An approximation algorithm for multi-objective optimization problems using a box-coverage

Gabriele Eichfelder () and Leo Warnow ()
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Gabriele Eichfelder: Technische Universität Ilmenau
Leo Warnow: Technische Universität Ilmenau

Journal of Global Optimization, 2022, vol. 83, issue 2, No 8, 329-357

Abstract: Abstract For a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the nondominated set. However, often these approximations are used for further evaluations. For those applications a polyhedron is a structure that is not easy to handle. In this paper, we introduce an approximation with a simpler structure respecting the natural ordering. In particular, we compute a box-coverage of the nondominated set. To do so, we use an approach that, in general, allows us to update not only one but several boxes whenever a new nondominated point is found. The algorithm is guaranteed to stop with a finite number of boxes, each being sufficiently thin.

Keywords: Multi-objective optimization; Approximation algorithm; Nondominated set; Enclosure; Box-coverage; 90C26; 90C29; 90C59; 65K05 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-021-01109-9

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