Discrete model and visualization interface for water distribution network design

The water distribution network design problem poses challenges for optimization due to the tightly constrained nature of the typical mathematical programming formulation. The optimization of existing water distribution networks has therefore often been tackled through the use of stochastic optimization procedures. However, even these suffer from the need to solve systems of nonlinear algebraic equations. This paper describes the implementation of a hybrid method which combines a fully discrete formulation and visualization procedure with mixed integer nonlinear programming (MINLP) solution methods. The discrete formulation is suitable for solution by stochastic and direct search optimization methods and provides a natural basis for visualization and, hence, user interaction. Visual hints allow a user to identify easily bottlenecks and the aspects of the design that most greatly affect the overall cost. The result is a tool which combines the global search capabilities of stochastic algorithms with the pattern recognition and tuning abilities of the user. The solutions obtained provide good initial points for subsequent optimization by rigorous MINLP solution methods.