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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