Abstract
Scalability has become a major issue and a hot topic of research for the GP community, as researchers are moving on to investigate more complex problems. Throughout nature and conventional human design principles, modular structures are extensively used to tackle complex problems by decomposing them into smaller, simpler subproblems, which can be independently solved. Modularity is defined as the degree to which an entity can be represented in terms of smaller functional blocks. These smaller functional blocks are known as modules. In this chapter, a new approach called Embedded CGP (ECGP), is described that is capable of dynamically acquiring, evolving, and reusing modules to exploit modularity. Alternative approaches for acquiring modules within ECGP are also discussed before describing Modular CGP (MCGP), an enhancement to ECGP that allows the use of nested modules to see if further performance improvements are possible. Finally, an approach that uses the concept of multiple chromosomes in order to allow CGP and ECGP to exploit modularity through compartmentalization is described.
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References
Angeline, P.J., Pollack, J.: Evolutionary Module Acquisition. In: Proc. Conference on Evolutionary Programming, pp. 154–163. MIT Press (1993)
Chellapilla, K.: A Preliminary Investigation into Evolving Modular Programs without Subtree Crossover. In: Proc. Conference on Genetic Programming, pp. 23–31. Morgan Kaufmann (1998)
Christensen, S., Oppacher, F.: An Analysis of Koza’s Computational Effort Statistic for Genetic Programming. In: Proc. European Conference on Genetic Programming, LNCS, vol. 2278, pp. 182–191. Springer (2002)
Collet, P., Lutton, E., Raynal, F., Schoenauer, M.: Polar IFS, + Parisian Genetic Programming = Efficient IFS Inverse Problem Solving. Genetic Programming and Evolvable Machines 1(4), 339–361 (2000)
Cong, J., Ding, Y.: Combinational Logic Synthesis for LUT Based Field Programmable Gate Arrays. ACM Transactions in Design Automation of Electronic Systems 1(2), 145–204 (1996)
Crawford-Marks, R., Spector, L.: Size Control Via Size Fair Genetic Operators in the PushGP Genetic Programming System. In: Proc. Genetic and Evolutionary Computation Conference (GECCO). Morgan Kaufmann (2002)
Glette, K., Gruber, T., Kaufmann, P., Torresen, J., Sick, B., Platzner, M.: Comparing Evolvable Hardware to Conventional Classifiers for Electromyographic Prosthetic Hand Control. In: Proc. NASA/ESA Conference on Adaptive Hardware and Systems (AHS’08), pp. 32–39. IEEE Computer Society (2008)
Karatsuba, A., Ofman, Y.: Multiplication of Multiplace Numbers on Automata. Dokl. Akad. Nauk SSSR 145(2), 293–294 (1962)
Kaufmann, P., Platzner, M.: MOVES: A Modular Framework for Hardware Evolution. In: Proc. Adaptive Hardware and Systems, pp. 447–454. IEEE Press (2007)
Kaufmann, P., Platzner, M.: Advanced Techniques for the Creation and Propagation of Modules in Cartesian Genetic Programming. In: Proc. Conference on Genetic and Evolutionary Computation, pp. 1219–1226. ACM Press (2008)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Natural Selection. MIT Press (1992)
Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. MIT Press (1994)
Lones, M.A., Tyrrell, A.M.: Biomimetic Representation with Genetic Programming Enzyme. Genetic Programming and Evolvable Machines 3(2), 193–217 (2002)
Mann, H.B., Whitney, D.R.: On a Test of Whether One of 2 Random Variables is Stochastically Larger than the Other. Annals of Mathematical Statistics 18, 50–60 (1947)
Miller, J.F.: An Empirical Study of the Efficiency of Learning Boolean Function using a Cartesian Genetic Programming Approach. In: Proc. Genetic and Evolutionary Computation Conference, pp. 1135–1142. Morgan Kaufmann (1999)
