GEP: Boolean 6-Multiplexer Problem


	Boolean 6-Multiplexer Problem
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Boolean 6-multiplexer

The task of the 6-bit Boolean multiplexer is to decode a 2 binary address (00, 01, 10, 11) and return the value of the correspondent data register (d₀, d₁, d₂, d₃). Thus, the Boolean 6-multiplexer is a function of 6 activities: two, a₀ and a₁, determine the address, and four, d₀ to d₃, determine the answer. To simplify, I use one character symbols {a,b,1,2,3,4} which correspond respectively to {a₀,a₁,d₀,d₁,d₂,d₃}. There are 2⁶=64 possible combinations for the 6 arguments and the entire set of 64 combinations was used as the fitness cases for evaluating fitness.

Table 1 Parameters for the 6-multiplexer problem
Function set	I
Terminal set	a,b,1,2,3,4
Number of fitness cases	64
Number of runs	100
Number of generations	50
Population size	250
Success rate	100%

Notes: I- if (x,y,z) function: if x is 1, the second argument is evaluated, otherwise the third argument is evaluated.

Table 2 Comparison of GP and GEP on the 6-multiplexer
	Exp	Gen	Pop	Fit. cases	Succ	R_z	F_z
GP	O'Reilly and Oppacher[1]	51	500	64	0.795	3	4,896,000
GEP	Table 1	50	250	64	1	1	800,000

Conclusion:
Again, GEP outperforms GP (6 times).

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Bibliography:
1. O'Reilly, U-M, and F. Oppacher (1996). A comparative analysis of GP. Chapter 2 of Advances in Genetic Programming 2, ed. P. J. Angeline and K. E. Kinnear, MIT Press.

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Last update: 23/July/2013