Characterization of rankings generated by pseudo-Boolean functions

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Date
2024-03-16
Author
Unanue Gual, Imanol
Merino Maestre, María ORCID
Lozano Alonso, José Antonio
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Swarm and Evolutionary Computation 86 : (2024) // Art. ID. 101540
URI
http://hdl.handle.net/10810/68311
Abstract
In this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pseudo-Boolean functions of degree , several observations are made. First, we verify that pseudo-Boolean functions of degree , where is the search space dimension, cannot generate all the possible rankings of the solutions. Secondly, the sufficient condition for a ranking to be generated by a pseudo-Boolean function of dimension is presented, and also the necessary condition is conjectured. Finally, we observe that the same argument is not sufficient to prove which ranking can be generated by pseudo-Boolean functions of degree .
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© 2024 The Author(s). Published by Elsevier B.V. This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.
Except where otherwise noted, this item's license is described as © 2024 The Author(s). Published by Elsevier B.V. This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.