A deceleration system consisting of staged parachute clusters and retro thrusters is optimized for the recovery of the first stage of a launch vehicle on sea. Optimal mass as well as reduction in speed by each parachute cluster and the retro thrusters is essential to minimize the inherent payload loss due to inclusion of additional systems. Three disciplines are involved in the study, namely parachute design, grain design and Three Degrees of Freedom (3-DOF) trajectory simulations. Parachute components are sized and their masses are estimated using a parachute design code. It computes the number of parachutes in the cluster, their sizes and opening loads for multiple reefing stages. Solid motor grain design is carried out, using high burn rate propellant, to provide high thrust to decelerate the launch vehicle stage to a near-zero descent rate at touchdown. A Multiobjective Multidisciplinary Design Optimization (\(\text{M}^{2}\)DO) problem has been formulated to minimize the mass of the deceleration system and minimize the touchdown speed of the recovered stage, subject to constraints on Maximum Expected Operating Pressure (MEOP), feasibility, etc. The optimization is carried out and the Pareto optimal front is obtained using an in-house multi-objective optimization algorithm, Attractor Anchored Multi-objective Evolutionary Algorithm (A\(^2\)-MOEA). A total of twenty-five design variables are considered including initial conditions for each deceleration stage, size of parachute cluster components for both drogue and main parachutes, and the size and shape of the solid motor grain for retro rockets. It is seen that the two objectives are conflicting. The Pareto optimal designs are discussed and the variation of design variables is presented.

由分阶段降落伞组和后推力器组成的减速系统经过优化，可恢复海上运载火箭的第一阶段。每个降落伞组和反向推进器的最佳质量以及速度的降低对于将由于包含其他系统而导致的固有有效载荷损失降至最低至关重要。该研究涉及三个学科，即降落伞设计，谷物设计和三自由度（3-DOF）轨迹模拟。使用降落伞设计代码确定降落伞组件的大小并估算其质量。它计算降落伞中降落伞的数量，降落伞的大小以及多个收帆阶段的开伞负荷。使用高燃烧率推进剂进行固体发动机颗粒设计，提供高推力，以在着陆时将运载火箭阶段减速至接近零的下降速度。多目标多学科设计优化（已制定了\（\ text {M} ^ {2} \） DO）问题，以最大程度地降低减速系统的质量，并最大程度地降低回收台的着陆速度，但要考虑最大预期工作压力（MEOP）的可行性使用内部多目标优化算法，吸引子锚定多目标进化算法（A \（^ 2 \），进行优化并获得帕累托最优前沿-MOEA）。总共考虑了25个设计变量，包括每个减速阶段的初始条件，伞形降落伞和主要降落伞的降落伞簇组件的大小以及后退火箭的固体发动机颗粒的大小和形状。可以看出，这两个目标是矛盾的。讨论了帕累托最优设计，并给出了设计变量的变化。