A multi-objective optimization method for polar icebreaker based on improved NSGA-III algorithm

Abstract

The application provides a polar icebreaker multi-objective optimization method based on an improved NSGA-III algorithm, and comprises the following steps: S1, outputting a design variable space; S2, constructing a multi-objective optimization mathematical model according to an actual working condition of polar navigation, and outputting a target function definition and a constraint condition expression in the mathematical model; S3, forming a design variable-performance target sample database; S4, independently training a machine learning regression model for each optimization target based on the sample database by using an integrated learning strategy; S5, performing optimization search in the output design variable space by using the improved NSGA-III algorithm, and outputting a Pareto optimal solution set meeting all constraint conditions after iterative optimization; and S6, outputting an optimal ship type design after verification. The application realizes significant reduction of icebreaking resistance, effectively controls wave resistance, and provides an efficient and systematic solution for ship type innovative design of the polar icebreaker in a complex ice-wave coupling environment.

Description

Technical Field

[0001] This invention relates to the field of ship design and optimization technology, and more particularly to a multi-objective optimization method for polar icebreakers based on an improved NSGA-III algorithm. Background Technology

[0002] With the increasing strategic value of the Arctic shipping routes, the demand for high-performance icebreakers is becoming increasingly urgent. Polar icebreakers face complex ice-wave coupled environments during operations, and their design must simultaneously consider strong icebreaking capabilities and good navigation efficiency in ice-free / wavey waters. The bow hull line is the most critical component affecting a ship's icebreaking and hydrodynamic performance.

[0003] In current technologies, the design of polar icebreakers primarily relies on the modification of existing designs and design experience. Engineers adjust parameters based on a series of hull test data or single performance indicators such as still water resistance, and then verify performance through a limited number of model tests or numerical simulations. In recent years, simulation-driven optimization methods have gradually emerged. For example, computational fluid dynamics methods are used to predict ship wave resistance, and nonlinear finite element methods are used to predict ice resistance, embedding these high-precision simulation tools into optimization loops. Some studies have attempted to optimize icebreaker hull designs using multi-objective evolutionary algorithms, considering two or three performance objectives simultaneously. To reduce simulation costs, some researchers use surrogate models such as Kriging models or support vector machines to replace direct numerical simulations, thereby accelerating the optimization iteration speed.

[0004] However, existing technologies have significant shortcomings. First, traditional design methods struggle to achieve a systematic balance between icebreaking resistance and wave resistance, often sacrificing one for the other and failing to obtain a truly comprehensive optimal solution. Second, high-fidelity simulations of ice resistance and wave resistance are extremely time-consuming, often requiring hours or even days for a single calculation. Directly applying this to population-based iterative optimization algorithms results in prohibitively high computational costs. Existing surrogate models are mostly single machine learning models, whose prediction accuracy and robustness are insufficient to meet the reliability requirements of multi-objective optimization for solution sets. Furthermore, conventional multi-objective evolutionary algorithms, when dealing with high-dimensional problems with four or more optimization objectives, suffer from slow convergence speeds, uneven Pareto front distribution, and are prone to getting trapped in local optima or generating clustered solutions, making it difficult to provide diverse design candidate solutions. Therefore, a systematic method that efficiently integrates high-precision simulation, low-cost prediction, and high-dimensional multi-objective optimization is urgently needed to overcome these shortcomings. Summary of the Invention

[0005] In view of this, the purpose of this invention is to propose a multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm, so as to solve the technical problems of difficult multi-performance balance design, high cost of high-precision simulation optimization, and low efficiency of multi-objective optimization in existing polar icebreakers.

