A multi-objective optimization design method for bulbous bow of large ship based on parameterized modeling

Abstract

This invention relates to the fields of shipbuilding and ocean engineering and fluid mechanics, specifically to a multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling, comprising the following steps: S1: Dividing the geometry of the bulbous bow into multiple sections along the transverse and longitudinal directions, and fitting the shape of each section with a high-order polynomial; S2: Defining minimizing wave-making resistance as the first objective function. The second objective function is to maximize the seakeeping performance of the ship. The collaborative optimization objective is as follows: S3: Solve using a decomposition-based multi-objective evolutionary algorithm; S4: Verify the rationality of the Pareto optimal solution set obtained in step S3 through CFD simulation. This invention integrates parametric modeling, surrogate model acceleration, multi-objective evolutionary algorithm, and high-fidelity verification into a complete closed-loop system, reducing reliance on designer experience and shifting the bulbous bow design process from traditional manual trial and error to systematic and automated numerical optimization.

Description

A Multi-Objective Optimization Design Method for Bulbous Bow of Large Ships Based on Parametric Modeling Technical Field

[0001] This invention relates to the fields of shipbuilding and marine engineering and fluid mechanics, and in particular to a multi-objective optimization design method for the bulbous bow of large ships based on parametric modeling. Background Technology

[0002] Large ships generate waves while navigating at sea, and the pressure difference between the bow and stern creates wave-making drag. Optimizing the shape of the bulbous bow can reduce wave-making drag, but improper design will also reduce the ship's seakeeping performance. Therefore, achieving a comprehensive optimization of the bulbous bow's drag reduction and seakeeping performance for large ships is a challenging problem for the shipbuilding and marine engineering industries. Summary of the Invention

[0003] In view of this, the purpose of this invention is to propose a multi-objective optimization design method for the bulbous bow of large ships based on parametric modeling, and to provide a multi-objective collaborative optimization method for bulbous bow that can simultaneously take into account wave-making resistance and seakeeping performance, has high computational efficiency, and can automatically obtain a series of optimal trade-off solutions.

[0004] To achieve the above objectives, this invention provides a multi-objective optimization design method for the bulbous bow of large ships based on parametric modeling, comprising the following steps:

[0005] S1: Parametric modeling: The geometry of the bulbous bow is divided into multiple sections along the transverse and longitudinal directions, and a high-order polynomial is used to fit the shape of each section. The coefficients of the high-order polynomial are used as optimization design variables, thereby transforming the geometry of the bulbous bow into a continuously adjustable parametric model.

[0006] S2: Construct a multi-objective optimization problem: Define minimizing wave-making resistance as the first objective function. The second objective function is to maximize the seakeeping performance of the ship. The collaborative optimization objective is set with constraints on bulbous bow displacement and wetted surface area.

[0007] S3: Optimization Solution Based on Decomposition and Surrogate Model: A multi-objective evolutionary algorithm based on decomposition is used for the solution. This process includes:

[0008] S31: Decompose the multi-objective optimization problem (wave-making resistance and seakeeping performance) into a single-objective optimization subproblem (wave-making resistance or seakeeping performance) using a set of uniformly distributed weight vectors;

[0009] S32: Using a small number of bulbous bow shape parameters, CFD simulations are performed to obtain wave-making drag and seakeeping performance training surrogate models, which replace time-consuming CFD simulations during algorithm iteration, and provide a fast, low-fidelity evaluation of candidate bulbous bow shape parameters.

[0010] S33: During the iteration of bulbous bow shape parameters, the bulbous bow shape parameters that violate the constraints of displacement and wetted surface area are dynamically processed through the penalty function to guide the search toward the feasible region;

[0011] S34: Based on the neighborhood relationship between the sub-problems of bulbous bow shape optimization, co-evolution is carried out, and the bulbous bow shape parameters of each sub-problem are updated by minimizing the Chebyshev aggregation function, and finally a set of Pareto optimal solutions that balances wavemaking drag and seakeeping performance is obtained.

[0012] S4: High-fidelity verification: Perform CFD simulation verification on the Pareto optimal solution set obtained in step S3 to verify the rationality of the optimal solution set.

