Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S2471 - S2485|
|Published online||02 March 2021|
An iterative vertex enumeration method for objective space based vector optimization algorithms
Bilkent University, Department of Industrial Engineering, Bilkent, Ankara 06800, Turkey
* Corresponding author: firstname.lastname@example.org
Accepted: 1 December 2020
An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex vector optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP, which is defined in the objective space, is solved in each iteration and it has a special structure. Namely, the recession cone of the polyhedron to be generated is the ordering cone. We consider and give a detailed description of a vertex enumeration procedure, which iterates by calling a modified “double description (DD) method” that works for such unbounded polyhedrons. We employ this procedure as a function of an existing objective space based vector optimization algorithm (Algorithm 1); and test the performance of it for randomly generated linear multiobjective optimization problems. We compare the efficiency of this procedure with another existing DD method as well as with the current vertex enumeration subroutine of Algorithm 1. We observe that the modified procedure excels the others especially as the dimension of the vertex enumeration problem (the number of objectives of the corresponding multiobjective problem) increases.
Mathematics Subject Classification: 90C29 / 52B11 / 68W27
Key words: Vertex enumeration / multiobjective optimization / vector optimization / polyhedral approximation
© EDP Sciences, ROADEF, SMAI 2021
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