Distributed Nonconvex Optimization for Control of Water Networks with Time-coupling Constraints

Bradley Jenks (), Aly-Joy Ulusoy (), Filippo Pecci () and Ivan Stoianov ()
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Bradley Jenks: Imperial College London
Aly-Joy Ulusoy: Imperial College London
Filippo Pecci: Princeton University
Ivan Stoianov: Imperial College London

Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), 2025, vol. 39, issue 1, No 24, 523-546

Abstract: Abstract In this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are exacerbated by the transition between pressure and water quality controls. The resulting optimization problem is a nonconvex, nonlinear program with nonseparable structure across time steps. This problem proves challenging for state-of-the-art nonlinear solvers, often precluding their direct use for near real-time control in large-scale networks. To overcome this computational burden, we investigate a distributed optimization approach based on the alternating direction method of multipliers (ADMM). In particular, we implement and evaluate two algorithms: a standard ADMM scheme and a two-level variant that provides theoretical convergence guarantees for our nonconvex problem. We use a benchmarking water network and a large-scale operational network in the UK for our numerical experiments. The results demonstrate good convergence behavior across all problem instances for the two-level algorithm, whereas the standard ADMM approach struggles to converge in some instances. With an appropriately tuned penalty parameter, however, both distributed algorithms yield good quality solutions and computational times compatible with near real-time (e.g. hourly) control requirements for large-scale water networks.

Keywords: Distributed optimization; Nonconvex optimization; Alternating direction method of multipliers; Water distribution networks (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11269-024-03985-8

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