Optimizing Fixture Layout for Compliant Part Assembly: A Kriging-Based Metaheuristic

This paper studies a fixture layout optimization problem for the ship assembly. Current studies focus on the positioning problem, i.e., optimizing the positions of a constant number of fixtures, while less considers the sizing problem, i.e., deciding the number of used fixtures. In most of the cases, it is difficult to assure that the adopted number of fixtures can lead to a layout that satisfies all the engineering requirements. The objective of this paper is to minimize the number of fixtures required while optimizing their positions, ensuring adherence to a set of engineering constraints. These include the maximum allowed nodal displacement and the assembly gap between two parts. We propose an efficient two-step metaheuristic approach. In the first step, fixtures are added iteratively to the parts until a feasible layout is achieved. In the second step, a large neighborhood search is employed to remove fixtures while maintaining the feasibility of the layout. To mitigate the computational cost required by finite element simulation, a Kriging model is proposed to evaluate the neighborhood solutions. Numerical experiments show that the proposed method can efficiently solve the fixture sizing and positioning problem in a case study of ship panel assembly. The efficacy of the Kriging model in accelerating layout optimization has been validated. Furthermore, the efficiency of the proposed method is demonstrated through comparisons with two existing approaches in the literature.
Note to Practitioners
—This paper was motivated by the problem of holding large compliant parts in the ship assembly process. Sheet metals with a low thickness-to-length ratio are susceptible to deformation during assembly when an inappropriate fixture layout is adopted. Existing approaches for layout design focus on optimizing the positions of the fixtures, while the number of fixtures needs to be determined based on engineering experience. This paper suggests a new approach to determine the minimum number of fixtures required, as well as their positions, to guarantee a set of quality requirements provided by the user. This approach employs the direct stiffness method to evaluate part deformation and an efficient metaheuristic to optimize the layout. During the optimization procedure, we use the Kriging technique to predict the layout’s performance, allowing us to obtain high-quality solutions with lower simulation efforts. We demonstrate that the proposed method can successfully generate a layout that satisfies the quality specifications in a case study of ship panel assembly. In comparison to two existing approaches, the proposed method yields a feasible layout with fewer fixtures, thereby reducing fixture setup time and building costs.