Business information systems for the cost/energy management of water distribution networks: a critical appraisal of alternative optimization strategies

The objective of this paper is to show how smart water networks enable new strategies for the energy cost management of the network, more precisely Pump Scheduling Optimization. This problem is traditionally solved using mathematical programming and, more recently, nature inspired metaheuristics. The schedules obtained by these methods are typically not robust both respect to random variations in the water demand and the non-linear features of the model. The authors consider three alternative optimization strategies: (i) global optimization of black-box functions, based on a Gaussian model and the use of the hydraulic simulator (EPANET) to evaluate the objective function; (ii) Multi Stage Stochastic Programming, which models the stochastic evolution of the water demand through a scenario analysis to solve an equivalent large scale linear program; and finally (iii), Approximate Dynamic Programming, also known as Reinforcement Learning. With reference to real life experimentation, the last two strategies offer more modeling flexibility, are demand responsive and typically result in more robust solutions (i.e. pump schedules) than mathematical programming. More specifically, Approximate Dynamic Programming works on minimal modelling assumption and can effectively leverage on line data availability into robust on-line Pump Scheduling Optimization.