Abstract: Augmented Lagrangian Coordination(ALC)methods are usually classified into centralized ALC and distributed ALC.Considering the limitations of both coordination methods in parallel solving,a distributed parallel augmented Lagrangian coordination MDO method was proposed to achieve parallel solving of sub problems within a distributed coordination framework.Consistency constraints were constructed from the delay coupling information passed in the distributed ALC structure,and the adaptive asynchronous multiplier update strategy was adopted to overcome the mismatch of the consistency constraints.The update scheme based on the coupling variables and multiplier pair penalty weights could avoid large penalty weights.The two improvements avoided divergence and oscillation situations,and the parallel solution of sub problems in distributed ALC was achieved.The feasibility of the proposed method was demonstrated by the simulation.Compared with the centralized ALC,the proposed method did not need to reconstruct the coordination relationship,and the parallelization degree and solution efficiency were higher.The solution of the engineering problem further verified the feasibility and effectiveness of the proposed method,and provided a reference for parallelizing sub problems in decomposition-based optimization methods.

Key words: augmented Lagrangian coordination, distributed, parallel computing, multidisciplinary design optimization, adaptive update strategy

摘要： 鉴于增广拉格朗日协调方法在并行求解上存在一定局限性,为在分布式协调的框架下对子问题进行并行求解,提出分布并行式增广拉格朗日协调的多学科设计优化方法。在分布式协调结构中通过滞后的耦合信息构建一致性约束,采用自适应异步乘子更新策略克服了一致性约束不匹配的问题。根据耦合变量与乘子对惩罚权重进行更新的方案可避免惩罚权重过大的问题。两项改进避免了解发散与振荡的情况,在分布式协调中实现了子问题的并行求解。通过实例仿真证明了所提方法的可行性,与集中式协调方法相比,所提方法无需重构协调关系,并行化程度与求解效率更高。通过求解工程问题进一步验证了所提方法的可行性与有效性,为基于分解的优化方法子问题的并行化求解提供了参考。

关键词: 增广拉格朗日协调, 分布式, 并行计算, 多学科设计优化, 自适应更新策略