Local Search and High Precision Gray Codes: Convergence Results and Neighborhoods
نویسندگان
چکیده
A proof is presented that shows how the neighborhood structure that is induced under a Gray Code representation repeats under shifting. Convergence proofs are also presented for steepest ascent using a local search bit climber and a Gray code representation: for unimodal 1-D functions and multimodal functions that are separable and unimodal in each dimension, the worst case number of steps needed to reach the global optimum is O(L) with a constant 2. We also show how changes in precision impact the Gray neighborhood. Finally, we also show how both the Gray and Binary neighborhoods are easily reachable from the Gray coded representation.
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