Filtering Algorithms for Biobjective Mixed Binary Linear Optimization Problems with a Multiple-Choice Constraint Academic Article

abstract

• This paper deals with a class of biobjective mixed binary linear programs having a multiple-choice constraint, which are found in applications such as Pareto setreduction problems, single-supplier selection, and investment decisions, among others. Two objective spacesearch algorithms are presented. The first algorithm, termed line search and linear programming filtering, is a two-phase procedure. Phase 1 searches for supported Pareto outcomes using the parametric weighted sum method, and Phase 2 searches for unsupported Pareto outcomes by solving a sequence of auxiliary mixed binary linear programs. An effective linear programming filtering procedure excludes any previous outcomes found to be dominated. The second algorithm, termed linear programming decomposition and filtering, decomposes the mixed binary problem by iteratively fixing binary variables and uses the linear programming filtering procedure to prune out any dominated outcomes. Computational experiments show the effectiveness of the linear programming filtering and suggest that both algorithms run faster than existing general-purpose objective spacesearch procedures.

authors

• Leon, Victor

published proceedings

• INFORMS JOURNAL ON COMPUTING

author list (cited authors)

• Jornada, D., & Leon, V. J.

citation count

• 1

complete list of authors

• Jornada, Daniel||Leon, V Jorge

publication date

• January 2020

publisher

• Institute for Operations Research and the Management Sciences (INFORMS)  Publisher

published in

• INFORMS Journal on Computing  Journal

keywords

• Biobjective Mixed Binary Programming
• Dominance Filtering
• Multiobjective Linear Programming
• Optimization Over The Efficient Set
• Pareto Set Reduction

Digital Object Identifier (DOI)

• 10.1287/ijoc.2019.0891

start page

• 57

end page

• 73

volume

• 32

issue

• 1

URL

• http://dx.doi.org/10.1287/ijoc.2019.0891