Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for the biobjective case

  • Authors:

  • Thomas Vincent;Florian Seipp;Stefan Ruzika;Anthony Przybylski;Xavier Gandibleux

  • Affiliations:

  • LINA-Laboratoire d'Informatique de Nantes Atlantique, UMR CNRS 6241, Université de Nantes, 2 Rue de la Houssinière BP 92208, 44322 Nantes Cedex 03, France;AG Optimization, Department of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 14 - 445, 67663 Kaiserslautern, Germany;AG Optimization, Department of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 14 - 445, 67663 Kaiserslautern, Germany;LINA-Laboratoire d'Informatique de Nantes Atlantique, UMR CNRS 6241, Université de Nantes, 2 Rue de la Houssinière BP 92208, 44322 Nantes Cedex 03, France;LINA-Laboratoire d'Informatique de Nantes Atlantique, UMR CNRS 6241, Université de Nantes, 2 Rue de la Houssinière BP 92208, 44322 Nantes Cedex 03, France

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2013

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Abstract

This work addresses the correction and improvement of Mavrotas and Diakoulaki's branch and bound algorithm for mixed 0-1 multiple objective linear programs. We first elaborate the issues encountered by the original algorithm and then propose a corrected version for the biobjective case using an exact representation of the nondominated set associated with an appropriate update procedure. Then we introduce several improvements using better bound sets and branching strategies and finally present some experiments to study the effectiveness of our propositions.