Abstract

This article addresses the problem of identifying the optimal decomposition of a design problem. Methods for solving decomposed mathematical programming problems require that an appropriate structure suitable for decomposition be identified. This first step consists of identifying linking (or coordinating) variables or functions that effect independent subproblems coordinated by a master problem. We present a network reliability-based solution of the optimal decomposition problem that avoids heuristics and subjective criteria for the identification of linking variables and evaluation of partitions. The relationships among design variables, i.e., the constraint functions, 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 problem is then reduced to one of finding the links that have the most effect on the overall network connectivity. Two measures of network reliability, all-terminal and pair-connected reliability, are used as measures of network (and design problem) connectivity. The optimal decomposition is attained by minimizing the network reliability while maximizing the number of operating links.

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