An Introduction to Genetic Algorithms - Boente

Chapter 2: Genetic Algorithms in Problem Solving
Apply selection, crossover, and mutation to the population to form a new population. In Koza's
method, 10% of the trees in the population (chosen probabilistically in proportion to fitness) are
copied without modification into the new population. The remaining 90% of the new population is
formed by crossovers between parents selected (again probabilistically in proportion to fitness) from
the current population. Crossover consists of choosing a random point in each parent and exchanging
the subtrees beneath those points to produce two offspring. Figure 2.3 displays one possible crossover
event. Notice that, in contrast to the simple GA, crossover here allows the size of a program to
increase or decrease. Mutation might performed by choosing a random point in a tree and replacing
the subtree beneath that point by a randomly generated subtree. Koza (1992) typically does not use a
mutation operator in his applications; instead he uses initial populations that are presumably large
enough to contain a sufficient diversity of building blocks so that crossover will be sufficient to put
together a working program.
Figure 2.3: An example of crossover in the genetic programming algorithm. The two parents are shown at the
top of the figure, the two offspring below. The crossover points are indicated by slashes in the parent trees.
Steps 3 and 4 are repeated for some number of generations.
It may seem difficult to believe that this procedure would ever result in a correct program—the famous
example of a monkey randomly hitting the keys on a typewriter and producing the works of Shakespeare
comes to mind. But, surprising as it might seem, the GP technique has succeeded in evolving correct
programs to solve a large number of simple (and some not−so−simple) problems in optimal control, planning,
sequence induction, symbolic regression, image compression, robotics, and many other domains. One
example (described in detail in Koza 1992) is the block−stacking problem illustrated in figure 2.4. The goal
was to find a program that takes any initial configuration of blocks—some on a table, some in a stack—and
places them in the stack in the correct order. Here the correct order spells out the word "universal." ("Toy"
problems of this sort have been used extensively to develop and test planning methods in artificial
intelligence.) The functions and terminals Koza used for this problem were a set of sensors and actions
defined by Nilsson (1989). The terminals consisted of three sensors (available to a hypothetical robot to be
controlled by the resulting program), each of which returns (i.e., provides the controlling Lisp program with) a
piece of information:
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