OPTIMIZATION OF REDUNDANCY IN WATER DISTRIBUTION NETWORKS USING GRAPH THEORETIC PRINCIPLES

An integer goal programming based approach to maximize reliability in water distribution networks is developed. Previous work has shown that graphs which are inherently the most invulnerable to failure have the same number of links incident at each node, i.e. they are regular in degree. The converse of this statement is not true. Regular graphs can contain weaknesses such as bridges, articulation nodes, and even total disconnections. The integer goal programming formulation in this paper is combined with a procedure which recognizes both explicit and implicit articulation points within the water distribution network to ensure that such weaknesses are excluded from the final solution. The integer program component of the approach attempts to maximize regularity within the network. In the goal programming context this is achieved by minimizing the sum of the deviations, at each node, in terms of the number of links incident upon it, from the average number of links incident on a node over the whole network. The integer requirement is imposed to prevent non-integer numbers of links being selected by the model.