A two-stage LP-NLP methodology for the least-cost design and operation of water distribution systems

This paper presents a two-stage method for simultaneous least-cost design and operation of looped water distribution systems (WDSs). After partitioning the network into a chord and spanning trees, in the first stage, a reformulated linear programming (LP) method is used to find the least cost design of a WDS for a given set of flow distribution. In the second stage, a non-linear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the WDS design obtained in stage one. The following features of the proposed two-stage method make it more appealing compared to other methods: (1) the reformulated LP stage can consistently reduce the penalty cost when designing a WDS under multiple loading conditions; (2) robustness as the number of loading conditions increases; (3) parameter tuning is not required; (4) the method reduces the computational burden significantly when compared to meta-heuristic methods; and (5) in oppose to an evolutionary "black box" based methodology such as a genetic algorithm, insights through analytical sensitivity analysis, while the algorithm progresses, are handy. The efficacy of the proposed methodology is demonstrated using two WDSs case studies.