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arXiv · 1707.09305

Monomial tropical cones for multicriteria optimization

Michael Joswig·Georg Loho
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Abstract

We present an algorithm to compute all $n$ nondominated points of a multicriteria discrete optimization problem with $d$ objectives using at most $\mathcal{O}(n^{\lfloor d/2 \rfloor})$ scalarizations. The method is similar to algorithms by Przybylski et al. (2010) and by Klamroth et al. (2015) with the same complexity. As a difference, our method employs a tropical convex hull computation, and it exploits a particular kind of duality which is special for the tropical cones arising. This duality can be seen as a generalization of the Alexander duality of monomial ideals.

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Michael Joswig, Georg Loho. 2017-07-28. Monomial tropical cones for multicriteria optimization. https://arxiv.org/abs/1707.09305

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