A new Lagrangian solution scheme for non-decomposable multidisciplinary design optimization problems

Multidisciplinary optimization problems exist in many disciplines and constitute a large percentage of problems in industry. Due to their wide-scale applicability, significant research efforts have been spent on developing effective methods that can not only derive accurate solutions but also improve the computational efficiency in the problem solving process. As a result, different algorithms are proposed to coordinate the solution of the different disciplines. However, in realistic problems, the coupling across these disciplines introduces difficulty in the coordination between them. In this paper, a new hybrid meta-heuristic method based on a Lagrangian relaxation of complicating constraints is introduced to reduce the coupling between disciplines in such systems. The proposed scheme identifies complicating constraints and implements a Lagrangian relaxation scheme that allows the constraint to be decomposed over different subproblems. This reduces the coupling across the disciplines and improves the coordination between them. The developed algorithm has been tested on numerical case studies as well as an engineering problem to demonstrate its efficacy as compared with existing methods in the literature for multidisciplinary optimization problems with strong links between subproblems as well as the scalability.