Matrix Analysis of Genetic Programming Mutation
Heuristic policies for combinatorial optimisation problems can be found by using Genetic programming (GP) to evolve a mathematical function over variables given by the current state of the problem, and whose value is used to determine action choices (such as preferred assignments or branches). If all variables have finite discrete domains, then the expressions can be converted to an equivalent lookup table or ‘decision matrix’. Spaces of such matrices often have natural distance metrics (after conversion to a standard form). As a case study, and to support the understanding of GP as a meta-heuristic, we extend previous bin-packing work and compare the distances between matrices from before and after a GP-driven mutation. We find that GP mutations often correspond to large moves within the space of decision matrices. This strengthens evidence that the role of mutations within GP might be somewhat different than their role within Genetic Algorithms.
KeywordsGenetic programming Genotype-phenotype mapping
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- 1.Allen, S., Burke, E.K., Hyde, M.R., Kendall, G.: Evolving reusable 3D packing heuristics with genetic programming. In: Proceedings of the ACM Genetic and Evolutionary Computation Conference (GECCO 2009), Montreal, Canada, pp. 931–938 (July 2009)Google Scholar
- 3.Burke, E.K., Hyde, M.R., Kendall, G.: Providing a memory mechanism to enhance the evolutionary design of heuristics. In: Proceedings of the IEEE World Congress on Computational Intelligence (WCCI 2010), Spain, pp. 3883–3890 (July 2010)Google Scholar
- 6.Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: Automatic heuristic generation with genetic programming: Evolving a jack-of-all-trades or a master of one. In: Proceedings of the 9th ACM Genetic and Evolutionary Computation Conference (GECCO 2007), London, UK, pp. 1559–1565 (July 2007)Google Scholar
- 7.Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: The scalability of evolved on line bin packing heuristics. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2007), Singapore, pp. 2530–2537 (September 2007)Google Scholar
- 10.Fukunaga, A.S.: Automated discovery of local search heuristics for satisfiability testing. Evolutionary Computation 16(1), 31–61 (2008)Google Scholar
- 15.McPhee, N.F., Miller, J.D.: Accurate replication in genetic programming. In: Eshelman, L. (ed.) Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA 1995), July 15-19, pp. 303–309. Morgan Kaufmann, Pittsburgh (1995)Google Scholar
- 17.Poli, R., Langdon, W.B., McPhee, N.F.: A field guide to genetic programming. lulu.com, freely available at (2008), http://www.gp-field-guide.org.uk
- 18.Soule, T., Foster, J.A.: Removal bias: a new cause of code growth in tree based evolutionary programming. In: 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, USA, May 5-9, pp. 781–786 (1998)Google Scholar