1,772 research outputs found
Convex Relaxations for Gas Expansion Planning
Expansion of natural gas networks is a critical process involving substantial
capital expenditures with complex decision-support requirements. Given the
non-convex nature of gas transmission constraints, global optimality and
infeasibility guarantees can only be offered by global optimisation approaches.
Unfortunately, state-of-the-art global optimisation solvers are unable to scale
up to real-world size instances. In this study, we present a convex
mixed-integer second-order cone relaxation for the gas expansion planning
problem under steady-state conditions. The underlying model offers tight lower
bounds with high computational efficiency. In addition, the optimal solution of
the relaxation can often be used to derive high-quality solutions to the
original problem, leading to provably tight optimality gaps and, in some cases,
global optimal soluutions. The convex relaxation is based on a few key ideas,
including the introduction of flux direction variables, exact McCormick
relaxations, on/off constraints, and integer cuts. Numerical experiments are
conducted on the traditional Belgian gas network, as well as other real larger
networks. The results demonstrate both the accuracy and computational speed of
the relaxation and its ability to produce high-quality solutions
Extended Formulations in Mixed-integer Convex Programming
We present a unifying framework for generating extended formulations for the
polyhedral outer approximations used in algorithms for mixed-integer convex
programming (MICP). Extended formulations lead to fewer iterations of outer
approximation algorithms and generally faster solution times. First, we observe
that all MICP instances from the MINLPLIB2 benchmark library are conic
representable with standard symmetric and nonsymmetric cones. Conic
reformulations are shown to be effective extended formulations themselves
because they encode separability structure. For mixed-integer
conic-representable problems, we provide the first outer approximation
algorithm with finite-time convergence guarantees, opening a path for the use
of conic solvers for continuous relaxations. We then connect the popular
modeling framework of disciplined convex programming (DCP) to the existence of
extended formulations independent of conic representability. We present
evidence that our approach can yield significant gains in practice, with the
solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201
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