[0006] The technical means employed in this invention are as follows:

[0007] A multi-objective optimization method for polar icebreakers based on an improved NSGA-III algorithm includes the following steps: S1. For the target icebreaker, establish a fully parameterized geometric model of the bow, extract the key design variables that control the changes in the bow line, define the feasible range of each key design variable, and output the design variable space. S2. Based on the actual working conditions of polar navigation, using the variables in the design variable space output by S1 as independent variables, construct a multi-objective optimization mathematical model with calm sea state wave resistance, moderate sea state wave resistance, first ice thickness ice resistance and second ice thickness ice resistance as optimization objectives and changes in the main hull size as constraints. Output the definition of the objective function and the expression of the constraint conditions in the mathematical model. S3. The design variable space output by S1 is sampled using the Sobol sequence to obtain the design variable values ​​of multiple sample ship types. According to the working conditions specified in the objective function definition output by S2, wave resistance is calculated using computational fluid dynamics and ice resistance is calculated using nonlinear finite element method. The design variable values ​​of each sample ship type are combined with the corresponding resistance values ​​to form a design variable-performance target sample database. S4. Based on the sample database output by S3, an ensemble learning strategy is used to independently train a machine learning regression model for each optimization objective. All trained regression models are integrated into a high-precision surrogate model. The high-precision surrogate model is used to input the design variable values ​​and output the corresponding predicted values ​​of the four optimization objectives. S5. The improved NSGA-III algorithm is used to perform optimization search in the design variable space output by S1. The improved NSGA-III algorithm uses the high-precision surrogate model output by S4 as the objective function calculator, and the constraint expression output by S2 as the basis for feasibility judgment. During each evaluation, the surrogate model quickly predicts the four optimization objective values ​​corresponding to the design variables and checks whether the design variables meet the constraints. After iterative optimization, the Pareto optimal solution set that meets all constraints is output. S6. Select a final optimized scheme from the Pareto optimal solution set output by S5, and use the computational fluid dynamics method and nonlinear finite element method in S3 to perform high-fidelity simulation verification on the final optimized scheme, and output the verified optimal ship design.

[0008] Furthermore, the key design variables mentioned in S1 include the ordinate of the control point Pz of the outer drift angle curve, the change in the longitudinal position of the center of buoyancy Delta_XCB, and the tangent angle Stem_angle of the bow profile at the waterline. Furthermore, the ensemble learning strategy described in S4 is as follows: for the four optimization objectives, the model with the highest prediction accuracy is independently selected from multiple base learners for each objective through cross-validation; the base learners include ridge regression, random forest, extreme random tree, and gradient boosting tree.

[0009] Furthermore, the improved NSGA-III algorithm includes the following steps: The population is initialized in the design variable space, and a set of uniformly distributed reference points are generated on the unit hyperplane of the target space. The system enters an iterative optimization loop. In each generation, offspring populations are generated from the current population through selection, crossover, and hybrid mutation operations, with the hybrid mutation operations performed at a preset probability. Perform polynomial mutation; otherwise, within the feasible region of the variable. Perform uniform random mutation within the internal domain; The parent and offspring populations are merged, and a rapid non-dominated sort is performed to classify individuals into different non-dominated layers. Calculate the ideal point and extreme point of the current population, and normalize the target value of the population accordingly. Then, associate each normalized individual with the reference point whose direction vector is closest to it. The environment selection is performed to build a new generation of population, that is, individuals are selected layer by layer from the optimal non-dominated layer until the preset population size is reached. When it is necessary to select from the same non-dominated layer, individuals associated with reference points with lower niche counts are given priority. Adaptive reference point adjustments are performed periodically, which involves calculating the individual density within the neighborhood of each reference point. and for densities exceeding a preset threshold The reference point, in its direction vector Add a normally distributed one to the top random perturbation The perturbated vector is then normalized to generate a new reference point. ; After the termination condition is met, the final population is output as the Pareto optimal solution set.

[0010] Furthermore, in the adaptive reference point adjustment strategy, the adjustment formula for the reference point rh is:

[0011] Where δ ~ N(0, σ²) I(ρh>τ), where I(·) is the indicator function, ρh is the population density in the neighborhood of the reference point rh, and τ is the density threshold.

