A MultiParametric optimization approach for bilevel mixedinteger linear and quadratic programming problems
Abstract
Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bilevel programming problems, namely (i) bilevel mixedinteger linear programming problems (BMILP) and (ii) bilevel mixedinteger convex quadratic programming problems (BMIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multiparametric programming theory, the main idea is to recast the lower level problem as a multiparametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multiparametric mixedinteger linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of singlelevel, independent, deterministic mixedinteger optimization problems. Extensions to problems including righthandside uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.
 Authors:

 Texas A & M Univ., College Station, TX (United States)
 Publication Date:
 Research Org.:
 American Institute of Chemical Engineers (AIChE), New York, NY (United States)
 Sponsoring Org.:
 USDOE Office of Energy Efficiency and Renewable Energy (EERE); National Science Foundation (NSF)
 OSTI Identifier:
 1613473
 Alternate Identifier(s):
 OSTI ID: 1547651
 Grant/Contract Number:
 EE0007888; CBET1705423; 1739977
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Computers and Chemical Engineering
 Additional Journal Information:
 Journal Volume: 125; Journal Issue: C; Journal ID: ISSN 00981354
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Computer science; Engineering; Bilevel programming; Multi parametric programming; Mixedinteger programming
Citation Formats
Avraamidou, Styliani, and Pistikopoulos, Efstratios N. A MultiParametric optimization approach for bilevel mixedinteger linear and quadratic programming problems. United States: N. p., 2019.
Web. doi:10.1016/j.compchemeng.2019.01.021.
Avraamidou, Styliani, & Pistikopoulos, Efstratios N. A MultiParametric optimization approach for bilevel mixedinteger linear and quadratic programming problems. United States. doi:10.1016/j.compchemeng.2019.01.021.
Avraamidou, Styliani, and Pistikopoulos, Efstratios N. Thu .
"A MultiParametric optimization approach for bilevel mixedinteger linear and quadratic programming problems". United States. doi:10.1016/j.compchemeng.2019.01.021. https://www.osti.gov/servlets/purl/1613473.
@article{osti_1613473,
title = {A MultiParametric optimization approach for bilevel mixedinteger linear and quadratic programming problems},
author = {Avraamidou, Styliani and Pistikopoulos, Efstratios N.},
abstractNote = {Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bilevel programming problems, namely (i) bilevel mixedinteger linear programming problems (BMILP) and (ii) bilevel mixedinteger convex quadratic programming problems (BMIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multiparametric programming theory, the main idea is to recast the lower level problem as a multiparametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multiparametric mixedinteger linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of singlelevel, independent, deterministic mixedinteger optimization problems. Extensions to problems including righthandside uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.},
doi = {10.1016/j.compchemeng.2019.01.021},
journal = {Computers and Chemical Engineering},
issn = {00981354},
number = C,
volume = 125,
place = {United States},
year = {2019},
month = {3}
}
Web of Science