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Programs manipulated by a GP are typically represented by trees corresponding to the parse tree of the program Each function call is represented by a node in the tree, and the arguments to the function are given by its descendant nodes For example, Figure 91 illustrates this tree representation for the function sin(x) + J To apply genetic programming to a particular domain, the user must define the primitive functions to be considered (eg, sin, cos, J , -, exponential~),as well as the terminals (eg, x, y , constants such as 2) The genetic programming algorithm then uses an evolutionary search to explore the vast space of programs that can be described using these primitives As in a genetic algorithm, the prototypical genetic programming algorithm maintains a population of individuals (in this case, program trees) On each iteration, it produces a new generation of individuals using selection, crossover, and mutation The fitness of a given individual program in the population is typically determined by executing the program on a set of training data Crossover operations are performed by replacing a randomly chosen subtree of one parent

Each of these basic methods takes in a numeric value and sends back another value Since the general usage is the same, this discussion uses sqrt() as an example of how the rest could be used to get their various values If you need to know what type of value is returned from a different method, refer to Table 12-2 to see what each method does The easiest way to use the sqrt() method is to input a positive number as the parameter to the method, as shown in the following example:

windowalert(Mathsqrt(4));

FIGURE 91 Program tree representation in genetic programming Arbitrary programs are represented by their parse trees

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the basic continuity test of copper cable The simplest source is a flashlight (possibly with a fiber cable adapter), and the simplest detector is the human eye (Fig 1113) Following the safety practices in the next section, be certain you know that a low-power visible light source is being used for this test and, even then, don t look directly into the end of the fiber However, as with copper cable, a much more complex test is needed to determine proper operation of the fiber link This is accomplished with a fiber-optic cable scanner, as shown in Fig 1114 In some cases, the scanner may be an adapter module that is used with a copper cable scanner However, because copper scanning is inherently more complex and expensive, and because different cable crews may be involved in installing fiber-optic cables, you may want to purchase a separate fiber-optic tester All fiber-optic cable testers for field use have a local and remote unit The local unit sends light of a known intensity down the cable under test The remote unit senses the absolute magnitude of the received light and calculates the loss A pass/fail indication is made and may be a function of the length of the cable The remote may be totally passive (to the installer) and simply report the results to the

This alerts the value of the positive square root of 4, which is 2 Instead of calculating a static number, you could get the user to input a number, and then send an alert to the user with the square root of the number input by the user You could do this using the following code, starting with the HTML code:

<body> <form> Enter a (positive) number or zero: <br /> <input type="text" id="sr_num" /> <input type="button" value="Get a Square Root" id="getroot" /> </form> </body>

FIGURE 92 Crossover operation applied to two parent program trees (top) Crossover points (nodes shown in bold at top) are chosen at random The subtrees rooted at these crossover points are then exchanged to create children trees (bottom)

12:

FIGURE 1114 Fiber cable tester (Courtesy of Fluke Networks)

Next, the JavaScript code:

program by a subtree from the other parent program Figure 92 illustrates a typical crossover operation Koza (1992) describes a set of experiments applying a GP to a number of applications In his experiments, 10% of the current population, selected probabilistically according to fitness, is retained unchanged in the next generation The remainder of the new generation is created by applying crossover to pairs of programs from the current generation, again selected probabilistically according to their fitness The mutation operator was not used in this particular set of experiments

If the number entered is negative, the viewer has to try again The value of the text box (with an id of sr_num) is retrieved The anonymous function to perform the task begins

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