  This paper proposes a general fixture layout design framework that directly
integrates the system equation with the convex relaxation method. Note that the
optimal fixture design problem is a large-scale combinatorial optimization
problem, we relax it to a convex semidefinite programming (SDP) problem by
adopting sparse learning and SDP relaxation techniques. It can be solved
efficiently by existing convex optimization algorithms and thus generates a
near-optimal fixture layout. A real case study in the half-to-half fuselage
assembly process indicates the superiority of our proposed algorithm compared
to the current industry practice and state-of-art methods.
