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Extra info for Foundations of Genetic Algorithms: 8th International Workshop, FOGA 2005, Aizu-Wakamatsu City, Japan, January 5-9, 2005, Revised Selected Papers (Lecture ... Computer Science and General Issues)
If f (X) < f (NBB ) set CASE = 1; else CASE = 2. /* Samples a reflected neighbor in quadrant BB */ /* CASE refers to Case 1 and Case 2 of the proof */ Setp 4: Let b represent the third bit in the best-so-far solution. If b = 0 fix the minor (second) bit. If b = 1 fix the major (first) bit. /* The current best must be in quadrant BB. The third bit determines if */ /* the local optima is bounded by the leftmost or rightmost quadrant of BB. */ Step 5: Relabel the points so that the new best-so-far is denoted NBB and its reflected neighbors NBB , NBB and NBB .
20 Wolfgang Lenders and Christel Baier 41. , Dynamic Variable Ordering for Ordered Binary Decision Diagrams, Proceedings of the International Conference on Computer-Aided Design, 1993 42. , "CUDD: CU Decision Diagram Package", University of Colorado at Boulder, 1998 43. , An Overview of Evolutionary Computation, Proceedings of the European Conference on Machine Learning, 1993 44. , Foundations of Genetic Algorithms 2, Morgan Kaufmann, 1993 45. , The Complexity of the Optimal Variable Ordering Problems of Shared Binary Decision Diagrams, Proceedings of the 4th International Symposium on Algorithms and Computation, 1993 46.
Of course one can use special operators to force a Binary search. Given a unimodal 1-D bijective function, one can evaluate the two points that make up the dominant Hamming cliff (complementary bit strings located at adjacent points), and determine the gradient at the Hamming Cliff and therefore determine in which half of the space the global optimum in located. The more important point, however, is that local neighborhood search in the standard Binary encoding neighborhoods does not have the same nice convergence properties as a reflected Gray code neighborhood.