A simple, efficient and versatile objective space algorithm for multiobjective integer programming

In the last years a multitude of algorithms have been proposed to solve multiobjective integer programming problems. However, only few authors offer open-source implementations. On the other hand, new methods are typically compared to code that is publicly available, even if this code is known to be...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 100; no. 1; pp. 351 - 384
Main Authors: Dächert, Kerstin, Fleuren, Tino, Klamroth, Kathrin
Format: Journal Article
Language:English
Published: Berlin, Heidelberg Springer 01.08.2024
Springer Berlin Heidelberg
Springer Nature B.V
Subjects:
Algorithms
Business and Management
Calculus of Variations and Optimal Control; Optimization
Integer programming
Local upper bounds
Mathematics
Mathematics and Statistics
Multiobjective optimization
Multiple objective analysis
Nondominated set
Objective space algorithms
Operations Research/Decision Theory
Original Article
Scalarization
Search region
Source code
Scalarization
Search region
Nondominated set
Multiobjective optimization
Objective space algorithms
Local upper bounds
ISSN:1432-5217, 1432-2994, 1432-5217
Online Access:Get full text
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Summary:In the last years a multitude of algorithms have been proposed to solve multiobjective integer programming problems. However, only few authors offer open-source implementations. On the other hand, new methods are typically compared to code that is publicly available, even if this code is known to be outperformed. In this paper, we aim to overcome this problem by proposing a new state-of-the-art algorithm with an open-source implementation in C++ . The underlying method falls into the class of objective space methods, i.e., it decomposes the overall problem into a series of scalarized subproblems that can be solved with efficient single-objective IP-solvers. It keeps the number of required subproblems small by avoiding redundancies, and it can be combined with different scalarizations that all lead to comparably simple subproblems. Our algorithm bases on previous results but combines them in a new way. Numerical experiments with up to ten objectives validate that the method is efficient and that it scales well to higher dimensional problems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1432-5217
1432-2994
1432-5217
DOI:10.1007/s00186-023-00841-0