Multistage Adaptive Robust Binary Optimization: Uncertainty Set Lifting versus Partitioning through Breakpoints Optimization

Farough Motamed Nasab and Zukui Li ()
Additional contact information
Farough Motamed Nasab: Department of Chemical & Materials Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada
Zukui Li: Department of Chemical & Materials Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada

Mathematics, 2023, vol. 11, issue 18, 1-24

Abstract: Two methods for multistage adaptive robust binary optimization are investigated in this work. These methods referred to as binary decision rule and finite adaptability inherently share similarities in dividing the uncertainty set into subsets. In the binary decision rule method, the uncertainty is lifted using indicator functions which result in a nonconvex lifted uncertainty set. The linear decision rule is further applied to a convexified version of the lifted uncertainty set. In the finite adaptability method, the uncertainty set is divided into partitions and a constant decision is applied for each partition. In both methods, breakpoints are utilized either to define the indicator functions in the lifting method or to partition the uncertainty set in the finite adaptability method. In this work, we propose variable breakpoint location optimization for both methods. Extensive computational study on an illustrating example and a larger size case study is conducted. The performance of binary decision rule and finite adaptability methods under fixed and variable breakpoint approaches is compared.

Keywords: adaptive optimization; decision rule; scenario tree; uncertainty set; lifting; robust optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/18/3883/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/18/3883/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:18:p:3883-:d:1238023

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().