Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model
For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal...
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doaj-f942c0c76e5b4c558a906fe89f7f927b2020-11-25T03:57:33ZengInternational Journal of Mathematical, Engineering and Management SciencesInternational Journal of Mathematical, Engineering and Management Sciences2455-77492455-77492020-12-01561249126910.33889/IJMEMS.2020.5.6.093Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming ModelAli Al-Hasani0Masar Al-Rabeeah1Santosh Kumar2Andrew Eberhard3School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia. Department of Mathematics, College of Sciences, University of Basrah, Al- Basrah, Iraq.School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia. Department of Mathematics, College of Sciences, University of Basrah, Al- Basrah, Iraq.School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia. Department of Mathematics and Statistics, University of Melbourne, Melbourne, Australia.School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia.For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity.https://www.ijmems.in/volumes/volume5/number6/93-IJMEMS-20-32-5-6-1249-1269-2020.pdfexact and approximate methods for ranked-optimal solutions; k-ranked optimal solutionsmulti-objective integer programming modelnon-dominated point setrank-based solution method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ali Al-Hasani Masar Al-Rabeeah Santosh Kumar Andrew Eberhard |
spellingShingle |
Ali Al-Hasani Masar Al-Rabeeah Santosh Kumar Andrew Eberhard Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model International Journal of Mathematical, Engineering and Management Sciences exact and approximate methods for ranked-optimal solutions ; k-ranked optimal solutions multi-objective integer programming model non-dominated point set rank-based solution method |
author_facet |
Ali Al-Hasani Masar Al-Rabeeah Santosh Kumar Andrew Eberhard |
author_sort |
Ali Al-Hasani |
title |
Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model |
title_short |
Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model |
title_full |
Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model |
title_fullStr |
Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model |
title_full_unstemmed |
Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model |
title_sort |
rank-based solution methods and their applications in determination of non-dominated points set for a multi-objective integer programming model |
publisher |
International Journal of Mathematical, Engineering and Management Sciences |
series |
International Journal of Mathematical, Engineering and Management Sciences |
issn |
2455-7749 2455-7749 |
publishDate |
2020-12-01 |
description |
For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity. |
topic |
exact and approximate methods for ranked-optimal solutions ; k-ranked optimal solutions multi-objective integer programming model non-dominated point set rank-based solution method |
url |
https://www.ijmems.in/volumes/volume5/number6/93-IJMEMS-20-32-5-6-1249-1269-2020.pdf |
work_keys_str_mv |
AT alialhasani rankbasedsolutionmethodsandtheirapplicationsindeterminationofnondominatedpointssetforamultiobjectiveintegerprogrammingmodel AT masaralrabeeah rankbasedsolutionmethodsandtheirapplicationsindeterminationofnondominatedpointssetforamultiobjectiveintegerprogrammingmodel AT santoshkumar rankbasedsolutionmethodsandtheirapplicationsindeterminationofnondominatedpointssetforamultiobjectiveintegerprogrammingmodel AT andreweberhard rankbasedsolutionmethodsandtheirapplicationsindeterminationofnondominatedpointssetforamultiobjectiveintegerprogrammingmodel |
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1724460109882458112 |