Barrier Trees on Poset-Valued Landscapes |
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Authors: | Peter F Stadler Christoph Flamm |
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Affiliation: | (1) Institut für Theoretische Chemie und Molekulare Strukturbiologie, Universität Wien, Währingerstrasse 17, A-1090 Wien, Austria;(2) Bioinformatik, Institut für Informatik, Universität Leipzig, Kreuzstraße 7b, D-04103 Leipzig, Germany;(3) Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM o[87501, USA |
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Abstract: | Fitness landscapes have proved to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. Usually, a fitness landscape is considered as a mapping from a configuration space equipped with some notion of adjacency, nearness, distance, or accessibility, into the real numbers. In the context of multi-objective optimization problems this concept can be extended to poset-valued landscapes. In a geometric analysis of such a structure, local Pareto points take on the role of local minima. We show that the notion of saddle points, barriers, and basins can be extended to the poset-valued case in a meaningful way and describe an algorithm that efficiently extracts these features from an exhaustive enumeration of a given generalized landscape. |
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Keywords: | partially ordered set landscape saddle points Pareto points barrier trees |
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