can provide high-quality solution sets within a reasonable time, helping shipping companies achieve a balance between environmental and economic benefits in the new context of green transformation.

[0171] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail with reference to the accompanying drawings and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention. In short, all technical solutions and improvements that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention patent.

Claims

1. A method for optimizing fleet route allocation, characterized in that, Includes the following steps: Data acquisition steps: Acquire ship data for each vessel in the fleet and route data for each route. The ship data includes the biofuel value required by the vessel in a given year; the route data includes the maximum number of vessels deployed on each route, the number of vessels deployed on each route in a given year, and the economic loss per vessel due to deploying one less vessel on a route. The steps for establishing a multi-objective optimization mathematical model are as follows: The objectives are to minimize the total biofuel consumption of the fleet during the planning period and to minimize the total economic loss caused by failure to meet the maximum deployment number on routes. Under multiple constraints, including the annual deployment limit for each route, fuel consumption limits, the total number of route changes for the fleet in any year, and the CII rating compliance limit for each vessel, a first objective function is established based on the biofuel required by the vessel in a given year. A second objective function is established based on the maximum number of vessels deployed on the route, the number of vessels deployed on the route in a given year, and the economic loss per vessel. A multi-objective optimization mathematical model is then constructed based on the first and second objective functions. Initial parent population construction steps: Construct an initial parent population consisting of multiple individuals, each individual representing an annual fleet route allocation scheme; The annual fleet route allocation scheme includes: randomly assigning vessels that meet the minimum vessel deployment requirements to each route until all routes meet the minimum vessel deployment requirements; then randomly assigning the remaining unassigned vessels to routes that have not yet met the maximum vessel deployment requirements until all remaining unassigned vessels have been allocated. Objective function value calculation steps: Calculate the first objective function value and the second objective function value corresponding to each individual in the initial parent population according to the first objective function and the second objective function respectively; and perform fast non-dominated sorting on all individuals in the initial parent population based on the calculated first objective function value and the second objective function value, thereby dividing the initial parent population into multiple first non-dominated levels arranged from high to low; Temporary population generation steps: Based on the first non-dominated level and using the selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm, process the current parent population to generate the offspring population, merge the current parent population with the offspring population to form a temporary population; and calculate the first objective function value and the second objective function value corresponding to each individual in the temporary population. Non-dominated sorting and crowding distance calculation steps: Based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, perform fast non-dominated sorting on all individuals in the temporary population, and then divide the temporary population into multiple second non-dominated levels arranged from high to low; then, based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, calculate the crowding distance of each individual in the same non-dominated level; New parent population generation steps: Based on the second non-dominant level and crowding distance, and using preset screening rules, a predetermined number of individuals are selected from the temporary population to form a new parent population. The optimal solution set calculation steps are as follows: Based on the new parent population, the temporary population generation step, the non-dominated sorting and crowding distance calculation step, and the new parent population generation step are repeatedly executed until the preset number of iterations is reached. The individual with the smallest objective function value in the new parent population at the preset number of iterations is taken as the Pareto optimal solution set of the multi-objective optimization mathematical model. According to the Pareto optimal solution set, the final fleet route allocation scheme is selected. This scheme achieves the dual minimization of total biofuel consumption and total economic loss under the premise of satisfying all the above constraints.

2. The fleet route allocation optimization method according to claim 1, characterized in that, In the steps of establishing the multi-objective optimization mathematical model, the multiple constraints include the first and second constraints based on the limit on the total number of ships deployed on each route per year, the third, fourth, and fifth constraints based on the limit on fuel consumption, the sixth constraint based on the limit on the total number of route changes of the fleet in any year, and the seventh, eighth, and ninth constraints based on the limit on the carbon intensity index level compliance of each ship.

3. The fleet route allocation optimization method according to claim 2, characterized in that, The data acquisition step also acquires CII regulatory data, which includes the target CII value of the vessel in a given year, the actual CII value of the vessel in a given year, and the required CII value of the vessel in a given year. Based on the required CII value, the boundary values ​​for the vessel to reach CII level C and the boundary values ​​for the vessel to reach CII level D in a given year are calculated. The vessel data also includes the total fuel consumption required by the vessel in a given year, the conventional fuel required by the vessel in a given year, the biofuel consumption of the vessel in a given year, the deadweight tonnage of the vessel, and the total annual sailing distance of the vessel. The route data also includes the minimum number of vessels deployed on each route and the maximum number of route changes allowed for the fleet. In the step of establishing the multi-objective optimization mathematical model, the first constraint is constructed based on the maximum number of ships deployed on the route and the number of ships deployed on the route in a certain year. The second constraint is constructed based on the minimum number of ships deployed on the route and the number of ships deployed on the route in a certain year, so as to ensure that the number of ships deployed on each route in each year is not less than the minimum number of ships deployed on the route and not greater than the maximum number of ships deployed on the route. The third constraint is constructed based on the total fuel consumption required by the ship in a certain year, the biofuel required by the ship in a certain year, and the conventional fuel required by the ship in a certain year. The fourth constraint is constructed based on the biofuel required by the ship in a certain year, and the fifth constraint is constructed based on the conventional fuel required by the ship in a certain year, to ensure that the total fuel consumption of the ship is the sum of the biofuel consumption and the conventional fuel consumption, and that both the biofuel consumption and the conventional fuel consumption are non-negative numbers. The sixth constraint is constructed based on the ship's biofuel consumption in a certain year and the maximum number of route changes allowed for the fleet, to ensure that the total number of route changes for the fleet during the planning period does not exceed the preset maximum number of allowed changes. The seventh constraint is constructed based on the target CII value of the ship in a given year and the actual CII value of the ship in a given year. The eighth constraint is constructed based on the actual CII value of the ship in a given year, the boundary value for the ship to reach CII level C in a given year, the target CII value of the ship in a given year, and the boundary value for the ship to reach CII level D in a given year. The ninth constraint is constructed based on the actual CII value of the ship in a given year, the target CII value of the ship in a given year, the biofuel value required by the ship in a given year, the total fuel consumption value required by the ship in a given year, the deadweight tonnage of the ship, and the total annual sailing distance of the ship, to ensure that the CII level of any ship in any single year shall not be level E, and that the CII level shall not be level D for three consecutive years.

4. The fleet route allocation optimization method according to claim 1, characterized in that, In the new parent population generation step, the selection rules include: selecting all individuals in the non-dominated hierarchy in descending order of non-dominated hierarchy; when selecting all individuals in a certain non-dominated hierarchy would cause the total number to exceed the predetermined number, then selecting individuals in that non-dominated hierarchy in descending order of their crowding distance, until the total number of selected individuals reaches the predetermined number.

5. The fleet route allocation optimization method according to claim 1, characterized in that, In the initial parent population construction step, each individual is encoded using an integer encoding method, and the encoding length is equal to the total number of ships in the fleet.

6. A fleet route allocation optimization system, characterized in that, The system includes, in sequence, a data acquisition module, a multi-objective optimization mathematical model establishment module, an initial parent population construction module, an objective function value calculation module, a temporary population generation module, a non-dominated sorting and crowding distance calculation module, a new parent population generation module, and an optimal solution set calculation module. The data acquisition module acquires ship data for each vessel in the fleet and route data for each route. The ship data includes the biofuel value required by the vessel in a given year. The route data includes the maximum number of vessels deployed on each route, the number of vessels deployed on each route in a given year, and the economic loss per vessel due to deploying one less vessel on a route. The multi-objective optimization mathematical model building module aims to minimize the total biofuel consumption of the fleet during the planning period and minimize the total economic loss caused by failure to meet the maximum deployment number of routes. Under multiple constraints, including the annual limit on the total number of ships deployed on each route, fuel consumption limits, the limit on the total number of route changes of the fleet in any year, and the CII level compliance limit for each ship, a first objective function is established based on the biofuel value required by the ship in a certain year, and a second objective function is established based on the maximum number of ships deployed on the route, the number of ships deployed on the route in a certain year, and the economic loss of each ship. A multi-objective optimization mathematical model is constructed based on the first objective function and the second objective function. The initial parent population construction module constructs an initial parent population consisting of multiple individuals, with each individual representing an annual fleet route allocation scheme. The annual fleet route allocation scheme includes: randomly assigning vessels that meet the minimum vessel deployment requirements to each route until all routes meet the minimum vessel deployment requirements; then randomly assigning the remaining unassigned vessels to routes that have not yet met the maximum vessel deployment requirements until all remaining unassigned vessels have been allocated. The objective function value calculation module calculates the first objective function value and the second objective function value corresponding to each individual in the initial parent population according to the first objective function and the second objective function respectively; and performs fast non-dominated sorting on all individuals in the initial parent population based on the calculated first objective function value and the second objective function value, thereby dividing the initial parent population into multiple first non-dominated levels arranged from high to low; The temporary population generation module processes the current parent population according to the first non-dominated level and uses selection, crossover, and mutation operations in the non-dominated sorting genetic algorithm to generate a child population, merges the current parent population with the child population to form a temporary population, and calculates the first objective function value and the second objective function value corresponding to each individual in the temporary population. The non-dominated sorting and crowding distance calculation module performs a fast non-dominated sorting on all individuals in the temporary population based on the first objective function value and the second objective function value corresponding to each individual in the temporary population, thereby dividing the temporary population into multiple second non-dominated levels arranged from high to low; and then calculates the crowding distance of each individual in the same non-dominated level based on the first objective function value and the second objective function value corresponding to each individual in the temporary population. The new parent population generation module selects a predetermined number of individuals from the temporary population to form a new parent population based on the second non-dominant level and crowding distance, and using preset screening rules. The optimal solution set calculation module, based on the new parent population, repeatedly executes the temporary population generation module, the non-dominated sorting and crowding distance calculation module, and the new parent population generation module until a preset number of iterations is reached. The individual with the smallest objective function value in the new parent population at the preset number of iterations is taken as the Pareto optimal solution set of the multi-objective optimization mathematical model. Based on the Pareto optimal solution set, the final fleet route allocation scheme is selected. This scheme achieves the dual minimization of total biofuel consumption and total economic loss while satisfying all the aforementioned constraints.

