Entropy-based reliable design of water distribution networks

Abstract

Water distribution networks are crucial for the wellbeing of communities, but their construction involves huge investment. The need to optimize investments has resulted in the development of methodologies to determine the minimum cost design of these infrastructures. However, as cost minimization tends to eliminate any redundancy in the networks, this kind of approach leads to less reliable solutions. From the reliability point of view, an ideal water distribution network should ensure reasonable service levels even when a failure occurs. But such a scenario, if possible, would certainly imply an intolerable level of investment. The following question therefore arises: by how much is it reasonable to increase investment to reduce the risk of failure? Trying to help decision makers answer this question, this work offers a tool to solve the reliable design of water distribution networks problem. It is based on an optimization model comprising two antagonistic objectives: minimizing the cost and maximizing reliability (here indirectly evaluated by the network entropy). The multiobjective problem is solved by the constraint method. The result is a set of cost minimization problems, each constrained by a different minimum level of entropy, which are solved by the Simulated Annealing method. This approach leads to a set of solutions known as Pareto solutions. Each of these solutions represents a different level of compromise between cost and reliability, and they can be very helpful for decision makers.