  The provision of self-cleaning velocities has been shown to reduce the risk
of discolouration in water distribution networks (WDNs). Despite these
findings, control implementations continue to be focused primarily on pressure
and leakage management. This paper considers the control of diurnal flow
velocities to maximize the self-cleaning capacity (SCC) of WDNs. We formulate a
new optimal design-for-control problem where locations and operational settings
of pressure control and automatic flushing valves are jointly optimized. The
problem formulation includes a nonconvex objective function, nonconvex
hydraulic conservation law constraints, and binary variables for modelling
valve placement, resulting in a nonconvex mixed integer nonlinear programming
(MINLP) optimization problem. Considering the challenges with solving nonconvex
MINLP problems, we propose a heuristic algorithm which combines convex
relaxations (with domain reduction), a randomization technique, and a
multi-start strategy to compute feasible solutions. We evaluate the proposed
algorithm on case study networks with varying size and degrees of complexity,
including a large-scale operational network in the UK. The convex multi-start
algorithm is shown to be a more robust solution method compared to an
off-the-shelf genetic algorithm, finding good-quality feasible solutions to all
design-for-control numerical experiments. Moreover, we demonstrate the
implemented multi-start strategy to be a fast and scalable method for computing
feasible solutions to the nonlinear SCC control problem. The proposed method
extends the control capabilities and benefits of dynamically adaptive networks
to improve water quality in WDNs.
