A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm | Zendy

Paschal Bisong Nyiam | Zendy; Abdellah Salhi | Zendy

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A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm

Author(s) -

Paschal Bisong Nyiam,

Abdellah Salhi

Publication year - 2021

Publication title -

advances in operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.379

H-Index - 14

eISSN - 1687-9155

pISSN - 1687-9147

DOI - 10.1155/2021/1857030

Subject(s) - simplex algorithm , simplex , algorithm , set (abstract data type) , linear programming , mathematics , extension (predicate logic) , extreme point , variable (mathematics) , mathematical optimization , space (punctuation) , computer science , combinatorics , mathematical analysis , programming language , operating system

The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered.

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