[0012] Furthermore, the strategy formula for the hybrid mutation operator is:

[0013] Where xL and xU are the lower and upper limits of the design variables.

[0014] Furthermore, in S2, the first ice thickness is 0.8 meters and the second ice thickness is 1.0 meter.

[0015] This invention also provides a multi-objective optimization system for polar icebreakers based on an improved NSGA-III algorithm, implemented based on the aforementioned multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm, including: The parametric modeling module is used to build a fully parametric geometric model of the bow, extract and output key design variables and their feasible ranges to the optimization algorithm engine module; The performance prediction module integrates a computational fluid dynamics solver and a nonlinear finite element solver to perform high-fidelity simulations of wave resistance and ice resistance on sample ship types, and outputs the generated design variable-performance target sample database to the proxy model management module. The agent model management module is used to store the sample database, train an ensemble learning agent model based on the database, and encapsulate the trained agent model into a callable objective function interface and provide it to the optimization algorithm engine module. The optimization algorithm engine module is used to run the improved NSGA-III algorithm. It obtains the design variable space from the parametric modeling module and the objective function interface from the surrogate model management module. During the optimization process, it repeatedly calls the interface to perform population evaluation and finally outputs the Pareto optimal solution set that meets the constraints to the post-processing and visualization module. The post-processing and visualization module receives the Pareto optimal solution set output by the optimization algorithm engine module, selects the final optimization scheme from it, and outputs the design variable values ​​and performance prediction values ​​of the optimized ship type.

[0016] The present invention also provides a storage medium comprising a stored program, wherein, when the program is executed, it performs any of the above-described multi-objective optimization methods for polar icebreakers based on the improved NSGA-III algorithm.

[0017] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes any of the above-mentioned multi-objective optimization methods for polar icebreakers based on the improved NSGA-III algorithm through the computer program.

[0018] Compared with the prior art, the present invention has the following advantages: This invention is the first to deeply integrate fully parametric modeling, high-precision ice / wave coupling performance prediction, data-driven surrogate model and advanced multi-objective optimization algorithm to form a complete simulation-surrogate-optimization closed-loop system suitable for the conceptual design of polar icebreakers, which solves the problem of comprehensively balancing multiple performance indicators in traditional design mode.

[0019] This invention constructs a high-quality initial sample library through Sobol sequence sampling and utilizes an ensemble learning surrogate model to replace expensive simulations, reducing the time for a single performance evaluation from hours to milliseconds, making it possible to apply high-precision simulation-driven optimization. The improved NSGA-III algorithm further enhances search efficiency and solution set quality in high-dimensional multi-objective spaces. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the overall process of the multi-objective optimization method for polar icebreakers according to the present invention.

[0022] Figure 2 This is a schematic diagram of the nonlinear finite element model of ship-ice collision in this invention.

[0023] Figure 3 This is a schematic diagram of the fully parameterized model and design variables of the bow of the ship according to the present invention.

[0024] Figure 4 This is a schematic diagram illustrating the prediction accuracy of each optimized target proxy model in this invention.

[0025] Figure 5 This is a schematic diagram of the optimized process of the present invention.

[0026] Figure 6 This is a schematic diagram of the Pareto front obtained by optimization in this invention.

[0027] Figure 7 This is a schematic diagram comparing the ship's geometry before and after optimization according to the present invention.

[0028] Figure 8 This is a schematic diagram comparing the wave-making of the bow of the ship before and after the optimization of this invention. Detailed Implementation

[0029] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0030] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0031] like Figure 1 As shown, this invention provides a multi-objective optimization method for polar icebreakers based on an improved NSGA-III algorithm, comprising the following steps: S1. For the target icebreaker, establish a fully parameterized geometric model of the bow, extract the key design variables that control the changes in the bow line, define the feasible range of each key design variable, and output the design variable space. Using a PC6-class icebreaker as the model, a fully parametric model was created using CAESES software. For example... Figure 3 As shown, the deformation of the bow profile is controlled by three key parameters: the ordinate of the control point Pz on the outer drift angle curve, the change in the longitudinal position of the center of buoyancy Delta_XCB, and the tangent angle Stem_angle at the waterline of the bow profile. The design variable range is set as follows: Pz ∈ [35, 45], Delta_XCB ∈ [-0.05%, 0.02%], Stem_angle ∈ [25°, 40°].

