Water supply network optimisation using equal flow algorithms

Algorithms to optimise water supply networks are developed and compared when a given set of transfer arcs is constrained to carry the same (or proportional) amounts of flow. Initially, a dynamic multi-period mathematical model is designed as a network flow model. A network simplex-based algorithm, Equalflow, and a subgradient-based algorithm, SUBeqf, are then presented. Both algorithms are characterised by polynomial complexity and can solve large-scale instances that arise when considering water system requirements. A specialised interface for water supply networks provides a data input processor to generate the overall multi-period network model in the implementation of the procedures. The implementation of the algorithms allows the consideration of different types of equal flow instances that take place in water resource system optimisation. The performances of the two algorithms and analysis of their computational efficiency with respect to state-of-the-art mathematical programming software are reported, considering equal-flow instances from a synthetically generated network and two water supply systems in the Sardinia region of Italy.