A robust global optimization approach to solving CO problems – enhanced design space decrease collaborative optimization

Abstract

Collaborative optimization (CO) is a decomposition-based multidisciplinary design optimization method that sometimes suffers from two predominant drawbacks: computational inefficiency and nonexistence of Lagrange multipliers when the system-level optimization solution is system-level feasible. To overcome aforementioned drawbacks, we propose enhanced design space decrease collaborative optimization (EDSDCO). It can notably simplify the system-level optimization problem through modifying the system-level consistency equality constraints that exist in the standard CO to create some linear inequality constraints with no tolerance. Thus, the aforementioned drawbacks, mainly resulted by the use of equality forms of consistency constraints, can be successfully overcome. During the process of optimization, the updated system-level solution space is constantly decreased; meanwhile, the original feasible region is entirely preserved throughout regardless of whether the constraints are convex. Consequently, the global optimum can be obtained when the system-level optimization solution moves into the original feasible region. In EDSDCO, the starting point is not introduced to the formulas of subsystem or system-level optimization. Therefore, the optimum obtained using EDSDCO cannot be affected by the parameters of the starting points, which certainly enhances EDSDCO’s robustness. EDSDCO converges faster than design space decrease collaborative optimization for two reasons: deleting more original infeasible region fragments per iteration and more efficient decision to choose the next solution subspace. In order to illustrate the proposed method’s capabilities, we describe the principles and process of EDSDCO and discuss its application to three optimization problems: a numerical test problem, gear reducer design problem, and combustion of propane problem.