Quantum field theory gives the excellent description for the electromagnetic, weak and strong fundamental interactions by means of perturbative expansion in the coupling constant. It allows to obtain results, which can be compared with experiments. In some cases the large logarithms are appeared in perturbative calculations and they should be sum exactly, i.e. in all orders of perturbative theory. Arising evolution equations are widely used for the theoretical description of the high energy scattering processes, which extensively studied at LHC and other experiments at colliders. During forty years of investigations a lot of remarkable properties related with these evolution equations were found. In particular, as the most important, the connection between high-energy scattering and the exactly solvable two-dimensional field-theoretical models was discovered. The similar integrability was discovered under investigation of composite operators in the planar limit of the famous AdS/CFT-correspondence. In this project we are going to extend the investigations of integrability for other evolution equations in the framework of planar gauge/string duality and beyond planar limit within the collaboration between Applicant as expert in considered evolution equations and the Research Group from Host Institute as experts in AdS/CFT integrability. We shall calculate the higher-loop anomalous dimensions of composite operators and study their properties. Obtained results will used for the test of available and the development of new methods.