Comparison of Two Interval Models for Interval-Valued Differential Evolution

Authors: Hidehiko Okada

Abstract:

The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks. 

Keywords: Evolutionary algorithms, differential evolution, neural network, neuroevolution, interval arithmetic.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088292

References:

[1] R. Storn and K. Price, Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, Vol.11, No.4, pp.341-359, 1997.
[2] T. Bäck, Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford Univ. Press, 1996.
[3] H. Okada, Proposal of fuzzy evolutionary algorithms for fuzzy-valued genotypes, Proc. of Int. Conf. on Instrumentation, Control, Information Technology and System Integration (SICE Annual Conference) 2012, pp.1538-1541, 2012.
[4] H. Ishibuchi, H. Tanaka and H. Okada, An architecture of neural networks with interval weights and its application to fuzzy regression analysis, Fuzzy Sets and Systems, Vol.57, No.1, pp.27-39, 1993.
[5] H. Okada: Interval-valued differential evolution for evolving neural networks with interval weights and biases, Proc. of the 6th International Workshop on Computational Intelligence & Applications (IWCIA2013), pp.81-84, 2013.
[6] G. Alefeld and J. Herzberger, Introduction to Interval Computation, Academic Press, 1983.