A reformulation-enumeration MINLP algorithm for gas network design

TL;DR

This paper introduces a novel MINLP algorithm for gas network design that combines convex reformulation and enumeration to efficiently solve nonconvex, nonlinear problems involving pipe diameters, flows, and potentials.

Contribution

It presents a reformulation-enumeration framework with a nested loop approach, improving solution efficiency for complex gas network design MINLPs.

Findings

Effective on benchmark networks

Reduces computational complexity

Provides high-quality solutions

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.