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An analysis of the genetic marker diversity algorithm for genetic programming

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Abstract

Many diversity techniques have been developed for addressing premature convergence, which is a serious problem that stifles the search effectiveness of evolutionary algorithms. However, approaches that aim to avoid premature convergence can often take longer to discover a solution. The Genetic Marker Diversity algorithm is a new technique that has been shown to find solutions significantly faster than other approaches while maintaining diversity in genetic programming. This study provides a more in-depth analysis of the search behavior of this technique compared to other state-of-the-art methods, as well as a comparison of the performance of these techniques on a larger and more modern set of test problems.

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Notes

  1. https://cs.gmu.edu/~sean/papers/gecco12benchmarks3.

  2. https://github.com/burks-pub/gecco2015.

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Acknowledgments

This work was supported in part by Michigan State University through computational resources provided by the Institute for Cyber-Enabled Research.

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Correspondence to Armand R. Burks.

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This material is based in part upon work supported by the National Science Foundation under Cooperative Agreement No. DBI-0939454. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Appendix: Listing of detailed results tables

Appendix: Listing of detailed results tables

This section lists the detailed results in table form for each metric discussed in Sect. 4. Table 14 shows the success rates of each algorithm on every problem in the test suite, and Tables 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 show the mean value of the given metric for each method across all 100 independent trials for each problem in the test suite.

Table 14 Success rates: percentage of trials in which a solution was found in each method across the test suite
Table 15 Convergence to solution: mean number of fitness evaluations taken to find a solution in the successful trials for each method for each problem in the test suite
Table 16 Max. genetic marker density \({L}_{1:2}\): mean maximum genetic marker density (of genetic markers composed of levels 1 and 2 in the trees) in the final population after 250,000 fitness evaluations for each method in each problem
Table 17 Max. genetic marker density \({L}_{2:3}\): mean maximum genetic marker density (of genetic markers composed of levels 2 and 3 in the trees) in the final population after 250,000 fitness evaluations for each method in each problem
Table 18 Max. genetic marker density \({L}_{3:4}\): mean maximum genetic marker density (of genetic markers composed of levels 3 and 4 in the trees) in the final population after 250,000 fitness evaluations for each method in each problem
Table 19 Max. genetic marker density \({L}_{4:5}\): mean maximum genetic marker density (of genetic markers composed of levels 4 and 5 in the trees) in the final population after 250,000 fitness evaluations for each method in each problem
Table 20 Max. genetic marker density \({L}_{5:6}\): mean maximum genetic marker density (of genetic markers composed of levels 5 and 6 in the trees) in the final population after 250,000 fitness evaluations for each method in each problem
Table 21 Behavioral diversity: mean behavioral diversity of the final population after 250,000 fitness evaluations for each method in each problem
Table 22 Total behavior groups: mean maximum number of groups of same-behavior individuals in the final population after 250,000 fitness evaluations for each method in each problem
Table 23 Mean max behavior group size: mean size of the largest group of same-behavior individuals in the final population after 250,000 fitness evaluations for each method in each problem, with a population size of 500
Table 24 Total unique fitness values: Mean total number of unique fitness values in the final population after 250,000 fitness evaluations for each method in each problem, with a population size of 500
Table 25 Fitness standard deviation: mean of the fitness standard deviation in the final population after 250,000 fitness evaluations for each method in each problem, where fitness ranges from 0 to 1

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Burks, A.R., Punch, W.F. An analysis of the genetic marker diversity algorithm for genetic programming. Genet Program Evolvable Mach 18, 213–245 (2017). https://doi.org/10.1007/s10710-016-9281-9

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