Nonlinear Programming Techniques for Operative Planning in Large Drinking Water Networks

Abstract

Mathematical decision support for operative planning in water supply systems is highly desirable; it leads, however, to very difficult optimization problems. We propose a nonlinear programming approach that yields practically satisfactory operating schedules in acceptable computing time even for large networks. Based on a carefully designed model supporting gradient-based optimization algorithms, this approach employs a special initialization strategy for convergence acceleration, special minimum up and down time constraints together with pump aggregation to handle switching decisions, and several network reduction techniques for further speed-up. Results for selected application scenarios at Berliner Wasserbetriebe demonstrate the success of the approach.

The integer approximation error in mixed-integer optimal control

“…Interesting recent developments include problem-specific reformulations and decompositions, as in [5] for drinking water networks. The authors reformulate the MIOCP as a large-scale, structured nonlinear program (NLP) and solve a small scale integer program on a second level to approximate the calculated continuous aggregated output of all pumps in a water works.…”

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

“…A clever problem-specific reformulation is proposed in [10,11]. For the optimal operation of a water network the authors propose to decompose the problem in the sense that a pure NLP is solved for the overall network with a (continuous) aggregated output of the discrete-valued pumps in each waterworks.…”

OPTIMIZING OPERATIONS OF LARGE WATER SUPPLY NETWORKS - A Case Study

“…These models are typically nonconvex MINLP's and are in general hard to solve. They are often solved by means of some NLP solvers, after the binary variables are relaxed or the model reformulated (Cembrano et al, 2000;Burgschweiger et al, 2009). Heuristic methods are also frequently used to solve these models (Savic and Walters, 1997;López-Ibáñez et al, 2008;Nicklow et al, 2010).…”