[0013] Preferably, in step S1, the bow geometry is divided into multiple sections, specifically: four transverse sections are obtained by uniformly dividing the bow along the transverse direction of the ship, and one longitudinal section is obtained by dividing the bow along the centerline of the ship.

[0014] Preferably, the higher-order polynomial is a function of the profile coordinates (x, y), and its expression is:

[0015]

[0016] in, The coefficients of the polynomial constitute the optimization design variables.

[0017] Preferably, in step S2, the ship's seakeeping performance is quantified by the sum of the amplitude operators of the ship's heave and pitch motion responses in regular waves, that is, the second objective function is specifically to minimize the sum of these motion response amplitude operators.

[0018] Preferably, in step S31, control parameters for the multi-objective evolutionary algorithm need to be set, including the population size determining the initial bulbous bow morphology parameter sample size, the upper limit of the number of iterations that can be performed, and operational parameters such as the crossover rate and mutation rate used to perturb the polynomial coefficients of the bulbous bow profile. A set of uniformly distributed weight vectors is constructed according to a preset number, and each weight vector represents an independent bulbous bow sub-optimization task. A set of weight vectors of the same size is generated according to the preset number, and each weight vector corresponds to a bulbous bow optimization sub-problem.

[0019] Preferably, in step S32, a small number of high-fidelity CFD simulation samples are used to train the surrogate model. Specifically, 50 initial bulbous bow shape parameter samples are randomly selected for CFD simulation, and the wave-making drag and seakeeping values ​​obtained from the simulation are used as training data to train the Kriging surrogate model.

[0020] Preferably, the specific steps in step S33 are as follows: calculate the drainage volume and wetted surface area of ​​each individual, and remove individuals that do not meet the constraints. The formula for calculating the drainage volume of the bulbous bow is as follows:

[0021]

[0022] in, The density of seawater, The volume of water displaced by the bulbous bow;

[0023] The formula for calculating the wetted surface area of ​​a bulbous bow is as follows:

[0024]

[0025] This is a three-dimensional parametric surface used to describe the shape of the bulbous bow, which is composed of coordinate functions. , and Together constitute; parameters and These variables, respectively, represent the longitudinal and transverse variations of the bulbous bow surface; the surface with respect to... and partial derivative vector and This describes the local variation trend of the surface in these two directions, and the magnitude of their product is used to represent the size of the area element at that location; parameter domain. The range of values ​​for the above parameter variables is given. Integrating this region yields the overall wetted surface area of ​​the bulbous bow.

[0026] Preferably, in step S33, for new individuals generated during the iteration process, if they violate constraints, the fitness is corrected by using a linear penalty value correction method through a penalty function before re-evaluation. When any constraint exceeds the limit for a candidate solution, the deviation of its corresponding bulbous bow wetted surface area or bulbous bow displacement is first calculated, and each deviation is linearly superimposed according to the preset penalty coefficient to form a total penalty value. Then, the penalty value is added to the original wave-making drag or seakeeping performance value to obtain the corrected fitness. If the constraints are satisfied, the process proceeds directly to the next step.

[0027] Preferably, in step S34, the specific steps are as follows:

[0028] S341: Establish neighborhood set: Calculate the Euclidean distance between each pair of weight vectors used to describe the shape change of the bulbous bow, and define a corresponding neighborhood set T(i) for each bulbous bow optimization subproblem based on the distance;

[0029] S342: Perform neighborhood-based iterative generation: In the region T(i) of each subproblem i, randomly select two parent solutions X from the set of candidate bulbous bow shape parameters. p X q (Corresponding to the two sets of bulbous bow profile polynomial coefficients), a new bulbous bow parameter set Y is generated using the simulated binary crossover operator and the polynomial mutation operator;

[0030] S343: Candidate Solution Determination and Subproblem Update: Includes the following sub-steps:

[0031] S3431: Perform the displacement and wetted surface area constraint check in step S33 on the new bulbous bow parameter set Y. If the constraint is violated, the predicted values ​​of its wave-making drag or seakeeping performance are corrected using a penalty function.

[0032] S3432: Using the trained Kriging bulbous bow shape model, predict the wave-making drag and seakeeping performance of the new bulbous bow parameter set Y;

[0033] S3433: Reference point: If the candidate solution's new bulbous bow parameter set Y shows an advantage over the reference point on any index, then the reference point is updated to ensure that the optimization process continues to move towards a better bulbous bow shape.

