Many-objective optimization refers to the optimization aiming at four or more objectives. More complex than multi-objective optimization, which copes with two or three objectives, many-objective optimization represents a challenging problem due to the complex trade-off relationships among the optimization objectives. In this study, a four-objective optimization system was proposed for reducing the resistance and the non-uniformity of wake flow of a deep-sea aquaculture vessel at design speed in full load and ballast conditions. The numerical optimization system was mainly composed of the uniform design (UD), free-form deformation method (FFD), radial basis neural network (RBFNN) and a series of genetic algorithms (GAs). During the optimization process, nine design variables were selected to reconstruct the hull geometry. UD and FFD were utilized to generate a series of derivative ship forms. According to CFD calculation results of all derivative ship forms, four surrogate models were constructed, using RBFNN optimized by the particle swarm optimization (PSO), to replace direct numerical calculations. To verify the prediction accuracy advantage of improved RBFNN-based surrogate models based on small sample size, the accuracy comparison was made among surrogate models based on RBFNN, kriging and support vector regression (SVR). Moreover, Sobol' method was employed to analyze the influence of design variables on the optimization objectives. GAs were applied to perform from single-objective to four-objective optimization of the resistance and non-uniformity of wake flow. Eventually, the optimal ship form was selected from the Pareto front of four-objective optimization. Numerical results of the optimized shape showed that the resistance and the non-uniformity of wake flow in full load and ballast conditions were reduced, and the results of the verification and validation (V&V) procedure proved the validation of the many-objective optimization system.

中文翻译：

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基于改进RBF神经网络代理模型的深海养殖船多目标优化

多目标优化是指针对四个或更多目标的优化。多目标优化比处理两个或三个目标的多目标优化更复杂，由于优化目标之间复杂的权衡关系，多目标优化代表了一个具有挑战性的问题。在这项研究中，提出了一种四目标优化系统，以减少深海水产养殖船在满载和压载条件下在设计航速下的阻力和尾流不均匀性。数值优化系统主要由均匀设计（UD）、自由变形法（FFD）、径向基神经网络（RBFNN）和一系列遗传算法（GA）组成。在优化过程中，选择了九个设计变量来重建船体几何形状。UD和FFD被用来生成一系列衍生的船型。根据所有衍生船型的CFD计算结果，构建了4个代理模型，采用粒子群优化（PSO）优化的RBFNN代替直接数值计算。为验证基于小样本改进的基于RBFNN的代理模型的预测精度优势，对基于RBFNN、克里金法和支持向量回归（SVR）的代理模型进行了精度比较。此外，采用Sobol 方法分析设计变量对优化目标的影响。应用遗传算法对尾流阻力和非均匀性进行了从单目标到四目标的优化。最终，最优船型是从四目标优化的帕累托前沿中选出的。优化形状的数值结果表明，满载和压载条件下的阻力和尾流不均匀性降低，验证和验证（V&V）程序的结果证明了多目标优化系统的有效性。