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Less well known is the use of information theory in simulated evolution by random search. For instance, the average speed of a random walk with Gaussian distributed steps in a hypercube or simplex is proportional to  -P log( P ), where P is the average probability that a step will lead to a new point inside the hypercube, Kjellström, 1969. This may be interpreted as the self-information –log(P) divided by the work or time – proportional to 1/P – needed to get the information on the average.

Less well known is the use of information theory in simulated evolution by random search. For instance, the average speed of a random walk with Gaussian distributed steps in a hypercube or simplex is proportional to  -P log( P ), where P is the average probability that a step will lead to a new point inside the hypercube, Kjellström, 1969. This may be interpreted as the self-information –log(P) divided by the work or time – proportional to 1/P – needed to get the information on the average.

The function -P log( P ) equals zero at the end points of the P-interval, 0 <= P <= 1, and attains its maximum at P = 1/e = 37%.  

The function -P log( P ) is positive in the P-interval, 0 <= P <= 1, equals zero at the end points and attains its maximum at P = 1/e = 37%.  

A more general theorem of efficiency based on information theory may be found in a paper by Kjellström, 1991.

A more general theorem of efficiency based on information theory may be found in a paper by Kjellström, 1991.