[0032] S2. Based on the actual working conditions of polar navigation, using the variables in the design variable space output by S1 as independent variables, construct a multi-objective optimization mathematical model with calm sea state wave resistance, moderate sea state wave resistance, first ice thickness ice resistance and second ice thickness ice resistance as optimization objectives and changes in the main hull size as constraints. Output the definition of the objective function and the expression of the constraint conditions in the mathematical model. The optimization objectives are defined as follows: wave resistance RwaveA in calm sea state (wave height 1.5m), wave resistance RwaveB in moderate sea state (wave height 2.0m), ice resistance Rice_0.8m at 0.8m ice thickness, and ice resistance Rice_1.0m at 1.0m ice thickness. The constraint is that the rate of change of displacement volume and wetted surface area of ​​the optimized hull form shall not exceed ±1% of that of the parent hull form.

[0033] S3. The design variable space output by S1 is sampled using the Sobol sequence to obtain the design variable values ​​of multiple sample ship types. According to the working conditions specified in the objective function definition output by S2, wave resistance is calculated using computational fluid dynamics and ice resistance is calculated using nonlinear finite element method. The design variable values ​​of each sample ship type are combined with the corresponding resistance values ​​to form a design variable-performance target sample database. 400 sample points were extracted within the design space using a Sobol sequence, and the corresponding hull geometry was automatically generated for each sample point. Wave resistance calculations were performed using STAR-CCM+ software, with two-phase flow CFD simulations conducted on the scaled-down model (see [link to computational domain settings]). Figure 2 Ice drag calculations were performed using LS-DYNA software, establishing a nonlinear finite element model of the ship-ice collision (see model details). Figure 2 The system simulates the continuous icebreaking process of ships and extracts the average ice resistance. Through batch processing, a sample database containing 400 sets of "3 design variables - 4 performance objectives" is constructed.

[0034] S4. Based on the sample database output by S3, an ensemble learning strategy is used to independently train a machine learning regression model for each optimization objective. All trained regression models are integrated into a high-precision surrogate model. The high-precision surrogate model is used to input the design variable values ​​and output the corresponding predicted values ​​of the four optimization objectives. 320 samples were randomly selected from 400 samples as the training set and 80 as the test set. The scikit-learn library in Python was used to train surrogate models for each of the four objectives. Five-fold cross-validation was used to compare the performance of algorithms such as Ridge Regression, Support Vector Machine, Random Forest, Extremely Randomized Tree, and Gradient Boosting Tree. The final selected models were: Rice_1.0m using Ridge Regression (test set R²=0.902), Rice_0.8m using Random Forest (R²=0.964), RwaveA using Extremely Randomized Tree (R²=0.985), and RwaveB using Gradient Boosting Tree (R²=0.953). The prediction accuracy of each model is compared below. Figure 4 As shown, the top left shows the prediction accuracy of icebreaking resistance with 0.8 meters of ice thickness; the top right shows the prediction accuracy of icebreaking resistance with 1 meter of ice thickness; the bottom left shows the prediction accuracy of wave resistance in calm sea conditions; and the bottom right shows the prediction accuracy of wave resistance in moderate sea conditions. All of these accuracy meet the requirements for engineering applications.

