A Horizontal Method of Localizing Values of a Linear Function in Permutation-Based Optimization

  • Liudmyla Koliechkina
  • Oksana PichuginaEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


This paper is dedicated to linear constrained optimization on permutation configurations’ set, namely, to permutation-based subset sum problem (PB-SSP). To this problem, a directed structural graph is associated connected with a skeleton graph of the permutohedron and allowing to perform a directed search to solve this linear program. To solve PB-SSP, a horizontal method for localizing values of a linear objective function is offered combining Graph Theory tools, geometric and structural properties of a permutation set mapped into Euclidean space, the behavior of linear functions on the set, and Branch and Bound techniques.


Discrete optimization Linear constrained optimization Combinatorial configuration Permutation Skeleton graph Grid graph  Search tree 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of LodzLodzPoland
  2. 2.National Aerospace University Kharkiv Aviation InstituteKharkivUkraine

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