Non Linear Optimization Models in Water Resource Systems

Summary

The progress made in past years in large-scale optimization algorithms led to a general interest in the possibility of applying mathematical optimization to real Water Resources Systems (WRS). As it is well known, this kind of problem typically generates computationally expensive models involving a large number of variables and constraints. Planning aspects can be represented by linear optimization models by introducing simplifications and approximations, even if linear assumptions are not strictly adherent to real WRS. In order to reach a more adequate level of adherence to the physical system more detailed models are resolved by taking into account non-linearity in objective function and constraints. An expansion technique interacting between primal and dual mathematical optimization models is proposed. This kind of approach is very useful to formulate trade-off between the dimension of water works, the reliability of the system and the prediction of short falls severity in demands. Moreover, the necessity to introduce system-vulnerability leads to solve a quadratic programming model taking into account additional non-linear costs due to the requirement of well operating during periods of drought. An adequate approach for the planning and maintenance optimization of pipes networks for water supply distribution, would consider the non-linear relations between head-loss in each pipe, its diameter, length and hydraulic property.

Standard non-linear optimization procedures frequently identify only local optima for this kind of problem. In recent years, a number of papers have demonstrated that optimization techniques, based on meta-heuristic algorithms, are particularly promising for solving problems related to water distribution systems. This new methodology may be considered as a useful alternative to traditional approaches, based on trial-and-error or mathematical programming methods. Some applications, results and perspectives are presented for the different approaches.