Graph-Theoretic Generation of Assembly Plans - Part II: Problem Decomposition and Optimization Algorithms

Abstract

Efficient generation of assembly plans has significant implications on manufacturing costs, however, the underlying mathematical problem is both theoretically and computationally intractable. In the previous paper (Part I), we developed a graph-theoretic framework for the general problem, and we described a constraint satisfaction construct that generates correct assembly precedence graphs given establishment conditions. In this paper, we develop additional components for the framework: a problem decomposition scheme which decomposes a general set of establishment conditions into generalized 2-SAT problems. After mapping these satisfiability problems into specialized decision graphs, we develop a branch-and-bound algorithm which generates optimal precedence graphs and optimal assembly plans from the decision graph. Our method generates assembly precedence graph(s) which satisfy two basic criteria: (i) All sequences defined by the precedence graph are feasible according to design specif..