[0034] S3434: For each subproblem in the neighborhood T(i) of the new bulbous bow parameter set Y. The Chebyshev convergence function is calculated. After updating the reference point, this index, under the current weights, reflects the most unfavorable wave-making drag or seakeeping performance, thus accurately reflecting the overall merits of the solution in the target space. During the comparison process, when the convergence index of a candidate solution is superior to the existing bulbous bow shape parameters, it is used to replace the original shape parameters, thereby updating the shape parameters of the subproblem.

[0035] S344: Stop iterating when the maximum number of iterations is reached; otherwise, repeat S342-S343 to finally output a set of Pareto optimal solutions.

[0036] Preferably, in step S4, the Pareto optimal solution set obtained in step S3 is re-imported into the CFD software for high-fidelity simulation; the drag and wave resistance performance before and after optimization are compared to verify the effectiveness and superiority of the solution obtained by the method of the present invention.

[0037] The beneficial effects of this invention are as follows:

[0038] I. Achieved efficient multi-objective collaborative optimization: This invention takes both wave-making drag and seakeeping performance as optimization objectives simultaneously, and adopts a decomposition-based multi-objective evolutionary algorithm, which can automatically obtain the complete Pareto optimal solution set in one optimization process, reducing the frequent use of CFD simulation and lowering the computational cost.

[0039] Second, it significantly improves optimization efficiency: By introducing a surrogate model (such as the Kriging model) trained on CFD samples for low-fidelity evaluation, most of the time-consuming CFD calculations in the optimization process are replaced with instantaneous predictions, which reduces the consumption of computing resources and shortens the design cycle.

[0040] Third, the accuracy and feasibility of the optimization model were improved: High-order polynomials were used to parametrically fit multiple profiles, achieving high-precision and continuous control over the complex bulbous bow shape. The shape of the bulbous bow can be continuously changed by adjusting parameters, reducing the repeated trial and error process of manual adjustment and improving modeling accuracy. At the same time, the penalty function mechanism dynamically handles the constraints of displacement and wetted surface area, effectively ensuring that the optimized solution meets the performance requirements. Attached Figure Description

[0041] Figure 1 is a flowchart of the overall process of the method of the present invention;

[0042] Figure 2 is a detailed flowchart of the optimization solution of step S3 of the present invention based on the multi-objective evolutionary algorithm and the surrogate model. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0044] As shown in Figures 1 and 2, a multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling includes the following steps:

[0045] S1: Parametric modeling: The geometry of the bulbous bow is divided into multiple sections along the transverse and longitudinal directions, and a high-order polynomial is used to fit the shape of each section. The coefficients of the high-order polynomial are used as optimization design variables, thereby transforming the geometry of the bulbous bow into a continuously adjustable parametric model.

[0046] In step S1, a preliminary model of the bulbous bow is established using 3D modeling software (such as SolidWorks). The bulbous bow is then uniformly divided laterally to obtain four representative transverse sections, and simultaneously divided along the ship's centerline to obtain a longitudinal section. The coordinate data of the contour points of these sections are exported, and high-order polynomial fitting is performed using mathematical software (such as Matlab). Specifically, the shape of each section is determined by a high-order polynomial with respect to coordinates (x, y). This indicates that the complex three-dimensional shape of the bulbous bow has been transformed into a series of polynomial coefficients. The combination of these coefficients will serve as design variables for subsequent optimization.

[0047] S2: Construct a multi-objective optimization problem: Define minimizing wave-making resistance as the first objective function. The second objective function is to maximize the seakeeping performance of the ship. The collaborative optimization objective is set with constraints on bulbous bow displacement and wetted surface area.

[0048] In step S2, the ship's seakeeping performance is quantified by the sum of the amplitude operators of the ship's heave and pitch motion responses in regular waves. Specifically, the second objective function is to minimize the sum of these motion response amplitude operators.

