Domestic research projects

arrs2.png

Research projects (co)funded by the Slovenian Research Agency.

 

  • Member of University of Ljubljana: UL Faculty of Mechanical Engineering
  • Project code: N1-0071
  • Project title: Extending first and second order algorithms for nested classes of optimization problems to solve computationally challenging industrial questions
  • Period: 01.01.2018 - 31.12.2020
  • Range on year: 0,59 FTE
  • Head: izr. prof. dr. Janez Povh
  • Research activity: Natural sciences and mathematics
  • Researchers: Link
  • Citations for bibliographic records: Link
Abstract:

This is a joint Slovenian-Hungary project where work is clearly distributed among both partnmers. The partners meet 2-3 tiems a year and in the meantime they cooperate remotely.

In this project, we will develop new solution methods for multi-linear optimization problems and apply them to solve some important real-life, industrial optimization problems like economical equilibrium problems (EEP), pooling problems (PP) and non-negative matrix factorization problem (NMFP). All these optimization problems fall into the class of NP-complete problems, thus algorithms with polynomial complexity could not be expected unless P = NP holds.

We expect that fast, although inexact, methods for large-scale instances of the problems will be demanded, combined with parallel implementations of the algorithms. Furthermore, we will also focus on developing and analysing solvability of dual problems of these optimization problems.  

Common features of these problems are that their non-convexity comes from the multiplications of different decision variables. Likewise, the feasible solution sets of these optimization problems are also non-convex and even not connected. These are the sources of major difficulties that we have to overcome. Available, general-purpose nonlinear programming (NLP) solvers will be used to solve small instances of these problems to have reference computations.

We are going to develop hybrid computational methods (HCM) for each class of listed problems. These HCMs will combine exact algorithms (the first- and second order algorithms) with different type of local search techniques, meta-heuristics, heuristics based on the structural properties of the problems.  Parallelization of HCMs will enable us to test different combinations of algorithms and techniques. 

     

The phases of the project and their realization:

The project has 5 work packages with several tasks:

WP1: Project management

This is ongoing activity of both parts of the project team.

WP2: Economic equilibrium problems (EEP)

This WP is led by Hungarian part of the team. ULFME is working on:

  • Matrix classes, generating P- and sufficient matrices
  • Developing and implementing new IPAs
  • Investigation of sufficient and general LCPs
  • Application of global optimization (GO) methods for solving general LCPs

We have preliminary results which will be submitted as a journal paper by the end of 2018.

WP3: Blending problems and their generalizations

ULFME is involved in:

  • Solving blending problems
  • Introduction of dual problem for bilinear optimization 

We formulated this problem as LCP and colelct data to perform first numerical tests.

WP4: Solving Nonnegative matrix three-factorization problem (NMTFP)

This WP is led by ULFME, which also works on:

  • approximate solving of NMTFP using first and second order methods
  • developing efficient code to solve NMTFP

We have prototypes of MATLAB code where gradient and Newton methods are used to solve 2-factor NMFP. Regarding accuracy, this is a state-of-the-art code that will be ported in C++ and parallelised to run efficiently of HPC available at ULFME.

WP5: Dissemination of the results

We present our results on regional and global conferences. First 3 papers are under preparation.