Journal
COMPUTERS & CHEMICAL ENGINEERING
Volume 125, Issue -, Pages 98-113Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compchemeng.2019.01.021
Keywords
Bilevel programming; Multi parametric programming; Mixed-integer programming
Funding
- National Science Foundation [CBET-1705423 [PAROC], 1739977 [INFEWS]]
- U.S. Department of Energy under RAPID SYNOPSIS Project [DE-EE0007888-09-03]
- Texas AM University
- Texas A&M Energy Institute
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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 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 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. (C) 2019 Elsevier Ltd. All rights reserved.
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