[0049] S3: Optimization Solution Based on Decomposition and Surrogate Model: A multi-objective (reduce wave-making drag, improve seakeeping performance) evolutionary algorithm based on decomposition is used for the solution. This process includes:

[0050] S31: Problem decomposition: The multi-objective optimization problem (wave-making resistance and seakeeping performance) is decomposed into single-objective optimization subproblems (wave-making resistance or seakeeping performance) through a set of uniformly distributed weight vectors;

[0051] In step S31, control parameters for the multi-objective evolutionary algorithm need to be set, including the population size determining the initial bulbous bow shape parameter sample size, the upper limit of the number of iterations, and operational parameters such as the crossover rate and mutation rate used to perturb the polynomial coefficients of the bulbous bow profile. A set of uniformly distributed weight vectors is constructed according to a preset number, with each weight vector representing an independent bulbous bow sub-optimization task. Under the action of the weight vectors, the wave-making drag and seakeeping target optimization tasks are transformed into two independent scalar sub-problems, and a certain number of candidate shape parameters are initialized within the value range of the bulbous bow shape parameter design variables as the initial population of the algorithm.

[0052] S32: Proxy Model Construction and Low-Fidelity Evaluation: CFD simulation is performed using a small number of bulbous bow shape parameters. The resulting wave-making drag and seakeeping performance are used to train a proxy model, which can replace time-consuming CFD calculations during algorithm iteration and perform fast low-fidelity evaluation of candidate bulbous bow shape parameters.

[0053] In step S32, a surrogate model is trained using wave-making drag and seakeeping performance obtained from a small number of high-fidelity CFD simulations. Specifically, 100 initial bulbous bow shape parameters are randomly generated within the design space. Then, 50 bulbous bow shape parameters are randomly selected from these parameters, and high-fidelity CFD simulations are performed to calculate their first objective function. (Wave resistance) and the second objective function (Volumetric resistance) value. Using these 50 sets of {design variables, objective function values} data as the training set, a Kriging surrogate model is trained.

[0054] S33: Constraint handling: During the iteration of bulbous bow shape parameters, the bulbous bow shape parameters that violate the constraints of displacement and wetted surface area are dynamically handled by the penalty function, guiding the search toward the feasible region;

[0055] The specific steps in step S33 are as follows: calculate the displacement and wetted surface area of ​​each individual, and remove individuals that do not meet the constraints. The formula for calculating the displacement of the bulbous bow is as follows:

[0056]

[0057] in, The density of seawater, The volume of water displaced by the bulbous bow;

[0058] The formula for calculating the wetted surface area of ​​a bulbous bow is as follows:

[0059]

[0060] This is a three-dimensional parametric surface used to describe the shape of the bulbous bow, which is composed of coordinate functions. , and Together constitute; parameters and These variables, respectively, represent the longitudinal and transverse variations of the bulbous bow surface; the surface with respect to... and partial derivative vector and This describes the local variation trend of the surface in these two directions, and the magnitude of their product is used to represent the size of the area element at that location; parameter domain. The range of values ​​for the above parameter variables is given. Integrating this region yields the overall wetted surface area of ​​the bulbous bow.

[0061] In step S33, for new individuals generated during the iteration process, if they violate constraints, the fitness is corrected by using a linear penalty function before evaluation. When any constraint exceeds the limit for a candidate solution, the deviation of the corresponding bulbous bow wetted surface area or bulbous bow displacement is first calculated, and the deviations are linearly superimposed according to the preset penalty coefficient to form a total penalty value. This penalty value is then added to the original wave-making drag or seakeeping performance value to obtain the corrected fitness. If the constraints are satisfied, the process proceeds directly to the next step.

[0062] S34: Based on the neighborhood relationship between the sub-problems of bulbous bow shape optimization, co-evolution is carried out, and the bulbous bow shape parameters of each sub-problem are updated by minimizing the Chebyshev aggregation function, and finally a set of Pareto optimal solutions that balances wavemaking drag and seakeeping performance is obtained.

