### Multiobjective Optimization of Rehabilitation and Leakage Detection Scheduling in Water Distribution Systems

Abstract

This paper presents a procedure for optimal medium-term scheduling (e.g., over a time window of
5 years) of rehabilitation and leakage detection interventions in a water distribution system given
predetermined budget constraints. The decisional variables are the interventions to be scheduled,
that is, which pipes to replace and when (in which year), and where and when (in which zone and
year) to carry out leakage detection surveys, while the objectives are to minimize the volumes of
water lost and break repair costs. The optimizer used is the NSGA II multiobjective genetic algorithm.
It is assumed that the budget allocated for leakage detection and pipe rehabilitation (proactive
interventions) represents a separate expenditure item from that for the repair of breaks (reactive
interventions). In particular, whereas repair costs are subject to minimization, the budget for proactive
interventions is allocated on a yearly basis during the scheduling period and a constraint is determined
by the fact that the amounts budgeted must be completely spent, year after year: this reflects the
customary practice of water utilities, which strive to spend the entire budget available to them, since
any residual amount may not be reallocated to the same expenditure item in the year or years to come.
The multiobjective optimization procedure does not produce one optimal solution, but rather the Pareto
front of nondominated solutions. Some considerations for identifying a range of solutions within this
front, from which to choose the one to apply, are thus discussed. The procedure is applied to a real
water distribution system using advanced models to represent the various processes that characterize
the problem, namely, leakages as a function of pipe age and pressure, actual nodal discharges released
as a function of head, time series of pipe breaks, etc. and the results obtained show that the proposed
procedure may be a useful decision support tool for scheduling leakage detection campaigns and
rehabilitation interventions.