Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The multidisciplinary combinatorial approach (MCA) and its applications in engineering
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
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This paper expands the use of network flows to the multidimensional case, in which network flows are associated with vectors, instead of the conventionally used scalar values. A method for solving a multidimensional max-flow problem is systematically developed, on the basis of the primal-dual algorithm. It is demonstrated that upon reduction to a one-dimensional case, the method is transformed to the known Ford and Fulkerson algorithm. This multidimensional flow network can be applied to a variety of engineering applications, as the variables underlying engineering systems frequently possess a vector form. In this paper, the multidimensional max-flow problem is shown to correspond to the problem of plastic analysis of trusses.