| Riccardo Poli and Nicholas Freitag McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part I. Evolutionary Computation, 11(1):53--66, 2003. |
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Riccardo Poli and Nicholas Freitag McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part I. Evolutionary Computation, 11(1):53--66, 2003.
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Riccardo Poli and Nicholas Freitag McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part II. Evolutionary Computation, 11(2):169--206, 2003.
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Riccardo Poli and Nicholas Freitag McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part I. Evolutionary Computation, 11(1):53--66, 2003.
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R. Poli and N. F. McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part II. Evolutionary Computation, 11(2), 2003.
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R. Poli and N. F. McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part I. Evolutionary Computation, 11(1):53--66, 2003.
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R. Poli. General schema theory for genetic programming with subtreeswapping crossover. In Genetic Programming, Proceedings of EuroGP 2001.
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Poli, R. (2001b). General schema theory for genetic programming with subtreeswapping crossover. In Miller, J. F., Tomassini, M., Lanzi, P. L., Ryan, C., Tettamanzi, A. G. B., and Langdon, W. B., editors, Genetic Programming, Proceedings of EuroGP'2001, volume 2038 of LNCS, pages 143--159, Lake Como, Italy. SpringerVerlag.
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Riccardo Poli, "General schema theory for genetic programming with subtree-swapping crossover", in Genetic Programming, Proceedings of EuroGP 2001.
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R. Poli. General schema theory for genetic programming with subtree-swapping crossover. In Genetic Programming, Proceedings of EuroGP 2001.
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R. Poli. General schema theory for genetic programming with subtreeswapping crossover. In Genetic Programming, Proceedings of EuroGP 2001.
No context found.
R. Poli. General schema theory for genetic programming with subtree-swapping crossover. In Genetic Programming, Proceedings of EuroGP
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Riccardo Poli, "General schema theory for genetic programming with subtree-swapping crossover", in Genetic Programming, Proceedings of EuroGP 2001.
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R. Poli. General schema theory for genetic programming with subtree-swapping crossover. In Genetic Programming, Proceedings of EuroGP 2001.
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Poli, R. (2001a) General schema theory for genetic programming with subtree-swapping crossover. In Genetic Programming, Proceedings of EuroGP 2001 LNCS Springer-Verlag, Milan.
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R. Poli, "General schema theory for genetic programming with subtree-swapping crossover," in Genetic Programming, Proceedings of EuroGP 2001.
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Riccardo Poli and Nicholas Freitag McPhee. General schema theory for genetic programming with subtreeswapping crossover: Part II. Evolutionary Computation, 11(2), 2003.
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Riccardo Poli and Nicholas Freitag McPhee. General schema theory for genetic programming with subtreeswapping crossover: Part I. Evolutionary Computation, 11(1):53--66, 2003.
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Riccardo Poli. General schema theory for genetic programming with subtree-swapping crossover. In Julian F. Miller, Marco Tomassini, Pier Luca Lanzi, Conor Ryan, Andrea G. B. Tettamanzi, and William B. Langdon, editors, Genetic Programming, Proceedings of EuroGP'2001.
....fitness) which implies the surprising result that a single program glitch is sufficient to drive the average program size of an infinite population. While the work reported here is all on GP with linear structures, the schema theorem used is a special case of a more general GP schema theorem [Poli, 2000b] We have chosen in these early applications to focus on linear structures because the theoretical analysis is more manageable and the computations are more tractable. This has yielded a number of important results for the linear case, and preliminary results further suggest that many of the key ....
....window on the large and complex picture of GP behavior. How do we get around those limitations In this paper we propose to use schema theory. 2 Schema theory for GP on linear structures In recent work the GA schema theory in [Stephens and Waelbroeck, 1999] has been extended to GP [Poli, 2000a, Poli, 2000b] Unlike most previous schema theory work, which provides lower bounds on the number of instances of a schema, this new work provides exact formulas for the transmission of schemata from one generation to the next. Genetic Programming is a highly complex process and, as might be expected, the ....
