dorsal/arxiv
View SchemaWater Demand Maximization: Quick Recovery of Nonlinear Physics Solutions
| Authors | Sai Krishna Kanth Hari, Russell Bent |
|---|---|
| Categories | |
| ArXiv ID | 2601.06755vv1 |
| URL | https://arxiv.org/abs/2601.06755 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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.
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"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.",
"arxiv_id": "2601.06755",
"authors": [
"Sai Krishna Kanth Hari",
"Russell Bent"
],
"categories": [
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"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Water Demand Maximization: Quick Recovery of Nonlinear Physics Solutions",
"url": "https://arxiv.org/abs/2601.06755",
"version": "v1"
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