[0035] S5. The improved NSGA-III algorithm is used to perform optimization search in the design variable space output by S1. The improved NSGA-III algorithm uses the high-precision surrogate model output by S4 as the objective function calculator, and the constraint expression output by S2 as the basis for feasibility judgment. During each evaluation, the surrogate model quickly predicts the four optimization objective values ​​corresponding to the design variables and checks whether the design variables meet the constraints. After iterative optimization, the Pareto optimal solution set that meets all constraints is output. The improved NSGA-III algorithm includes the following steps: The population is initialized in the design variable space, and a set of uniformly distributed reference points are generated on the unit hyperplane of the target space. The system enters an iterative optimization loop. In each generation, offspring populations are generated from the current population through selection, crossover, and hybrid mutation operations, with the hybrid mutation operations performed at a preset probability. Perform polynomial mutation; otherwise, within the feasible region of the variable. Perform uniform random mutation within the internal domain; The parent and offspring populations are merged, and a rapid non-dominated sort is performed to classify individuals into different non-dominated layers. Calculate the ideal point and extreme point of the current population, and normalize the target value of the population accordingly. Then, associate each normalized individual with the reference point whose direction vector is closest to it. The environment selection is performed to build a new generation of population, that is, individuals are selected layer by layer from the optimal non-dominated layer until the preset population size is reached. When it is necessary to select from the same non-dominated layer, individuals associated with reference points with lower niche counts are given priority. Adaptive reference point adjustments are performed periodically, which involves calculating the individual density within the neighborhood of each reference point. and for densities exceeding a preset threshold The reference point, in its direction vector Add a normally distributed one to the top random perturbation The perturbated vector is then normalized to generate a new reference point. ; After the termination condition is met, the final population is output as the Pareto optimal solution set.

[0036] The improved NSGA-III algorithm includes the following two improvement mechanisms: (1) Adaptive reference point adjustment strategy: Periodically apply random perturbation to the direction of reference points with too many associated individuals based on the current population distribution density in the normalized target space and renormalize them, so that the search direction can dynamically spread from the clustered area to the sparse area. (2) Hybrid mutation operator: selects between polynomial mutation and uniform mutation with a preset probability pm, where polynomial mutation is used for local fine search and uniform mutation is used for global exploration in the entire feasible domain of design variables.

[0037] This paper introduces two key improvements to the classic NSGA-III framework to further enhance optimization performance: First, an adaptive reference point adjustment strategy. Classic algorithms use a fixed set of reference points, which may fail to effectively guide the search when the Pareto front is irregular or the population distribution shifts. The algorithm in this paper periodically (e.g., every...) adjusts the reference points. (Generation) The reference points are dynamically adjusted based on the current population distribution density in the normalized target space. Specifically, the reference points are calculated for each generation. Population density within a certain neighborhood For reference points with excessively high density, a small random perturbation is added to their direction vector. And renormalize it: · in, This is an indicator function. This operation causes the search direction to diffuse from clustered regions to sparse regions, thereby dynamically improving the distribution of the population.

[0038] Second, a hybrid mutation operator: To enhance the algorithm's global exploration capability and prevent premature convergence, this paper designs a hybrid mutation operator. This operator combines two mutation methods with a preset probability: polynomial mutation. The mixed strategy is used for localized, fine-grained searches near the parent individual; uniform mutation is used for completely random sampling across the entire feasible region of the variable to achieve large jumps and explore new regions. The formula for the mixed strategy is expressed as:

[0039] in, This represents the probability of using polynomial mutation. This mechanism balances the development and exploration capabilities of the algorithm.

[0040] An improved NSGA-III algorithm was implemented using Python's pymoo library. Algorithm parameter settings: population size 92, crossover probability 0.9, crossover exponent 15, mutation exponent 20. Two improvements were enabled: 1) Adaptive reference point adjustment every 20 generations (density threshold τ = population size / number of reference points). 2); 2) Use a hybrid mutation operator (pm=0.8). The optimization process is as follows: Figure 5 As shown, after running the algorithm for 100 generations, a well-distributed Pareto optimal solution set is obtained, such as... Figure 6As shown, the left figure is a schematic diagram of the ice resistance part of the Pareto solution, and the right figure is a schematic diagram of the wave resistance part of the Pareto solution.

