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Finding the Nondominated Set and Efficient Integer Vectors for a Class of Three-Objective Mixed-Integer Linear Programs
Date
2023-03-01
Author
Ceyhan, Gokhan
Köksalan, Mustafa Murat
Lokman, Banu
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We consider a class of three-objective mixed-integer linear programs (MILPs) where at least one of the objective functions takes only discrete values. These problems commonly occur in MILPs where one or more of the three objective functions contain only integer decision variables. In such problems, the nondominated set consists of the union of nondominated edges and individual nondominated points. The nondominated edges can provide valuable insights on the trade-offs between the two continuous objectives at different levels of the discrete-valued objective. We develop an objective-space search algorithm that keeps partitioning the search space by progressively creating cones in the twodimensional feasible space of the two continuous objectives for relevant values of the discrete-valued objective. The algorithm generates the nondominated points or edges in the nonincreasing order of the feasible values of the selected discrete-valued objective. Additionally, the algorithm uncovers all efficient integer variable vectors, including different vectors that lead to the same nondominated points or edges. We apply the algorithm to the day-ahead electricity market clearing problem.
Subject Keywords
multiobjective
,
mixed-integer linear program
,
objective-space search algorithm
,
ALGORITHM
,
POINTS
,
SPACE
URI
https://hdl.handle.net/11511/103011
Journal
MANAGEMENT SCIENCE
DOI
https://doi.org/10.1287/mnsc.2023.4712
Collections
Department of Industrial Engineering, Article
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
G. Ceyhan, M. M. Köksalan, and B. Lokman, “Finding the Nondominated Set and Efficient Integer Vectors for a Class of Three-Objective Mixed-Integer Linear Programs,”
MANAGEMENT SCIENCE
, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/103011.