Two-Level Nonlinear Mixed Discrete-Continuous Optimization-Based Design: An Application to Printed Circuit Board Assemblies

Abstract

In this paper, a new approach for optimization-based design of nonlinearly mixed discrete-continuous problems has been developed. The approach is based on a two-level decomposition strategy in which the entire domain of variables is partitioned into two levels, one involving the continuous variables and the other involving the discrete variables. Variables in one level are optimized for fixed values of the variable from the other level. A modified penalty function is formed, based on monotonicity analysis, to solve for the discrete variables, and a conventional optimization method is used to solve for the continuous variables. To improve the computational effectiveness of the approach, a constrained derivative relationship is also adopted. The performance of the entire algorithm is then demonstrated through an example involving a simplified model for printed circuit board assemblies. The objective in the example is to maximize assembly reliability by: (1) adding redundant components to the boards, and (2) optimally distributing allocated mass flow to the individual channels of the circuit boards. Number of variables in the example is then varied to investigate the effectiveness and potential of the approach for large-scale problems.