Loading...
Loading...

Go to the content (press return)

Modelling and optimization of large-scale structured problems and applications

Type of activity
Competitive project
Acronym
MOLSA
Funding entity
AGENCIA ESTATAL DE INVESTIGACION
Funding entity code
RTI2018-097580-B-I00
Amount
82.885,00 €
Start date
2019-01-01
End date
2022-12-31
Keywords
cadena de suministro, ciencia de datos, data protection, data science, electricity markets, energías renovables, interior-point methods, logistics, logística, mercado eléctrico, métodos de punto interior, optimización estocástica, problemas estructurados, protección de datos, renewables, stochastic optimization, structured problems, supply chain
Abstract
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).
Scope
Adm. Estat
Plan
Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020
Call year
2019
Funcding program
Programa Estatal de I+D+i Orientada a los Retos de la Sociedad
Funding call
Retos de Investigación: Proyectos de I+D+i
Grant institution
Agencia Estatal De Investigacion

Participants