**Domingo Ortiz-Boyer dortiz@uco.es
César Hervás-Martínez chervas@uco.es
Nicolás García-Pedrajas npedrajas@uco.es
Department of Computing and Numerical Analysis
University of Córdoba, Spain**

In this paper we propose a crossover operator for evolutionary
algorithms with real values that is based on the statistical theory of
population distributions. The operator is based on the theoretical
distribution of the values of the genes of the best individuals in
the population. The proposed operator takes into account the
localization and dispersion features of the best individuals of the
population with the objective that these features would be inherited
by the offspring. Our aim is the optimization of the balance between
exploration and exploitation in the search process.

In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests.

As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods.

- Introduction
- CIXL2 Operator

- Benchmark Problems
- Evolutionary Algorithm
- Structure of the Individual and Population Size
- Selection
- Population Update Model
- Initialization
- Mutation
- Stop Criterion

- Analysis of CIXL2
- Comparative Study of the Crossovers
- Comparison with Estimation of Distribution Algorithms
- Application to Artificial Intelligence

- Conclusions and Future Work
- Results of the Statistical Study
- Convergence Graphics
- Bibliography
- About this document ...