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

Avraamidou, Styliani; Pistikopoulos, Efstratios N.

doi:10.1016/j.compchemeng.2019.01.021

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

Journal Article · Wed Mar 06 23:00:00 EST 2019 · Computers and Chemical Engineering

DOI:https://doi.org/10.1016/j.compchemeng.2019.01.021· OSTI ID:1613473

Avraamidou, Styliani ^[1]; Pistikopoulos, Efstratios N. ^[2]

Texas A & M Univ., College Station, TX (United States); Texas A&M University
Texas A & M Univ., College Station, TX (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: American Institute of Chemical Engineers (AIChE), New York, NY (United States)

Sponsoring Organization:: USDOE Office of Energy Efficiency and Renewable Energy (EERE); National Science Foundation (NSF)

Grant/Contract Number:: EE0007888

OSTI ID:: 1613473

Alternate ID(s):: OSTI ID: 1547651

Journal Information:: Computers and Chemical Engineering, Journal Name: Computers and Chemical Engineering Journal Issue: C Vol. 125; ISSN 0098-1354

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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