[0041] S6. Select a final optimized scheme from the Pareto optimal solution set output by S5, and use the computational fluid dynamics method and nonlinear finite element method in S3 to perform high-fidelity simulation verification on the final optimized scheme, and output the verified optimal ship design.

[0042] Based on the actual operation reports of the Chinese polar research vessel, four target weights were assigned: RwaveB (42%), RwaveA (18%), Rice_0.8m (24%), and Rice_1.0m (16%). The scheme with the highest weighted score from the Pareto solution set was selected as the final optimized hull form. A comparison of design variables and performance before and after optimization is shown in Table 1 attached to the accompanying drawings in the specification. The design variables of the optimized hull form were substituted into step S3 for high-fidelity simulation verification. The results showed a high degree of agreement with the predicted values ​​of the surrogate model (error <1%), verifying the reliability of the optimization results. The optimized hull form has a more slender and steep bow, as shown in the comparison... Figure 7 As shown, the left image is the model of the parent ship, and the right image is the optimized ship model; the wave-making effect is significantly reduced, compared to, for example Figure 8 As shown, the left figure is the wave scalar diagram of the parent ship, and the right figure is the wave scalar diagram of the optimized ship; the resistance is reduced by 20.31% with ice thickness of 0.8m and by 7.98% with ice thickness of 1.0m, and the wave resistance is also slightly reduced, resulting in a significant improvement in overall performance.

[0043] Table 1 Comparison of Ship Types Before and After Optimization

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective optimization method for polar icebreakers based on an improved NSGA-III algorithm, characterized in that, Includes the following steps: S1. For the target icebreaker, establish a fully parameterized geometric model of the bow, extract the key design variables that control the changes in the bow line, define the feasible range of each key design variable, and output the design variable space. S2. Based on the actual working conditions of polar navigation, using the variables in the design variable space output by S1 as independent variables, construct a multi-objective optimization mathematical model with calm sea state wave resistance, moderate sea state wave resistance, first ice thickness ice resistance and second ice thickness ice resistance as optimization objectives and changes in the main hull size as constraints. Output the definition of the objective function and the expression of the constraint conditions in the mathematical model. S3. The design variable space output by S1 is sampled using the Sobol sequence to obtain the design variable values ​​of multiple sample ship types. According to the working conditions specified in the objective function definition output by S2, wave resistance is calculated using computational fluid dynamics and ice resistance is calculated using nonlinear finite element method. The design variable values ​​of each sample ship type are combined with the corresponding resistance values ​​to form a design variable-performance target sample database. S4. Based on the sample database output by S3, an ensemble learning strategy is used to independently train a machine learning regression model for each optimization objective. All trained regression models are integrated into a high-precision surrogate model. The high-precision surrogate model is used to input the design variable values ​​and output the corresponding predicted values ​​of the four optimization objectives. S5. The improved NSGA-III algorithm is used to perform optimization search in the design variable space output by S1. The improved NSGA-III algorithm uses the high-precision surrogate model output by S4 as the objective function calculator, and the constraint expression output by S2 as the basis for feasibility judgment. During each evaluation, the surrogate model quickly predicts the four optimization objective values ​​corresponding to the design variables and checks whether the design variables meet the constraints. After iterative optimization, the Pareto optimal solution set that meets all constraints is output. S6. Select a final optimized scheme from the Pareto optimal solution set output by S5, and use the computational fluid dynamics method and nonlinear finite element method in S3 to perform high-fidelity simulation verification on the final optimized scheme, and output the verified optimal ship design.

2. The multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm according to claim 1, characterized in that, The key design variables mentioned in S1 include the ordinate of the control point Pz of the outer drift angle curve, the change in the longitudinal position of the center of buoyancy Delta_XCB, and the tangent angle Stem_angle of the bow profile at the waterline.

