Learning to Describe Collective Search Behavior of Evolutionary Algorithms in Solution Space
Evolutionary algorithms (EAs) are a kind of population-based meta-heuristic optimization methods, which have proven to have superiorities in solving NP-complete and NP-hard optimization problems. But until now, there is lacking in the researches of effective representation method to describe the collective search behavior of the Evolutionary Algorithm, while it is useful for researchers and engineers to understand and compare different EAs better. In the past, most of the theoretical researches cannot directly guide for practical applications. To bridge the gap between theoretical research and practice, we present a generic and reusable framework for learning features to describe collective behavior of EAs in this paper. Firstly, we represent the collective behavior of EAs with a parent-child difference of population distribution encoded by self-organizing map (SOM). Then, we train a Convolutional Neural Network (CNN) to learn problem-invariant features from the samples of EAs’ collective behavior. Lastly, experiment results demonstrate that our framework can effectively learn discriminative features representing collective behavior of EAs. In the behavioral feature space stretched by the obtained features, the collective behavior samples of various EAs on various testing problems exhibit obvious aggregations that highly correlated with EAs but very weakly related to testing problems. We believe that the learned features are meaningful in analyzing EAs, i.e. it can be used to measure the similarity of EAs according to their inner behavior in solution space, and further guide in selecting an appropriate combination of sub-algorithm of a hybrid algorithm according to the diversity of candidate sub-algorithm instead of blind.
KeywordsEvolutionary algorithms Collective behavior Representation learning Convolutional neural network Self-organizing map
The work is supported by the National Natural Science Foundation of China under grand No. 61473271 and No. 61331015.
- 2.Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1097–1105 (2012)Google Scholar
- 3.Turkey, M., Poli, R.: An empirical tool for analysing the collective behaviour of population-based algorithms. In: Di Chio, C., Agapitos, A., Cagnoni, S., Cotta, C., de Vega, F.F., Di Caro, G.A., Drechsler, R., Ekárt, A., Esparcia-Alcázar, A.I., Farooq, M., Langdon, W.B., Merelo-Guervós, J.J., Preuss, M., Richter, H., Silva, S., Simões, A., Squillero, G., Tarantino, E., Tettamanzi, A.G.B., Togelius, J., Urquhart, N., Uyar, A.Ş., Yannakakis, G.N. (eds.) EvoApplications 2012. LNCS, vol. 7248, pp. 103–113. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29178-4_11 CrossRefGoogle Scholar
- 5.Collins, T.: The application of software visualization technology to evolutionary computation. In: A case study in genetic algorithms. Dissertation, The Open University (1998)Google Scholar
- 7.Pang, C., Wang, M., Liu, W., Li, B.: Learning features for discriminative behavior analysis of evolutionary algorithms via slow feature analysis. In: Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion, pp. 1437–1444. ACM, July 2016Google Scholar
- 11.Tang, K., Li, X., Suganthan, P.N., Yang, Z., Weise, T.: Benchmark functions for the CEC 2008 special session and competition on large scale global optimization. Nat. Inspired Comput. Appl. Lab. (2009)Google Scholar
- 12.Duch, W., Naud, A.: Multidimensional scaling and Kohonen’s self-organizing maps. In: Proceedings of 2nd Conference on “Eural Networks and Their Applications”, Szczyrk, Poland, pp. 138–143 April 1996Google Scholar
- 15.Berkes, P.: Pattern recognition with slow feature analysis. Comput. Neurosci. (2005)Google Scholar
- 16.Glorot, X., Bordes, A., Bengio, Y.: Deep sparse rectifier neural networks. In: AISTATS, vol. 15, p. 275 April 2011Google Scholar
- 18.Girshick, R., Donahue, J., Darrell, T., Malik, J.: Rich feature hierarchies for accurate object detection and semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 580–587 (2014)Google Scholar