Optimization Online


Probabilistic Variational Formulation of Binary Programming

Arturo Berrones(arturo.berronessn***at***uanl.edu.mx)
Jonás Velasco(jvelasco***at***cimat.mx)
Juan Banda(juan.bandamr***at***uanl.edu.mx)

Abstract: A probabilistic framework for large classes of binary integer programming problems is constructed. The approach is given by a mean field annealing scheme where the annealing phase is substituted by the solution of a dual problem that gives a lower (upper) bound for the original minimization (maximization) integer task. This bound has an information theoretic interpretation by which a principled feasible solution generator is constructed. The method is tested in linear and quadratic knapsack problems for which is capable to find high quality solutions in running times that are orders of magnitude shorter than state of the art algorithms. Experimental evidence indicates that for the quadratic case, the mean field approximation improves with problem size for unstructured instances. This is reminiscent of the exact mean field limit found in several spin glass models.

Keywords: heuristics, stochastic search, binary optimization

Category 1: Integer Programming (0-1 Programming )

Category 2: Nonlinear Optimization (Quadratic Programming )

Citation: Universidad Autónoma de Nuevo León, Facultad de Ingeniería Mecánica y Eléctrica, Posgrado en Ingeniería de Sistemas, AP 126, Cd. Universitaria, San Nicolás de los Garza, NL 66450, México, Nov 2017. / CONACYT- Centro de Investigación en Matemáticas (CIMAT), A.C., Fray Bartolomé de las Casas 314, Barrio La Estación, CP 20259, Aguascalientes, Ags, México, Nov 2017.

Download: [PDF]

Entry Submitted: 11/01/2017
Entry Accepted: 11/01/2017
Entry Last Modified: 11/01/2017

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society