A Network Reliability Approach to Optimal Decomposition of Design Problems

Methods for solving partitioned mathematical programming problems require that an appropriate structure suitable for decomposition be identified. This first step consists of identifying linking variables that effect independent subproblems coordinated by a master problem. This article presents a network reliability-based solution of the optimal decomposition problem that avoids subjective criteria to identify linking variables and partitions. The relationships among design variables are modeled as the processing units of a network. The design variables themselves are modeled as the communication links between these units. The optimal decomposition is attained by minimizing the network reliability while maximizing the number of operating links.