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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Stadler, P.F., Flamm, C. Barrier Trees on Poset-Valued Landscapes. Genetic Programming and Evolvable Machines 4, 7–20 (2003). https://doi.org/10.1023/A:1021821009420
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DOI: https://doi.org/10.1023/A:1021821009420