Water Demand Maximization: Quick Recovery of Nonlinear Physics Solutions

TL;DR

This paper introduces a robust method for recovering feasible solutions to nonlinear water demand maximization problems from MILP relaxations, significantly improving solution quality and computational efficiency.

Contribution

It proposes a novel solution recovery approach combined with iterative partition refinement to efficiently find high-quality feasible solutions for nonlinear water demand maximization.

Findings

Outperforms baseline methods in solution quality

Reduces computation time compared to direct MINLP solving

Consistently recovers feasible solutions close to the optimum

Abstract

Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is computationally challenging. A common strategy to address this challenge is to solve mixed-integer linear program (MILP) relaxations derived by partitioning variable domains and constructing linear over- and under-estimators to nonlinear constraints over each partition. While MILP relaxations are easier to solve up to a modest level of partitioning, their solutions often violate nonlinear water flow physics. Thus, recovering feasible MINLP solutions from the MILP relaxations is crucial for enhancing MILP-based approaches. In this paper, we propose a robust solution recovery method that efficiently computes feasible MINLP solutions from MILP relaxations, regardless of partition granularity. Combined with iterative partition refinement, our method generates a sequence of feasible solutions that progressively approach the optimum. Through extensive numerical experiments, we demonstrate that our method outperforms baseline methods and direct MINLP solves by consistently recovering high-quality feasible solutions with significantly reduced computation times.