基于鲁棒性的船体中横剖面多目标优化

工程应用中在进行鲁棒性优化设计时，要求所求出的解既要具有较高的质量，又要满足一定的鲁棒性要求。将鲁棒性优化问题转化为一个双目标的优化问题，即一个目标为解的最优性，另一个目标为解的鲁棒性，并针对一艘最大应力接近许用应力的多用途船进行基于鲁棒性的中横剖面优化设计。首先，用支持向量机的方法建立船体舱段的近似模型，用于求取舱段的最大应力，并结合蒙特卡罗积分的思想构造出表示最大应力鲁棒性的函数；随后，以最大应力最小和最大应力的鲁棒性函数值最小为目标函数，设计出一种求解鲁棒性最优解的粒子群多目标优化算法。优化结果不仅能降低船体结构的最大应力，同时还可较大程度地提高最大应力的鲁棒性，证明了该方法的可行性。

Multi-Objective Optimization Method for the Transverse Section of A Midship Based on Robustness

The relatively high quality and robustness are quite essential in the engineering robust optimiza-tion design. Therefore, in this paper, the robust optimization problem is converted into a two-objective opti-mization problem, with one objective being the optimization of solutions, and another being the robustnessof solutions. The robust optimization design is implemented to the transverse section of a multi-purposeship whose maximum stress is close to the allowable stress. Firstly, the approximate model of the hull cabinis constructed by using the method of Support Vector Machines（SVM） to obtain the maximum stress. Then,by combining with the idea of Monte Carlo integration, the function that represents the robustness of themaximum stress is constructed. Finally, aiming to minimize the maximum stress and the robustness func-tion, the multi-objective optimization method is proposed to solve the robust optimization task. Optimiza-tion results not only demonstrate a reduction in the maximum stress of the hull structure, but also a great im-provement in the robustness of the maximum stress, proving the feasibility of the presented method.