### Guglielmo Lulli (Lancaster University)

#### Exploiting network structures in mathematical modelling and optimization

*Wednesday 7 December 2016 at 15.00, JCMB 5215*

##### Abstract

Network optimization has been one of the most prolific research topics in
operational research and computer science. Although, network optimization
reached a "maturity" phase, it is often vital to capitalize on network
(sub)structures in order to develop "efficient" formulations and/or solution
methods when solving application oriented optimization problems.

In this talk, I will present two applications that benefitted from
exploiting/embedding the network substructure of the corresponding problem.

The first application is on Air Traffic Flow Management. A new integer
programming formulation is introduced, whose distinguishing feature is that it
represents rerouting decisions in a compact way by imposing sets of "local"
conditions. The second application is on the unit commitment problem. For this
problem, a new formulation based on state-transition variables is presented.
The use of state-transition decision variables embeds a network sub-structure
in the new formulation and naturally includes valid inequalities, commonly used
to strengthen other formulations. The new formulation leads to improved
solution times especially in longer time-horizon instances.

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