Linear approximation filter strategy for collaborative optimization with combination of linear approximations

An alternative formulation of collaborative optimization (CO) combined with linear approximations (CLA-CO) is recently developed to improve the computational efficiency of CO. However, for optimization problems with nonconvex constraints, conflicting linear approximations may be added into the system level in the CLA-CO iteration process. In this case, CLA-CO is inapplicable because the conflicting constraints lead to a problem that does not have any feasible region. In this paper, a linear approximation filter (LAF) strategy for CLA-CO is proposed to address the application difficulty with nonconvex constraints. In LAF strategy, whether conflict exists is first identified through transforming the identification problem into the existence problem of feasible region of linear programming; then, the conflicting linear approximations are coordinated by eliminating the larger violated linear approximations. Thereafter, the minimum violated linear approximation replaces the accumulative linear approximations as the system-level constraint. To evaluate the violation of linear approximation, a quantification of the violation is introduced based on the CO process. By using the proposed LAF strategy, CLA-CO can solve the optimization problems with nonconvex constraints. The verification of CLA-CO with LAF strategy to three optimizations, a numerical test problem, a speed reducer design problem, and a compound cylinder design problem, illustrates the capabilities of the proposed LAF strategy.