Local Search and High Precision Gray Codes: Convergence Results and Neighborhoods

Darrell Whitley whitley@cs.colostate.edu; Laura Barbulescu laura@cs.colostate.edu; Jean-Paul Watson watsonj@cs.colostate.edu    Department of Computer Science, Colorado State University, Fort Collins, Colorado 80523 USA


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 OL with a constant ...

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