Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 206

programming algorithms. This is due to the tree forms of LISP S-expressions
which are equivalent to parse trees. For example, the LISP program chunk “ a + b * c ”
is presented as a parse tree in Figure 5.4.
Koza gives a program example that presents the LISP expression

(+ 1 2 (IF (> TIME 10) 3 4))

as the corresponding tree structure (Figure 5.5).

+

1 2 IF

>

3

4

Time

10

Tree structure for ( + 1 2 ( IF ( > Time 10 ) 3 4 ))

Figure 5.5. Tree structure of a LISP expression (+ 1 2 ( IF ( > TIME 10) 3 4))

Genetic programs run by executing program induction , i.e . they automatically
learn within the search space what programs are required in order to improve the
problem solution and in this way finally find the best one. The search space here is
the space of all possible programs, including the user-defined function set
(programming or arithmetic operations, mathematical, logic, and other domain-
specific functions) and the terminals set (containing variables and constants
appropriate to the problem domain). While searching for the best solution, the
genetic programming algorithm makes use of the statistical closure property of
functions to accept as arguments the function return values of any other functions
and the data from the terminal set.

5.3.1 Initialization

The first operational step of genetic programming is its initialization, which mainly
includes generation of the initial population, i.e . of the random composition of the
function and terminal sets. In fact, at this point a collection of random trees is
generated representing the initial program configurations. Later, the trees will be
the subject of specific successive handling by genetic operators (reproduction,
crossover, etc .) They are generated by firm allocation of the function root node.
Thereafter, the children are created and a recourse through the tree carried out