Finding all nondominated points of multi-objective integer programs
We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional...
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| Vydané v: | Journal of global optimization Ročník 57; číslo 2; s. 347 - 365 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Boston
Springer US
01.10.2013
Springer Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional binary variables and constraints. The other algorithm employs a search procedure and solves a number of models to find the next point avoiding any additional binary variables. Both algorithms guarantee to find all nondominated points for any MIP problem. We test the performance of the algorithms on randomly-generated instances of the multi-objective knapsack, multi-objective shortest path and multi-objective spanning tree problems. The computational results show that the algorithms work well. |
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| AbstractList | We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional binary variables and constraints. The other algorithm employs a search procedure and solves a number of models to find the next point avoiding any additional binary variables. Both algorithms guarantee to find all nondominated points for any MIP problem. We test the performance of the algorithms on randomly-generated instances of the multi-objective knapsack, multi-objective shortest path and multi-objective spanning tree problems. The computational results show that the algorithms work well. Keywords Multiple criteria * Combinatorial optimization * Nondominated point We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional binary variables and constraints. The other algorithm employs a search procedure and solves a number of models to find the next point avoiding any additional binary variables. Both algorithms guarantee to find all nondominated points for any MIP problem. We test the performance of the algorithms on randomly-generated instances of the multi-objective knapsack, multi-objective shortest path and multi-objective spanning tree problems. The computational results show that the algorithms work well. We develop exact algorithms for multi-objective integer programming (MIP) problems. The algorithms iteratively generate nondominated points and exclude the regions that are dominated by the previously-generated nondominated points. One algorithm generates new points by solving models with additional binary variables and constraints. The other algorithm employs a search procedure and solves a number of models to find the next point avoiding any additional binary variables. Both algorithms guarantee to find all nondominated points for any MIP problem. We test the performance of the algorithms on randomly-generated instances of the multi-objective knapsack, multi-objective shortest path and multi-objective spanning tree problems. The computational results show that the algorithms work well. [PUBLICATION ABSTRACT] |
| Audience | Academic |
| Author | Köksalan, Murat Lokman, Banu |
| Author_xml | – sequence: 1 givenname: Banu surname: Lokman fullname: Lokman, Banu email: banu.lokman@tedu.edu.tr organization: Industrial Engineering Department, TED University – sequence: 2 givenname: Murat surname: Köksalan fullname: Köksalan, Murat organization: Industrial Engineering Department, Middle East Technical University |
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| Keywords | Nondominated point Combinatorial optimization Multiple criteria |
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| SubjectTerms | Algorithms Computer Science Decision making Experiments Graph theory Industrial engineering Integer programming Linear programming Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Methods Objectives Operations research Operations Research/Decision Theory Optimization Real Functions Searching Shortest-path problems |
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| Title | Finding all nondominated points of multi-objective integer programs |
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