Many real-world optimization problems, among which those arising in Energy Systems and Public Transport Optimization, are complex for multiple reasons, such as containing at the same time nonlinear elements and discrete/combinatorial decisions. The combination of these factors gives rise to a large variety of different structures that can be–and need be, given the complexity of the problems–exploited to develop more efficient algorithmic approaches.
CommaLAB has been working on the subject for many years, developing general methodologies to tackle Mixed-Integer NonLinear Problems with specific forms of structure that have applications in different fields such as energy, telecommunications, finance and others. To pursue these lines of research we have obtained competitive funding, for instance by the University of Pisa for the Project “Mathematical models and computational methods for complex networks“, by the Italian Ministry for the projects PRIN 2009 “Integrated Approaches for Discrete and Non Linear Optimization” and PRIN 2012 “Mixed-Integer Nonlinear Optimization: Approaches and Applications“, and by the European Union for the ITN networks MINO: Mixed-Integer Nonlinear Optimization and MINOA: Mixed-Integer Nonlinear Optimization Applications.