[0063] Step S34 specifically includes the following steps:

[0064] S341: Establish neighborhood set: Calculate the Euclidean distance between each pair of weight vectors used to describe the shape change of the bulbous bow, and define a corresponding neighborhood set T(i) for each bulbous bow optimization subproblem based on the distance;

[0065] S342: Perform neighborhood-based iterative generation: In the region T(i) of each subproblem i, randomly select two parent solutions X from the set of candidate bulbous bow shape parameters. p X q (Corresponding to the two sets of bulbous bow profile polynomial coefficients), a new bulbous bow parameter set Y is generated using the simulated binary crossover operator and the polynomial mutation operator;

[0066] S343: Candidate Solution Determination and Subproblem Update: Includes the following sub-steps:

[0067] S3431: Perform the displacement and wetted surface area constraint check in step S33 on the new bulbous bow parameter set Y. If the constraint is violated, the predicted values ​​of its wave-making drag or seakeeping performance are corrected using a penalty function.

[0068] S3432: Using the trained Kriging bulbous bow shape model, predict the wave-making drag and seakeeping performance of the new bulbous bow parameter set Y;

[0069] S3433: Reference point: If the candidate solution's new bulbous bow parameter set Y shows an advantage over the reference point on any index, then the reference point is updated to ensure that the optimization process continues to move towards a better bulbous bow shape.

[0070] S3434: For each subproblem in the neighborhood T(i) of the new bulbous bow parameter set Y. The Chebyshev convergence function is calculated. After updating the reference point, this index, under the current weights, reflects the most unfavorable wave-making drag or seakeeping performance, thus accurately reflecting the overall merits of the solution in the target space. During the comparison process, when the convergence index of a candidate solution is superior to the existing bulbous bow shape parameters, it is used to replace the original shape parameters, thereby updating the shape parameters of the subproblem.

[0071] S344: Stop iterating when the maximum number of iterations is reached; otherwise, repeat S342-S343 to finally output a set of Pareto optimal solutions.

[0072] S4: High-fidelity verification: Perform CFD simulation verification on the Pareto optimal solution set obtained in step S3 to verify the rationality of the optimal solution set.

[0073] The Pareto optimal solution set obtained in step S3 (e.g., selecting 3-5 representative bulbous bow parameters) is re-imported into CFD software for simulation. The drag and seakeeping performance before and after optimization are compared to verify the effectiveness and superiority of the solution obtained by the method of this invention. The results show that the optimized bulbous bow design can achieve a good balance between wave-making drag and seakeeping performance, confirming the practical value of this invention.

Claims

1. A multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling, characterized in that, Includes the following steps: S1: Parametric Modeling: The bow geometry is divided into multiple sections along the transverse and longitudinal directions, and a high-order polynomial is used to fit the shape of each section. The coefficients of the high-order polynomial are used as optimization design variables, thereby transforming the bow geometry into a continuously adjustable parametric model; S2: Constructing a Multi-Objective Optimization Problem: The first objective function is defined as minimizing wave-making drag. The second objective function is to maximize the seakeeping performance of the ship. The collaborative optimization objective is set with constraints on bulbous bow displacement and wetted surface area. S3: Optimization Solution Based on Decomposition and Surrogate Model: A multi-objective evolutionary algorithm based on decomposition is used for the solution. Includes: S31: Decomposing a multi-objective optimization problem into single-objective optimization subproblems using a set of uniformly distributed weight vectors; S32: CFD simulations are performed using a small number of bulbous bow shape parameters to obtain surrogate models for wave-making drag and seakeeping performance training. These models replace time-consuming CFD calculations during algorithm iteration, enabling rapid, low-fidelity evaluation of candidate bulbous bow shape parameters. S33: During the iteration of bulbous bow shape parameters, penalty functions are used to dynamically handle bulbous bow shape parameters that violate displacement and wetted surface area constraints, guiding the search towards the feasible region. S34: Co-evolution is performed based on the neighborhood relationships between bulbous bow shape optimization sub-problems. The bulbous bow shape parameters of each sub-problem are updated by minimizing the Chebyshev aggregation function, ultimately obtaining a Pareto optimal solution set that balances wave-making drag and seakeeping performance. S4: High-fidelity verification: CFD simulations are performed on the Pareto optimal solution set obtained in step S3 to verify its rationality.

2. The multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 1, characterized in that, In step S1, the bow geometry is divided into multiple sections, specifically: four transverse sections are obtained by uniformly dividing along the transverse direction of the ship, and one longitudinal section is obtained by dividing along the centerline of the ship.

3. The multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 2, characterized in that, The higher-order polynomial is a function of the profile coordinates (x, y), and its expression is: ;in, The coefficients of the polynomial constitute the optimization design variables.

