**The essence of combinatorial optimization problems - José Antonio Lozano**

*Abstract*: The goal of this talk is to provide new views on combinatorial optimization problems. Particularly we consider two different scenarios which produce different rich information about the problems. In a first scenario we consider instances of combinatorial optimization problems as ranking of the elements of the search space. This allows us to compute those instances that are in the intersection between different combinatorial optimization problems. In a second scenario we use the Fourier transform. After calculating the Fourier coefficients of several problems we manage to discover their intrinsic dimensionalities, i.e. the minimum number of parameters required to define an instance of the problem. Furthermore, the Fourier coefficients equip us with the possibility to exactly compute the dimension of the intersection between different problems. This can give the base for transferring algorithms designed for one problem to a different problem.

**Jose A. Lozano** leads the Intelligent Systems Group at the University of the Basque Country UPV/EHU, in Spain. Since January 2019 he is the scientific director of the Basque Center for Applied Mathematics (Spain). Prof. Lozano has authored more than 110 ISI journal papers, some of them have become highly cited papers. His current research interests include combinatorial optimization, machine learning and its synergies with optimization in general and supervised classification, time series analysis and Bayesian inference in particular. He is the editor-in-chief of the Genetic and Evolutionary Computation Conference (GECCO 2020).