The purpose of the present work is to improve the performance of the standard collaborative optimization (CO) approach based on an existing dynamic relaxation method. This approach may be weakened by starting design points. First, a New Relaxation (NR) method is proposed to solve the difficulties in convergence and low accuracy of CO. The new method is based on the existing dynamic relaxation method and it is achieved by changing the system-level consistency equality constraints into relaxation inequality constraints. Then, a Modified Collaborative Optimization (MCO) approach is proposed to eliminate the impact of the information inconsistency between the system-level and the discipline-level on the feasibility of optimal solutions. In the MCO approach, the impact of the inconsistency is treated by transforming the discipline-level constrained optimization problems into an unconstrained optimization problem using an exact penalty function. Based on the NR method, the performance of the MCO approach carried out by solving two multidisciplinary optimization problems. The obtained results show that the MCO approach has improved the convergence of CO significantly. These results prove that the present MCO succeeds in getting feasible solutions while the CO fails to provide feasible solutions with the used starting design points.

中文翻译：

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基于松弛法的多学科协同优化复杂问题求解

本工作的目的是提高基于现有动态松弛方法的标准协同优化 (CO) 方法的性能。这种方法可能会因开始设计点而被削弱。首先，提出了一种新的松弛(NR)方法来解决CO收敛困难和精度低的问题。新方法是在现有动态松弛方法的基础上，通过将系统级一致性等式约束变为松弛不等式来实现的约束。然后，提出了一种改进的协同优化（MCO）方法，以消除系统级和学科级之间的信息不一致对优化解决方案可行性的影响。在 MCO 方法中，通过使用精确惩罚函数将学科级别的约束优化问题转换为无约束优化问题来处理不一致的影响。基于 NR 方法，MCO 方法的性能通过解决两个多学科优化问题来实现。所得结果表明，MCO方法显着改善了CO的收敛性。这些结果证明，当前的 MCO 成功地获得了可行的解决方案，而 CO 未能提供具有所用起始设计点的可行解决方案。所得结果表明，MCO方法显着改善了CO的收敛性。这些结果证明，当前的 MCO 成功地获得了可行的解决方案，而 CO 未能提供具有所用起始设计点的可行解决方案。所得结果表明，MCO方法显着改善了CO的收敛性。这些结果证明，当前的 MCO 成功地获得了可行的解决方案，而 CO 未能提供具有所用起始设计点的可行解决方案。