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Two adjacent pipe diameters at the optimal solution in the water distribution network models
Author(s) -
Fujiwara Okitsugu,
Dey Debashis
Publication year - 1987
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr023i008p01457
Subject(s) - regular polygon , pipe network analysis , set (abstract data type) , mathematical optimization , adjacency list , distribution (mathematics) , function (biology) , property (philosophy) , power (physics) , link (geometry) , mathematics , computer science , topology (electrical circuits) , mechanics , geometry , combinatorics , mathematical analysis , physics , thermodynamics , philosophy , epistemology , evolutionary biology , biology , programming language
In the study of optimization models for the design of water distribution networks, most of the literature has either indicated or explicitly claimed that at the optimal solution each link will consist of at most two pipe segments with adjacent diameters. This paper presents the necessary and sufficient conditions that a given set of pipe diameters is in an optimal solution and as a special case shows that the adjacency property holds if and only if pipe costs are a strictly convex function of a power of pipe diameters.