Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

TL;DR

This paper introduces advanced polyhedral relaxations and novel optimization techniques to improve the computational efficiency of solving the complex optimal pump scheduling problem in water distribution networks.

Contribution

The paper develops tight polyhedral relaxations, valid inequalities, and bound tightening methods that significantly enhance solution bounds for the OWF problem.

Findings

Improved primal and dual bounds over 45 instances.

Polyhedral relaxations outperform existing methods.

New valid inequalities and bound tightening techniques are effective.

Abstract

The classic pump scheduling or Optimal Water Flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over forty-five literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.