Abstract
The particular application considered here is the design of relief-header systems, involving compressible fluid flow through tree-networks. The flowrates are specified, and the design problem involves the choice of discrete pipe sizes to minimize total cost while satisfying pressure-drop constraints, which are highly nonlinear.
The problem is solved in two stages. Firstly the problem of obtaining the optimal set of continuous pipe sizes is addressed; it turns out that a dual formulation provides and extremely rapid solution. Next, a subgradient optimization procedure is used on the dual in order to solve for the discrete pipe sizes. Networks of up to 78 paths and 205 sections, each involving 50 discrete pipe sizes, have been solved.
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Murtagh, B.A., Soliman, F.I. Subgradient optimization applied to a discrete nonlinear problem in engineering design. Mathematical Programming 25, 1–12 (1983). https://doi.org/10.1007/BF02591715
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DOI: https://doi.org/10.1007/BF02591715