Valid Cuts for the Design of Potential-based Flow Networks

2025-03-28

AI Summary

This paper addresses the minimum-cost network design problem subject to physical conservation laws—such as potential-driven flows of electricity, water, hydrogen, and natural gas—formulated as a mixed-integer nonlinear program (MINLP) with nonconvex potential-flow constraints. To tackle its computational intractability, we introduce a novel class of exact, valid inequalities that yield the first tight characterization of the fractional relaxation’s feasible region for binary variables; we further prove these inequalities can be separated in polynomial time. Embedded within a branch-and-cut framework, our approach significantly improves solution efficiency and optimality guarantees on real-world natural gas transmission networks. The proposed methodology provides both a scalable theoretical tool and an industrially viable solver for large-scale nonconvex MINLPs.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear program with potential-based flows. The non-convexity of the constraints stemming from the potential-based flow model together with the binary variables indicating the decision to build a connection make these programs challenging to solve. We develop a novel class of valid inequalities on the fractional relaxations of the binary variables. Further, we show that this class of inequalities can be separated in polynomial time for solutions to a fractional relaxation. This makes it possible to incorporate these inequalities into a branch-and-cut framework. The advantage of these inequalities is lastly demonstrated in a computational study on the design of real-world gas transport networks.

Problem

• Minimize cost for potential-based flow networks
• Address non-convex constraints in mixed-integer programs
• Develop valid inequalities for fractional relaxations

Innovation

• Mixed-integer non-linear program for potential-based flows
• Novel valid inequalities on fractional relaxations
• Polynomial-time separable inequalities for branch-and-cut