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I was reading "Optical Recognition Systems" book and in chapter 3.3.2.3 where methods for full genetic programming are described, a paper is describing an ADF (automatically defined functions) like this:

The ADFs have the terminal set Tf ={X, N, S, W, E, NE, NW, SE, SW} and the function set Ff = {AND, OR, NOT}. The main program has the terminal set Tc = {I, L, NIL} and a set of functions (Fc) containing movement functions, logical operators, four ADFs and the HOMING operator.

I am confused about the meaning of HOMING operator. An explanation or some links to point me in the right direction would be great.

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The 1993 paper by John R. Koza (a pioneer of genetic programming), Simultaneous Discovery of Detectors and a Way of Using the Detectors via Genetic Programming, can be accessed on CiteSeer. The HOMING operator is described as:

The one-argument HOMING operator evaluates its argument and, in addition, has the side effect of rubber-banding the turtle to its position at the start of the evaluation of the HOMING. HOMING is equivalent to the brackets in a Lindenmayer system.

From my limited understanding, it is a formal programming operator, within which a certain number of instructions are performed (like motion to North, East, South-West, etc.). It memorizes some initial state (or bookmark), and returns to it when all inner instructions have been executed. In the paper context, it refers to a turtle moving from pixel to pixel to detect a letter in a pixel grid. At the end of its journey, the turtle shall go back to its original location (rubber-banding), or HOME.

Maybe the illustration of the bracket effect in an L-system (Lindenmayer system) given in section Turtle branching from Drawing simple generative organics with L-systems can help a bit:

https://twitter.com/i/status/1208386711249735680

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