4. The multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 1, characterized in that, In step S2, the ship's seakeeping performance is quantified by the sum of the amplitude operators of the ship's heave and pitch motion responses in regular waves. Specifically, the second objective function is to minimize the sum of these motion response amplitude operators.

5. The multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 1, characterized in that, In step S31, it is necessary to set the bulbous bow shape control parameters for the multi-objective evolutionary algorithm.

6. A multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 5, characterized in that, In step S32, a surrogate model is trained using a small number of high-fidelity CFD simulation samples. Specifically, 50 initial bulbous bow shape parameter samples are randomly selected for CFD simulation. The wave-making drag and seakeeping values ​​obtained from the simulation are used as training data to train the Kriging surrogate model. This model will be used in subsequent iterations to quickly predict the objective function values ​​of the new bulbous bow shape parameters.

7. A multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 6, characterized in that, The specific steps in step S33 are as follows: calculate the displacement and wetted surface area of ​​each individual, and remove individuals that do not meet the constraints. The formula for calculating the displacement of the bulbous bow is as follows: ;in, The density of seawater, The bulbous bow has a displacement volume; the wetted surface area of ​​the bulbous bow is calculated using the following formula: ； This is a three-dimensional parametric surface used to describe the shape of the bulbous bow, which is composed of coordinate functions. 、 and Together constitute; parameters and These variables, respectively, represent the longitudinal and transverse variations of the bulbous bow surface; the surface with respect to... and The partial derivative vector and This describes the local variation trend of the surface in these two directions, and the magnitude of their product is used to represent the size of the area element at that location; parameter domain. The range of values ​​for the above parameter variables is given. Integrating this region yields the overall wetted surface area of ​​the bulbous bow.

8. A multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 7, characterized in that, In step S33, if the new bulbous bow shape parameters generated during the iteration process violate the constraints of displacement and wetted surface area, they are corrected by a penalty function and then evaluated again. If the constraints are satisfied, the process proceeds directly to the next step.

9. A multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 8, characterized in that, In step S34, specifically The steps include: S341: Establishing a neighborhood set: Calculate the Euclidean distance between each pair of weight vectors used to describe the changes in the bulbous bow shape, and define a corresponding neighborhood set T(i) for each bulbous bow optimization subproblem based on the distance; S342: Performing neighborhood-based iterative generation: In the region T(i) of each subproblem i, randomly select two parent solutions X from the candidate bulbous bow shape parameter set. p X q A new bulbous bow shape parameter set Y is generated using a simulated binary crossover operator and a polynomial mutation operator; S343: Candidate solution determination and sub-problem update: including the following sub-steps: S3431: Check the displacement and wetted surface area constraints of the new bulbous bow shape parameter set Y in step S33. If the constraints are violated, the predicted values ​​of wave-making drag or seakeeping performance are corrected using a penalty function; S3432: Predict the wave-making drag and seakeeping performance of the new bulbous bow shape parameter set Y using the trained Kriging bulbous bow shape model; S3433: Reference point: If the candidate solution, the new bulbous bow shape parameter set Y, shows an advantage over the reference point on any index, then the reference point is updated to ensure that the optimization process continues towards a better bulbous bow shape; S3434: For each subproblem in the neighborhood T(i) where the new bulbous bow shape parameter set Y is located. The Chebyshev aggregation function is calculated. After updating the reference point, the performance of this index under the current weight reflects the most unfavorable wavemaking resistance or wavekeeping ability, thus accurately reflecting the overall quality of the solution in the target space. During the comparison process, when the aggregation index of the candidate solution is better than the existing solution, it is used to replace the original solution, thereby updating the solution of the subproblem. S344: Stop the iteration when the maximum number of iterations is reached, otherwise repeat S342-S343, and finally output a set of Pareto optimal solutions.

10. A multi-objective optimization design method for the bulbous bow of a large ship based on parametric modeling as described in claim 9, characterized in that, In step S4, the Pareto optimal solution set obtained in step S3 is re-imported into the CFD software for high-fidelity simulation; the wave-making drag and seakeeping performance before and after optimization are compared to verify the rationality of the optimal bulbous bow shape parameters.

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