Inner approximation algorithm for solving linear multiobjective optimization problems
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined parts: single-objective linear optimization on one hand, and a combinatorial part closely related to vertex...
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| Vydané v: | Optimization Ročník 70; číslo 7; s. 1487 - 1511 |
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| Jazyk: | English |
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Taylor & Francis
03.07.2021
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| Abstract | Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined parts: single-objective linear optimization on one hand, and a combinatorial part closely related to vertex enumeration on the other. Their separation provides a deeper insight into Benson's algorithm, and points toward a dual approach. Two skeletal algorithms are defined which focus on the combinatorial part. Using different single-objective optimization problems yields different algorithms, such as a sequential convex hull algorithm, another version of Benson's algorithm with the theoretically best possible iteration count, and the dual algorithm of Ehrgott et al. [A dual variant of Benson's 'outer approximation algorithm' for multiple objective linear programming. J Glob Optim. 2012;52:757-778]. The implemented version is well suited to handle highly degenerate problems where there are many linear dependencies among the constraints. On problems with 10 or more objectives, it shows a significant increase in efficiency compared to Bensolve - due to the reduced number of iterations and the improved combinatorial handling. |
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| AbstractList | Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined parts: single-objective linear optimization on one hand, and a combinatorial part closely related to vertex enumeration on the other. Their separation provides a deeper insight into Benson's algorithm, and points toward a dual approach. Two skeletal algorithms are defined which focus on the combinatorial part. Using different single-objective optimization problems yields different algorithms, such as a sequential convex hull algorithm, another version of Benson's algorithm with the theoretically best possible iteration count, and the dual algorithm of Ehrgott et al. [A dual variant of Benson's ‘outer approximation algorithm’ for multiple objective linear programming. J Glob Optim. 2012;52:757–778]. The implemented version is well suited to handle highly degenerate problems where there are many linear dependencies among the constraints. On problems with 10 or more objectives, it shows a significant increase in efficiency compared to Bensolve – due to the reduced number of iterations and the improved combinatorial handling. Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined parts: single-objective linear optimization on one hand, and a combinatorial part closely related to vertex enumeration on the other. Their separation provides a deeper insight into Benson's algorithm, and points toward a dual approach. Two skeletal algorithms are defined which focus on the combinatorial part. Using different single-objective optimization problems yields different algorithms, such as a sequential convex hull algorithm, another version of Benson's algorithm with the theoretically best possible iteration count, and the dual algorithm of Ehrgott et al. [A dual variant of Benson's 'outer approximation algorithm' for multiple objective linear programming. J Glob Optim. 2012;52:757-778]. The implemented version is well suited to handle highly degenerate problems where there are many linear dependencies among the constraints. On problems with 10 or more objectives, it shows a significant increase in efficiency compared to Bensolve - due to the reduced number of iterations and the improved combinatorial handling. |
| Author | Csirmaz, Laszlo |
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| CitedBy_id | crossref_primary_10_1016_j_ejco_2021_100014 crossref_primary_10_1007_s10898_025_01512_6 crossref_primary_10_1016_j_mineng_2024_108793 crossref_primary_10_1007_s00186_023_00847_8 crossref_primary_10_1007_s00170_021_07943_1 |
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| SubjectTerms | Algorithms Approximation Combinatorial analysis Computational geometry Convexity double description duality Enumeration Linear programming Mathematical analysis Multiobjective optimization Multiple objective analysis objective space Optimization vertex enumeration |
| Title | Inner approximation algorithm for solving linear multiobjective optimization problems |
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