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Title: A Multi-Parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems

Abstract

Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.

Authors:
 [1];  [1]
  1. 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; CBET-1705423; 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 0098-1354
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Computer science; Engineering; Bilevel programming; Multi parametric programming; Mixed-integer programming

Citation Formats

Avraamidou, Styliani, and Pistikopoulos, Efstratios N. A Multi-Parametric optimization approach for bilevel mixed-integer 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 Multi-Parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems. United States. doi:10.1016/j.compchemeng.2019.01.021.
Avraamidou, Styliani, and Pistikopoulos, Efstratios N. Thu . "A Multi-Parametric optimization approach for bilevel mixed-integer 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 Multi-Parametric optimization approach for bilevel mixed-integer 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 bi-level programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side 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 = {0098-1354},
number = C,
volume = 125,
place = {United States},
year = {2019},
month = {3}
}

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