Water Demand Maximization: Quick Recovery of Nonlinear Physics Solutions
Sai Krishna Kanth Hari, Russell Bent
TL;DR
The paper tackles the challenge of determining maximum feasible water demand in water distribution networks, cast as a nonconvex MINLP due to nonlinear hydraulics and discrete decisions. It introduces a robust recovery framework that derives feasible MINLP solutions from MILP relaxations with arbitrary partition granularity, by combining neighborhood search with iterative partition refinement and a tie-breaking MILP. The approach yields a sequence of improving feasible solutions, often matching or approaching global optima much faster than direct MINLP solves or spatial branch-and-bound, especially on larger networks where exact methods struggle. This has practical impact for rapid, reliable planning and operation of water networks, and the framework is broadly applicable to other infrastructure optimization problems governed by nonlinear physics and discrete decisions.
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.