A reformulation-enumeration MINLP algorithm for gas network design

• Published in: Journal of global optimization Vol. 90; no. 4; pp. 931 - 963
• Main Authors: Li, Yijiang, Dey, Santanu S., Sahinidis, Nikolaos V.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2024; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computer Science; Construction costs; Decomposition; Enumeration; Experiments; Integer programming; Mathematics; Mathematics and Statistics; Mixed integer; Natural gas; Nested loops; Network design; Network management systems; Nominations; Nonlinearity; Operations Research/Decision Theory; Optimization; Real Functions; Mixed-integer nonlinear program; Global optimization; Network design
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-024-01424-x

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.