Miller, J.F., Smith, S.L.: Redundancy and Computational Efficiency in Cartesian Genetic Programming. IEEE Transactions on Evolutionary Computation 10(2), 167–174 (2006)
Miller, J.F., Thomson, P.: Cartesian Genetic Programming. In: Proc. European Conference on Genetic Programming, LNCS, vol. 1802, pp. 121–132. Springer (2000)
Niehaus, J., Banzhaf, W.: More on Computational Effort Statistics for Genetic Programming. In: Proc. European Conference on Genetic Programming, LNCS, vol. 2610, pp. 164–172. Springer (2003)
Poli, R.: Parallel Distributed Genetic Programming. In: D. Corne, M. Dorigo, F. Glover (eds.) New Ideas in Optimization, pp. 403–432. McGraw-Hill (1999)
Poli, R., Page, J.: Solving High-order Boolean Parity Problems with Smooth Uniform Crossover, Sub-machine Code GP and Demes. Genetic Programming and Evolvable Machines 1(1), 37–56 (2000)
Rosca, J.P.: Genetic Programming Exploratory Power and the Discovery of Functions. In: Proc. Conference of Evolutionary Programming, pp. 719–736. MIT Press (1995)
Rosca, J.P.: Towards Automatic Discovery of Building Blocks in Genetic Programming. In: Working Notes for the AAAI Symposium on Genetic Programming, pp. 78–85. AAAI (1995)
Rosca, J.P., Ballard, D.H.: Learning by Adapting Representations in Genetic Programming. In: Proc. International Conference on Evolutionary Computation, pp. 407–412 (1994)
Schwefel, H.P.: Kybernetische Evolution als Strategie der experimentellen Forschung in der Strömungstechnik. Master’s thesis, Technical University Berlin (1965)
Spector, L.: Simultaneous Evolution of Programs and their Control Structures. In: Advances in Genetic Programming II. MIT Press (1996)
Spector, L., Robinson, A.: Genetic Programming and Autoconstructive Evolution with the Push Programming Language. Genetic Programming and Evolvable Machines 3(1), 7–40 (2002)
Torresen, J.: Evolving Multiplier Circuits by Training Set and Training Vector Partitioning. In: Proc. International Conference on Evolvable Systems (ICES), LNCS, vol. 2606, pp. 228–237. Springer (2003)
Walker, J.A., Miller, J.F.: Evolution and Acquisition of Modules in Cartesian Genetic Programming. In: Proc. European Conference on Genetic Programming, LNCS, vol. 3003, pp. 187–197. Springer (2004)
Walker, J.A., Miller, J.F.: Improving the Evolvability of Digital Multipliers using Embedded Cartesian Genetic Programming and Product Reduction. In: Proc. International Conference on Evolvable Systems, LNCS, vol. 3637, pp. 131–142. Springer (2005)
Walker, J.A., Miller, J.F.: Investigating the Performance of Module Acquisition in Cartesian Genetic Programming. In: Proc. Genetic and Evolutionary Computation Conference, vol. 2, pp. 1649–1656. ACM Press (2005)
Walker, J.A., Miller, J.F.: Automatic Acquisition, Evolution and Re-use of Modules in Cartesian Genetic Programming. IEEE Transactions on Evolutionary Computation 12, 397–417 (2008)
Walker, M., Edwards, H., Messom, C.: Confidence Intervals for Computational Effort Comparisons. In: Proc. European Conference on Genetic Programming, LNCS, vol. 4445, pp. 23–32. Springer (2007)
Walker, M., Edwards, H., Messom, C.: The Reliability of Confidence Intervals for Computational Effort Comparisons. In: Proc. Genetic and Evolutionary Computation Conference, pp. 1716–1723. ACM (2007)
Wilcoxon, F.: Individual Comparisons by Ranking Methods. Biometrics Bulletin 1, 80–83 (1945)
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Walker, J.A., Miller, J.F., Kaufmann, P., Platzner, M. (2011). Problem Decomposition in Cartesian Genetic Programming. In: Miller, J. (eds) Cartesian Genetic Programming. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17310-3_3
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DOI: https://doi.org/10.1007/978-3-642-17310-3_3
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