Abstract
We report what we believe to be the first comparative study of multi-objective genetic programming (GP) algorithms on benchmark symbolic regression and machine learning problems. We compare the Strength Pareto Evolutionary Algorithm (SPEA2), the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Pareto Converging Genetic Algorithm (PCGA) evolutionary paradigms. As well as comparing the quality of the final solutions, we also examine the speed of convergence of the three evolutionary algorithms. Based on our observations, the SPEA2-based algorithm appears to have problems controlling tree bloat—that is, the uncontrolled growth in the size of the chromosomal tree structures. The NSGA-II-based algorithm on the other hand seems to experience difficulties in locating low error solutions. Overall, the PCGA-based algorithm gives solutions with the lowest errors and the lowest mean complexity.
Similar content being viewed by others
References
Alpaydin E (1999) Combined 5 × 2 cv F-test for comparing supervised classification learning algorithms. Neural Comput 11: 1885–1892
Bleuler S, Brack M, Theile L, Zitzler E (2001) Multiobjective genetic programming: reducing bloat using SPEA2. In: Proceedings of congress on evolutionary computation. Seoul, Korea
Chellapilla K (1997) Evolving computer programs without subtree crossover. IEEE Trans Evol Comput 1: 209–216
Coello CAC, van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multiobjective problems. Kluwer, New York
Daida JM, Li H, Tang R, Hilss AM (2003) What makes a problem GP-hard? Validating a hypothesis of structural causes. In: Lecture notes in computer science, vol 2724. Springer, Heidelberg, pp 1665–1677
Deb K, Pratap A, Agarawal S, Meyarivan T (2003) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6: 182–197
Dietterich T (1998) Approximate statistical tests for comparing supervised classification learning algorithms. Neural Comput 10: 1895–1923
Ekárt A, Németh SZ (2001) Selection based on the Pareto nondomination criterion for controlling code growth in genetic programming. Genet Program Evolvable Mach 2: 61–73
Ito T, Iba H, Sato S (1998) Non-destructive depth-dependent crossover for genetic programming. In: First European Workshop on Genetic Programming
Jaszkiewicz A (2002) Genetic local search for multi-objective combinatorial optimization. Eur J Oper Res 137: 50–71
Koza JR (1994) Genetic programming II: automatic discovery of reusable programs. MIT, Cambridge
Kumar R, Rockett PI (2002) Improved sampling of the Pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm. Evol Comput 10: 283–314
Lim T S, Loh W Y, Shih Y S (2000) A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms. Mach Learn 40: 203–228
Rodríguez-Vázquez K, Fonseca CM, Fleming PJ (2004) Identifying the structure of non-linear dynamic systems using multiobjective genetic programming. IEEE Trans Syst, Man Cybernetics—Part A: Syst Hum 34: 531–547
Vapnik VN (2000) The Nature of statistical learning theory. Springer, New York
Zhang Y (2006) Multiobjective genetic programming optimal search for feature extraction. PhD Thesis, University of Sheffield
Zhang Y, Rockett PI (2005), Evolving optimal feature extraction using multi-objective genetic programming: a methodology and preliminary study on edge detection. In: GECCO 2005. Washington, DC
Zhang Y, Rockett PI (2006) Feature extraction using multi-objective genetic programming. In: Jin Y (eds) (ed) Multi-objective machine learning.. Springer, Heidelberg
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3: 257–271
Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8: 173–195
Zitzler E, Thiele L, Laumanns M, Fonseca CM, da Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans on Evol Comput 7: 117–132
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, Y., Rockett, P. A Comparison of three evolutionary strategies for multiobjective genetic programming. Artif Intell Rev 27, 149–163 (2007). https://doi.org/10.1007/s10462-008-9093-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-008-9093-2