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As the classical water-supply looped-network optimization problem is mathematically nonconvex and multimodal, the resulting solution of most approaches is uncertain in the sense of how close it is to the "best" solution. In many cases, this "best"' or "global" solution is invoked and pursued without a clear understanding of its meaning. This paper discusses what is involved in "global" solutions and the role that pipe flow distribution can play to deal with nonconvexity and multimodality in a new context. The author has introduced this new context recently after formulating a new objective function capable of finding that a looped network can be economically more attractive than its related branched one. Therefore, the convenience of an approach dealing with flows and heads, as relevant decision variables, is encouraged in this paper and its advantages enumerated under the new concepts. The entropy approach is studied critically and an example is provided for comparison with the proposed approach. [ABSTRACT FROM AUTHOR]

The economic advantages of a looped network have not been considered in any of the optimization models found in the literature. This paper introduces a new formulation and methodology in an attempt to give a practical solution to this problem. The new formulation consists of a non-linear optimization model solved by classical differential calculus and the Newton-Raphson technique. An example shows how the looped network can be less costly than a branched one. Previous research usually optimizes the network for a given design demand. Also the value that should be specified as the desired network reliability has not been reported so far. This work introduces a methodology to obtain not only an adequate value for the reliability of a looped network but also the appropriate design demand as well based on a thorough cost analysis. A second example illustrates the detailed performance of this methodology. [ABSTRACT FROM AUTHOR]