90C30 Nonlinear programming
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The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.
The operative planning problem in natural gas distribution networks is addressed. An optimization model focusing on the governing PDE and other nonlinear aspects is presented together with a suitable discretization for transient optimization in large networks by SQP methods. Computational results for a range of related dynamic test problems demonstrate the viability of the approach.
Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization.