QA235 : Approximation of Nondominated Solutions In Linear Multiple Objective Optimization
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2014
Authors:
Abstarct: In this thesis, At first we introduce the efficient and weakly efficient solutions of a
multiobjective optimization problem. Then, the scalarization method that is a method of
solving multiobjective optimization problems, is expressed. In the following, with helping
from geometric diuality theorem we show the correspondence between the primal and dual
problems and using geometric duality theorem we express the Benson’s outer algorithm.
The Benson’s algorithm outer find the Nondominated points of outcome set. After that,
We explain The Benson’s algorithm dual and by applying changes on Benson’s algorithm
dual we present approximation version of Benson’s algorithm dual. This algorithm by
generating an outer approximation and inner approximation of Nondominated set, creates
a set of ε-Nondominated points and we prove that the inner approximation is a set of
ε-weakly Nondominated points. At the end, We describe the usage of algorithms in beam
intensity optimization problems in Radiotherapy.
Keywords:
#Multiobjective linear programming #Pareto optimal #objective space #Geometric duality #Benson’s algorithm #outer approximation #ε-nondominated set #radiotherapy Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: