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Figure 104 Genetic Programming Mutation Operators
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Permutation operator: This operator is similar to the swap mutation If a function has n parameters, the permutation operator generates a random permutation from the possible n! permutations of parameters The arguments of the function are then permutated according to this randomly generated permutation Editing operator: This operator is used to restructure individuals according to prede ned rules For example, a subtree that represents the Boolean expression, x AND x is replaced with the single node, x Editing rules can also be used to enforce semantic rules Building block operator: The objective of the building block operator is to automatically identify potentially useful building blocks A new function node is de ned for an identi ed building block and is used to replace the subtree represented by the building block The advantage of this operator is that good building blocks will not be altered by reproduction operators
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Building Block Genetic Programming
The GP process discussed thus far generates an initial population of individuals where each individual represents a tree consisting of several nodes and levels An alternative approach has been developed in [248, 742] speci cally for evolving decision trees referred to as a building-block approach to GP (BGP) In this approach, initial individuals consist of only a root and the immediate children of that node Evolution starts on these small initial trees When the simplicity of the population s individuals can no longer account for the complexity of the problem to be solved, and no improvement in the tness of any of the individuals within the population is observed, individuals are expanded Expansion occurs by adding a randomly generated building block (ie a new node) to individuals In other words, grow mutation is applied This expansion occurs at a speci ed expansion probability, pe , and therefore not all of the individuals are expanded Described more formally, the building-block approach starts with models with a few degrees of freedom most likely too few to solve the problem to the desired degree of accuracy During the evolution process, more degrees of freedom are added when no further improvements are observed In between the triggering of expansion, crossover and mutation occur as for normal GP This approach to GP helps to reduce the computational complexity of the evolution process, and helps to produce smaller individuals
Applications
GP was developed to evolve computer programs [478, 479] Programs have been evolved for a wide range of problem types as illustrated in [479] These problem types
108 Assignments
Table 102 Genetic Programming Applications Application Decision trees Game-playing Bioinformatics Data mining Robotics References [248, 479, 685, 742] [479, 481] [484, 485] [648, 741, 917] [206, 486, 347]
include Boolean expressions, planning, symbolic function identi cation, empirical discovery, solving systems of equations, concept formation, automatic programming, pattern recognition, game-playing strategies, and neural network design Table 102 provides a summary of other applications of GP A very complete list of GP publications and applications can be found at http://wwwcsbhamacuk/~ubl/biblio/gp-html/
Assignments
1 Explain how a GP can be used to evolve a program to control a robot, where the objective of the robot is to move out of a room (through the door) lled with obstacles 2 First explain what a decision tree is, and then show how GP can be used to evolve decision trees 3 Is it possible to use GP for adaptive story telling 4 Given a pre-condition and a post-condition of a function, is it possible to evolve the function using GP 5 Explain why BGP is computationally less expensive than GP 6 Show how a GP can be used to evolve polynomial expressions 7 Discuss how GP can be used to evolve the evaluation function used to evaluate the desirability of leaf nodes in a game tree