A Deterministic Lagrangian-based Global Optimization Approach for Large Scale Decomposable Problems

We propose a deterministic approach for global optimization of large-scale nonconvex quasiseparable problems encountered frequently in engineering systems design, such as multidisciplinary design optimization and product family optimization applications. Our branch and bound-based approach applies Lagrangian decomposition to 1) generate tight lower bounds by exploiting the structure of the problem and 2) enable parallel computing of subsystems and the use of efficient dual methods for computing lower bounds. We apply the approach to the product family optimization problem and in particular to a family of universal electric motors with a fixed platform configuration taken from the literature. Results show that the Lagrangian bounds are much tighter than convex underestimating bounds used in commercial software, and the proposed lower bounding scheme shows encouraging efficiency and scalability, enabling solution of large, highly nonlinear problems that cause difficulty for existing solvers. The deterministic approach also provides lower bounds on the global optimum, eliminating uncertainty of solution quality produced by popular applications of stochastic and local solvers. For instance, our results demonstrate that prior product family optimization results reported in the literature obtained via stochastic and local approaches are suboptimal, and application of our global approach improves solution quality by about 10%. The proposed method provides a promising scalable approach for global optimization of large-scale systems-design problems.