# A multi-parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems Academic Article •
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### abstract

• 2019 Elsevier Ltd Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. In this work, 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.

### published proceedings

• COMPUTERS & CHEMICAL ENGINEERING

### author list (cited authors)

• Avraamidou, S., & Pistikopoulos, E. N.

• 26

### complete list of authors

• Avraamidou, Styliani||Pistikopoulos, Efstratios N

• June 2019
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