Variable Bound Tightening and Valid Constraints for Multiperiod Blending

Yifu Chen () and Christos T. Maravelias ()
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Yifu Chen: Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706
Christos T. Maravelias: Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544; Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544

INFORMS Journal on Computing, 2022, vol. 34, issue 4, 2073-2090

Abstract: Multiperiod blending has a number of important applications in a range of industrial sectors. It is typically formulated as a nonconvex mixed integer nonlinear program (MINLP), which involves binary variables and bilinear terms. In this study, we first propose a reformulation of the constraints involving bilinear terms using lifting. We introduce a method for calculating tight bounds on the lifted variables calculated by aggregating multiple constraints. We propose valid constraints derived from the reformulation-linearization technique (RLT) that use the bounds on the lifted variables to further tighten the formulation. Computational results indicate our method can substantially reduce the solution time and optimality gap. Summary of Contribution: In this paper, we study the multiperiod blending problem, which has a number of important applications in a range of industrial sectors, such as refining, chemical production, mining, and wastewater management. Solving this problem efficiently leads to significant economic and environmental benefits. However, solving even medium-scale instances to global optimality remains challenging. To address this challenge, we propose a variable bound tightening algorithm and tightening constraints for multiperiod blending. Computational results show that our methods can substantially reduce the solution time and optimality gap.

Keywords: preprocessing; reformulation-linearization technique; variable lifting; bilinear terms (search for similar items in EconPapers)
Date: 2022
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