Convex Relaxation for Optimal Fixture Layout Design

TL;DR

This paper introduces a convex relaxation framework for optimal fixture layout design, transforming a large-scale combinatorial problem into an efficiently solvable convex SDP problem, demonstrated through a real case study.

Contribution

It presents a novel convex relaxation approach for fixture layout optimization, enabling efficient solutions for large-scale problems with improved practical applicability.

Findings

The method produces near-optimal fixture layouts.

It outperforms current industry practices.

Efficiently solves large-scale combinatorial problems.

Abstract

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.