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

Abstract 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.