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Unformatted text preview: 4.7 Graph-based Approaches 201 could regarded it also as an evolutionary programming 42 method. Lately, researchers also begin to focus on eﬃcient crossover techniques for CGP . Neutrality in CGP Cartesian Genetic Programming explicitly utilizes different forms of neutrality 43 in order to foster the evolutionary progress. Normally, neutrality can have positive as well as negative effects on the evolvability of a system. Yu and Miller [2297, 2296] outline different forms of neutrality in Cartesian Genetic Programming which also apply to other forms of GP or GAs: 1. Inactive genes define cells that are not connected to the outputs in any way and hence cannot inﬂuence the output of the program. Mutating these genes therefore has no effect on the fitness and represents explicit neutrality . 2. Active genes have direct inﬂuence on the results of the program. Neutral mutations here are such modifications that have no inﬂuence on the fitness. This implicit neutrality is the results of functional redundancy or introns. Their experiments indicate that neutrality can increase the chance of success of Genetic Programming for needle-in-a-haystack fitness landscapes and in digital circuit evolution . Embedded Cartesian Genetic Programming In 2005, Walker and Miller  published their work on Embedded Cartesian Genetic Programming (ECGP), a new type of CGP with a module acquisition  method in form of automatic module creation [2135, 2136, 2137]. Therefore, three new operations are intro- duced: 1. Compress randomly selects two points in the genotype and creates a new module containing all the nodes between these points. The module then replaces these nodes with a cell that invokes it. The compress operator has the effect of shortening the genotype of the parent and of making the nodes in the module immune against the standard mutation operation but does not affect its fitness. Modules are more or less treated like functions so cell to which a module number has been assigned now uses that module as “cell function”. 2. Expand randomly selects a module and replaces it with the nodes inside. Only the cell which initially replaced the module cells due to the Compress operation can be expanded in order to avoid bloat. 3. The new operator Module Mutation changes modules by adding or removing inputs and outputs and may also carry out the traditional one-point mutation on the cells of the module. General Information Areas Of Application Some example areas of application of Cartesian Genetic Programming are: Application References Electrical Engineering and Circuit Design [1420, 2110, 1421, 1419, 1081, 2136] 42 See Chapter 6 on page 231 for more details on evolutionary programming....
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