Inventory of the 12 007 Low-Dimensional Pseudo-Boolean Landscapes Invariant to Rank, Translation, and Rotation
Many randomized optimization algorithms are rank-invariant, relying solely on the relative ordering of solutions rather than absolute fitness values. We introduce a stronger notion of rank landscape invariance: two problems are equivalent if their ranking, but also their neighborhood structure and symmetries (translation and rotation), induce identical landscapes. This motivates the study of rank landscapes rather than individual functions. While prior work analyzed the rankings of injective function classes in isolation, we provide an exhaustive inventory of the invariant landscape classes for pseudo-Boolean functions of dimensions 1, 2, and 3, including non-injective cases. Our analysis...
| Authors | Arnaud Liefooghe, Sébastien Verel |
|---|---|
| Primary category | cs.AI |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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