A maximum entropy based approach to the layout optimization of water distribution systems

This paper investigates the idea that minimum cost maximum entropy designs of water distribution systems can be used to identify good layouts of water distribution systems in the sense that designs based on these layouts could achieve a reasonable compromise between reliability and cost. The proposed approach presupposes that there is a sufficiently strong relationship between entropy and reliability to achieve this purpose. Evidence is provided to support this view. A fundamental issue relating to the invariance of the entropy function with respect to permutations of its arguments is also addressed. The proposed technique is assessed using an example, which shows that the method yields good solutions to the joint layout, reliability and pipe-size optimization problem. It is also shown that if two or more layouts of a water distribution system have the same maximum entropy value, then minimum cost maximum entropy designs based on these layouts can be expected to be similar in terms of their overall performance.