Bibliographic citations
Aragonés, N., (2024). Principios de descarte en optimización combinatoria de funciones supermodulares y cuasisupermodulares sobre el reticulado booleano finito [Universidad Nacional de Trujillo]. https://hdl.handle.net/20.500.14414/21192
Aragonés, N., Principios de descarte en optimización combinatoria de funciones supermodulares y cuasisupermodulares sobre el reticulado booleano finito []. PE: Universidad Nacional de Trujillo; 2024. https://hdl.handle.net/20.500.14414/21192
@phdthesis{renati/1050247,
title = "Principios de descarte en optimización combinatoria de funciones supermodulares y cuasisupermodulares sobre el reticulado booleano finito",
author = "Aragonés Salazar, Nelson Omar",
publisher = "Universidad Nacional de Trujillo",
year = "2024"
}
In this thesis, the problem of finding extremes (maximum and minimum) of supermodular and quasi-supermodular functions defined in a finite boolean lattice, from the discard principles approach, is studied. Discard principles allow avoiding exhaustive evaluation over the search space (set of admissible variants) by making it possible to discard sets of variants in which it is established that the optimal variant is not found. Starting from the concept of relative complement of an element with respect to a segment in a finite lattice, the three discard principles raised by V.P. Cherenin and V. R. Khachaturov for the case of minimization of a defined supermodular function in the finite boolean lattice were stablished. It has been possible to extend these results to the case of maximization of supermodular functions as well as for the minimization and maximization of quasisupermodular functions in the class of subsets of a given finite set, as well as its generalization for the case of supermodular and quasisupermodular functions defined on the abstract finite boolean lattice.
This item is licensed under a Creative Commons License