3. The multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm according to claim 1, characterized in that, The ensemble learning strategy described in S4 is as follows: for the four optimization objectives, the model with the highest prediction accuracy is independently selected from multiple base learners for each objective through cross-validation; the base learners include ridge regression, random forest, extreme random tree, and gradient boosting tree.

4. The multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm according to claim 1, characterized in that, The improved NSGA-III algorithm includes the following steps: The population is initialized in the design variable space, and a set of uniformly distributed reference points are generated on the unit hyperplane of the target space. The system enters an iterative optimization loop. In each generation, offspring populations are generated from the current population through selection, crossover, and hybrid mutation operations, with the hybrid mutation operations performed at a preset probability. Perform polynomial mutation; otherwise, within the feasible region of the variable. Perform uniform random mutation within the internal domain; The parent and offspring populations are merged, and a rapid non-dominated sort is performed to classify individuals into different non-dominated layers. Calculate the ideal point and extreme point of the current population, and normalize the target value of the population accordingly. Then, associate each normalized individual with the reference point whose direction vector is closest to it. The environment selection is performed to build a new generation of population, that is, individuals are selected layer by layer from the optimal non-dominated layer until the preset population size is reached. When it is necessary to select from the same non-dominated layer, individuals associated with reference points with lower niche counts are given priority. Adaptive reference point adjustments are performed periodically, which involves calculating the individual density within the neighborhood of each reference point. and for densities exceeding a preset threshold The reference point, in its direction vector Add a normally distributed one to the top random perturbation The perturbated vector is then normalized to generate a new reference point. ; After the termination condition is met, the final population is output as the Pareto optimal solution set.

5. The multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm according to claim 4, characterized in that, In the adaptive reference point adjustment strategy, the adjustment formula for reference point rh is: Where δ ~ N(0, σ²) I(ρh>τ), where I(·) is the indicator function, ρh is the population density in the neighborhood of the reference point rh, and τ is the density threshold.

6. The multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm according to claim 4, characterized in that, The strategy formula for the hybrid mutation operator is: Where, x L and x U To design the lower and upper limits of variables.

7. The multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm according to claim 1, characterized in that, In S2, the first ice thickness is 0.8 meters and the second ice thickness is 1.0 meter.

8. A multi-objective optimization system for polar icebreakers based on an improved NSGA-III algorithm, implemented based on the multi-objective optimization method for polar icebreakers based on an improved NSGA-III algorithm as described in any one of claims 1-7, characterized in that... include: The parametric modeling module is used to build a fully parametric geometric model of the bow, extract and output key design variables and their feasible ranges to the optimization algorithm engine module; The performance prediction module integrates a computational fluid dynamics solver and a nonlinear finite element solver to perform high-fidelity simulations of wave resistance and ice resistance on sample ship types, and outputs the generated design variable-performance target sample database to the proxy model management module. The agent model management module is used to store the sample database, train an ensemble learning agent model based on the database, and encapsulate the trained agent model into a callable objective function interface and provide it to the optimization algorithm engine module. The optimization algorithm engine module is used to run the improved NSGA-III algorithm. It obtains the design variable space from the parametric modeling module and the objective function interface from the surrogate model management module. During the optimization process, it repeatedly calls the interface to perform population evaluation and finally outputs the Pareto optimal solution set that meets the constraints to the post-processing and visualization module. The post-processing and visualization module receives the Pareto optimal solution set output by the optimization algorithm engine module, selects the final optimization scheme from it, and outputs the design variable values ​​and performance prediction values ​​of the optimized ship type.

9. A storage medium, characterized in that, The storage medium includes a stored program, wherein, when the program is executed, it performs the multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm as described in any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the multi-objective optimization method for polar icebreakers based on the improved NSGA-III algorithm as described in any one of claims 1 to 8 through the computer program.

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