The size of the optimization problems (linear, non-linear, and integer) that must be solved at present has grown orders of magnitude in the last 30 years, to the point that problems unthinkable a few years ago are already being addressed by leading technology companies. (For example, Google informed us in August 2018 -in its New York offices, where we were invited to give a talk on the optimization methods developed by our group-, that they must deal with linear optimization problems of hundreds and billions of variables and therefore are developing alternatives to the simplex method.) The ultimate goal of this project is to develop optimization methods for large problems (which usually implies a certain structure in the problem), both deterministic and stochastic, and their application to real cases. The project therefore pursues both methodological and applied objectives. At the methodological level, the main objectives are: - The group has developed a specialized interior point method for large angular problems (implemented in the BlockIP package: http://www-eio.upc.edu/~jcastro/BlockIP.html). Although this method has outperformed the best current commercial optimization packages in various applications, it should be improved in several aspects, including: (1) Addition of quadratic constraints. (2) Improvement of the preconditioned conjugate gradient used in BlockIP by new preconditioners. (3) Application in cutting plane and column generation algorithms (possibly in integer problems). (4) Parallelization of the algorithm and the package BlockIP. - The group has addressed the modeling and resolution of multistage stochastic programming problems that give rise to large-scale mixed quadratic programming (MINLP) problems. There has been much progress in the formulation of multistage scenario trees that define the MINLP problem as well as in some specialized resolution algorithms. However, in this project we plan to extend the existing methods through (1) the improvement in the generation of scenario trees through statistical models of forecasting and algorithms of generation and reduction of scenario trees; (2) extend the current works on metaheuristic parallelization of the algorithm Branch-and-Fix Coordination (BFC) to non-linear convex non-linear stochastic problems, and (3) to develop a dual-type decomposition algorithm (Parallel Proximal Bundle Methods, PPBM) for the resolution of multistage stochastic programming problems. At the application level, the main objectives would be: . Using BlockIP and other decomposition methods to solve data protection problems using the "interval protection" technique. - Solution of stochastic optimization problems through BlockIP. - Solution of very large-scale logistic problems (up to billions of variables) through BlockIP, including network transportation and content locations problems. - Solution of multistage stochastic problems for the Integration of renewable energies (PEM-IER problem). - Solution of multistage stochastic problems for the strategic design of the supply chain (problem PEM-DECS).
Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020
Programa Estatal de I+D+i Orientada a los Retos de la Sociedad