A Cellular Genetic Algorithm with Disturbances: Optimisation by Kirley M. PDF

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3 Simple Binary Search for Real Valued Encodings A similar search can be done using real valued representation that also cuts the search space in half after 2 evaluations. We again assume a 1-D bijective function. Evaluate points at 0, N/4, N/2, 3N/4, N-1 (rounding if necessary). Note this explicitly divides the space into 4 regions. After the minimum is identified, an optimum must lie in one of two quadrants. For example, let F be the evaluation function. If F (0) > F (N/4) < F (N/2) < F (3N/4) < F (N − 1) then the optimum must be between F (0) and F (N/2).

Genetic Quad Search. In GECCO 2003, pages 1469–1480. Springer, 2003. [Whi99] D. Whitley. A Free Lunch Proof for Gray versus Binary Encodings. In GECCO-99, pages 726–733. Morgan Kaufmann, 1999. [WM95] David H. Wolpert and William G. Macready. No free lunch theorems for search. Technical Report SFI-TR-95-02-010, Santa Fe Institute, July 1995. [WRB04] D. Whitley, J. Rowe, and K. Bush. Subthreshold Seeking Behavior and Robust Local Search. In GECCO 2004, pages v2:282–293. Springer, 2004. edu Abstract.

The following is an example of M4 . -> 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3 2 2 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 3 3 3 3 3 3 3 3 2 2 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 3 3 3 3 2 2 3 3 3 3 1 3 3 3 3 3 3 1 3 2 2 3 2 2 1 Gray, Binary and Real Valued Encodings: Quad Search and Locality Proofs 31 The arrow points to row 2x−1 + 2x−2 − 1 which has a special importance. The first 2x−2 elements have value x − 1, and the remaining elements are identical to the last row of matrix Mx−1 .

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A Cellular Genetic Algorithm with Disturbances: Optimisation Using Dynamic Spatial Interactions by Kirley M.


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