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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Bibliographic Details
Published in:Optimization Vol. 70; no. 7; pp. 1487 - 1511
Main Author: Csirmaz, Laszlo
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.07.2021
Taylor & Francis LLC
Subjects:
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
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary: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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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1737692