A new modified deflected subgradient method

A new modified deflected subgradient method

A new deflected subgradient algorithm is presented for computing a tighter lower bound of the dual problem. These bounds may be useful in nodes evaluation in a Branch and Bound algorithm to find the optimal solution of large-scale integer linear programming problems. The deflected direction search u...

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Main Authors: Rachid Belgacem, Abdessamad Amir
Format: Article
Language:English
Published: Elsevier 2018-10-01
Series:Journal of King Saud University: Science
Online Access:http://www.sciencedirect.com/science/article/pii/S1018364717304081
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spelling doaj-67c82d3bf2be461eb6f254ed41e71e012020-11-25T02:26:19ZengElsevierJournal of King Saud University: Science1018-36472018-10-01304561567A new modified deflected subgradient methodRachid Belgacem0Abdessamad Amir1Université Hassiba Benbouali de Chlef, Chlef 02000, Algeria; Corresponding author.Universié Abdelhamid Ibn Badis de Mostaganem, Mostaganem 02700, AlgeriaA new deflected subgradient algorithm is presented for computing a tighter lower bound of the dual problem. These bounds may be useful in nodes evaluation in a Branch and Bound algorithm to find the optimal solution of large-scale integer linear programming problems. The deflected direction search used in the present paper is a convex combination of the Modified Gradient Technique and the Average Direction Strategy. We identify the optimal convex combination parameter allowing the deflected subgradient vector direction to form a more acute angle with the best direction towards an optimal solution. The modified algorithm gives encouraging results for a selected symmetric travelling salesman problem (TSPs) instances taken from TSPLIB library. MSC: 90C26, 90C10, 90C27, 90C06, Keywords: Integer linear programming, Subgradient method, Nonsmooth optimization, Travelling salesman problemhttp://www.sciencedirect.com/science/article/pii/S1018364717304081
collection DOAJ
language English
format Article
sources DOAJ
author Rachid Belgacem
Abdessamad Amir
spellingShingle Rachid Belgacem
Abdessamad Amir
A new modified deflected subgradient method
Journal of King Saud University: Science
author_facet Rachid Belgacem
Abdessamad Amir
author_sort Rachid Belgacem
title A new modified deflected subgradient method
title_short A new modified deflected subgradient method
title_full A new modified deflected subgradient method
title_fullStr A new modified deflected subgradient method
title_full_unstemmed A new modified deflected subgradient method
title_sort new modified deflected subgradient method
publisher Elsevier
series Journal of King Saud University: Science
issn 1018-3647
publishDate 2018-10-01
description A new deflected subgradient algorithm is presented for computing a tighter lower bound of the dual problem. These bounds may be useful in nodes evaluation in a Branch and Bound algorithm to find the optimal solution of large-scale integer linear programming problems. The deflected direction search used in the present paper is a convex combination of the Modified Gradient Technique and the Average Direction Strategy. We identify the optimal convex combination parameter allowing the deflected subgradient vector direction to form a more acute angle with the best direction towards an optimal solution. The modified algorithm gives encouraging results for a selected symmetric travelling salesman problem (TSPs) instances taken from TSPLIB library. MSC: 90C26, 90C10, 90C27, 90C06, Keywords: Integer linear programming, Subgradient method, Nonsmooth optimization, Travelling salesman problem
url http://www.sciencedirect.com/science/article/pii/S1018364717304081
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AT abdessamadamir anewmodifieddeflectedsubgradientmethod
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