Quantifying the economy of flow distribution in water supply looped networks

Optimization of water supply looped networks has attracted a great deal of attention from researchers for more than 30 years. As the classical water supply looped network optimization problem is mathematically non-convex 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 only intuitively 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 non-convexity and multimodality in a new context. The author has introduced this new context recently after formulating a new objective function capable of finding a looped network that 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.