[Article contains additional citation context not shown here]
Poli, R. (2000b). General schema theory for genetic programming with any subtree-swapping crossover. Technical Report CSRP-00-16, University of Birmingham, UK.
....gives us a very restricted view of what is happening, and more analytical methods are needed. One such method is to consider one or more aspects of the internal population dynamics during a run. Recently a lot of work has been done to develop exact schema theories for Genetic Programming [10][11] which, among other things, give us a description of the expected changes 20 40 60 80 100 (percent) Generation Fitness value against generation Truncating Figure 2: GP Performance of the artificial ant problem using a hardware GP system. Average of 500 runs. in the program length ....
....using limiting crossover with fitness and the single child variant. Maximum length limited to 8. From the hardware implementation. mal program lengths suggests that allowing programs to be unlimited in length may be detrimental to using GP effectively. 5 Further work From the results in [10] we would expect similar behavior when these techniques are applied to standard tree based GP, and this is currently being investigated. Other techniques have been suggested for controlling the program size during evolution, such as the smooth operators [9] homologous and size fair operators [4] ....
R. Poli. General schema theory for genetic programming with subtree-swapping crossover. In J. Miller, M. Tomassini, P. Lanz, C. Ryan, G. Andrea, B. Tettamanzi, and W. Langdon, editors, Genetic Programming, LNCS, pages 143--159, Lake Como, Italy, Apr. 2001. EvoNET, Springer-Verlag.
....gives us a very restricted view of what is happening, and more analytical methods are needed. One such method is to consider one or more aspects of the internal population dynamics during a run. Recently a lot of work has been done to develop exact schema theories for Genetic Programming [11][12] which, among other things, give us a description of the expected changes in the program length distribution during a GP run. The asymptotic distribution of program lengths is important to us because it is a way of comparing the sampling behavior (search bias) of different crossover operators ....
....performance. The effect of adjusting the program length limit so that the peak in the length distribution is closer to the peak of optimal program lengths suggests that allowing programs to be unlimited in length may be detrimental to using GP effectively. 5 Further work From the results in [11] we would expect similar behavior when these techniques are applied to standard tree based GP, and this is currently being investigated. Other techniques have been suggested for controlling the program size during evolution, such as the smooth operators [10] homologous and size fair operators ....
R. Poli. General schema theory for genetic programming with subtreeswapping crossover. In J. Miller, M. Tomassini, P. Lanz, C. Ryan, G. Andrea, B. Tettamanzi, and W. Langdon, editors, Genetic Programming, Proceedings of EuroGP'2001.
....include: The size function 35 which represents the number of nodes present in the subtree rooted at coordinates 71 in tree , with the convention that 35 J if 65 indicates an inexistent node. The size function can be defined using the name function (see [13]) The arity function 42 which returns the arity of the node at coordinates 55 in . For example, for the tree in Fig. 4, 3 , 0 H 3 , T 8 J and T J . The type function V which returns the data type of the node at ....
....[6] then 2P 5 2: 0750 J n2P 0 8 2: T g H , 2: T g a 2P 8 Z 2: T g a 2P 8 5 Z H , and 2P 35 v for all other coordinate pairs. There are many possible uses for 2: V and other probability distributions over node reference systems (see [13]) However, here we will concentrate on their use in modelling crossover operators. In general in order to model crossover operators we need to use the following conditional probability distribution function over the space P : 2: J J A node at depth and column is ....
[Article contains additional citation context not shown here]
R. Poli. General schema theory for genetic programming with subtree-swapping crossover. Technical Report CSRP-00-16, University of Birmingham, School of Computer Science, November 2000.
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Poli, R. and McPhee, N. (2003b). General schema theory for genetic programming with subtreeswapping crossover: Part ii. Evolutionary Computation, 11(2):169--206.
No context found.
Poli, R. and McPhee, N. (2003a). General schema theory for genetic programming with subtreeswapping crossover: Part i. Evolutionary Computation, 11(1):53--66.
No context found.
R. Poli and N.F. McPhee. General schema theory for genetic programming with subtree-swapping crossover: Part i. Evolutionary Computation, 11(1):53--66, 2003.
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