7. The fleet route allocation optimization system according to claim 6, characterized in that, In the multi-objective optimization mathematical model establishment module, the multiple constraints include the first and second constraints established by limiting the total number of ships deployed on each route per year, the third, fourth and fifth constraints established by limiting fuel consumption, the sixth constraint established by limiting the total number of route changes of the fleet in any year, and the seventh, eighth and ninth constraints established by limiting the carbon intensity index level compliance of each ship.

8. The fleet route allocation optimization system according to claim 7, characterized in that, The data acquisition module also acquires CII regulatory data, which includes the target CII value of the vessel in a given year, the actual CII value of the vessel in a given year, and the required CII value of the vessel in a given year. Based on the required CII value, the boundary values ​​for the vessel to reach CII level C and the boundary values ​​for the vessel to reach CII level D in a given year are calculated. The vessel data also includes the total fuel consumption required by the vessel in a given year, the conventional fuel required by the vessel in a given year, the biofuel consumption of the vessel in a given year, the deadweight tonnage of the vessel, and the total annual sailing distance of the vessel. The route data also includes the minimum number of vessels deployed on each route and the maximum number of route changes allowed for the fleet. In the multi-objective optimization mathematical model building module, the first constraint is constructed based on the maximum number of ships deployed on the route and the number of ships deployed on the route in a certain year. The second constraint is constructed based on the minimum number of ships deployed on the route and the number of ships deployed on the route in a certain year, so as to ensure that the number of ships deployed on each route in each year is not less than the minimum number of ships deployed on the route and not greater than the maximum number of ships deployed on the route. The third constraint is constructed based on the total fuel consumption required by the ship in a certain year, the biofuel required by the ship in a certain year, and the conventional fuel required by the ship in a certain year. The fourth constraint is constructed based on the biofuel required by the ship in a certain year, and the fifth constraint is constructed based on the conventional fuel required by the ship in a certain year, to ensure that the total fuel consumption of the ship is the sum of the biofuel consumption and the conventional fuel consumption, and that both the biofuel consumption and the conventional fuel consumption are non-negative numbers. The sixth constraint is constructed based on the ship's biofuel consumption in a certain year and the maximum number of route changes allowed for the fleet, to ensure that the total number of route changes for the fleet during the planning period does not exceed the preset maximum number of allowed changes. The seventh constraint is constructed based on the target CII value of the ship in a given year and the actual CII value of the ship in a given year. The eighth constraint is constructed based on the actual CII value of the ship in a given year, the boundary value for the ship to reach CII level C in a given year, the target CII value of the ship in a given year, and the boundary value for the ship to reach CII level D in a given year. The ninth constraint is constructed based on the actual CII value of the ship in a given year, the target CII value of the ship in a given year, the biofuel value required by the ship in a given year, the total fuel consumption value required by the ship in a given year, the deadweight tonnage of the ship, and the total annual sailing distance of the ship, to ensure that the CII level of any ship in any single year shall not be level E, and that the CII level shall not be level D for three consecutive years.

9. The fleet route allocation optimization system according to claim 6, characterized in that, In the new parent population generation module, the selection rules include: selecting all individuals in the non-dominated hierarchy in descending order of non-dominated hierarchy; when selecting all individuals in a certain non-dominated hierarchy would cause the total number to exceed the predetermined number, then selecting individuals in that non-dominated hierarchy in descending order of their crowding distance, until the total number of selected individuals reaches the predetermined number.

10. The fleet route allocation optimization system according to claim 9, characterized in that, In the initial parent population construction module, each individual is encoded using an integer encoding method, and the encoding length is equal to the total number of ships in the fleet.

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