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A reformulation-enumeration MINLP algorithm for gas network design

Yijiang Li, Santanu S. Dey, Nikolaos V. Sahinidis

TL;DR

This paper proposes a decomposition framework that utilizes a two-stage procedure that involves a convex reformulation of the original problem to solve the gas network design problem.

Abstract

Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas network design problem is generally modelled as a nonconvex mixed-integer nonlinear integer programming problem (MINLP). The challenges of solving the resulting MINLP arise due to the nonlinearity and nonconvexity. In this paper, we propose a framework to study the "design variant" of the problem in which the variables are the diameter choices of the pipes, the flows, the potentials, and the states of various network components. We utilize a nested loop that includes a two-stage procedure that involves a convex reformulation of the original problem in the inner loop and an efficient enumeration scheme in the outer loop. We conduct experiments on benchmark networks to validate and analyze the performance of our framework.

A reformulation-enumeration MINLP algorithm for gas network design

TL;DR

This paper proposes a decomposition framework that utilizes a two-stage procedure that involves a convex reformulation of the original problem to solve the gas network design problem.

Abstract

Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas network design problem is generally modelled as a nonconvex mixed-integer nonlinear integer programming problem (MINLP). The challenges of solving the resulting MINLP arise due to the nonlinearity and nonconvexity. In this paper, we propose a framework to study the "design variant" of the problem in which the variables are the diameter choices of the pipes, the flows, the potentials, and the states of various network components. We utilize a nested loop that includes a two-stage procedure that involves a convex reformulation of the original problem in the inner loop and an efficient enumeration scheme in the outer loop. We conduct experiments on benchmark networks to validate and analyze the performance of our framework.
Paper Structure (24 sections, 1 theorem, 38 equations, 8 tables, 2 algorithms)

This paper contains 24 sections, 1 theorem, 38 equations, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Problem description
  4. Technical background
  5. Pipes
  6. Short pipes
  7. Resistors
  8. Compressors
  9. Valves
  10. Control valves
  11. Design problem
  12. Decomposition framework
  13. CVXNLP
  14. Primal bound loop
  15. Binary search on budget
  16. ...and 9 more sections

Key Result

Theorem 1

If the potential loss function $\phi(\cdot)$ is strictly monotonically increasing function of flowrate, $q$, with $\phi(0) = 0$, then there exists a solution $(\pi, q)$ to the network analysis equations if and only if there exists a solution $(\hat{q}^+, \hat{q}^-, \hat{\lambda}, \hat{\mu}^+, \hat{\

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • proof