CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features

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

Localization transition induced by learning in random searches

We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the resetting rate crosses a threshold above which non-diffusive stationary states emerge, localized around the inhomogeneity. The threshold depends on the trapping strength and on the walker's return probability in the memoryless case. The transition belongs to the same class as the self-consistent theory of Anderson localization. These results show that similarly to many living organisms and unlike the well-studied Markovian walks, non-Markov movement processes can allow agents to learn about their environment and promise to bring adaptive solutions in search tasks.Comment: 5 pages, 5 figures + 4 pages of Supplemental Information. Accepted in Physical Review Letter

The Law of the Minimum and Sources of Nonzero Skewness for Crop Yield Distributions

Crop yields are not commonly found to be normally distributed, but the cause of the non-normal distribution is unclear. The non-normality might be due to weather variables and/or an underlying von Liebig law of the minimum (LoM) production function. Our objective is to determine the degree to which an underlying linear response stochastic plateau production function can explain the skewness of Oklahoma wheat yields at varied nitrogen rates. We use farm-level wheat data from a long-term experiment in Oklahoma, which is a unique data set to the literature. The Tembo et al. (2008) production function provides negative skewness at all levels of nitrogen with skewness near zero for both very high and very low levels of nitrogen. Observed skewness for wheat yields, however, is positive. The variation in the plateau by year shows positive skewness. Skewness in yield potential related to weather should be considered as a possible explanation of skewness.linear plateau model, non-normal distributions, skewness, wheat, yield distribution, Production Economics, Risk and Uncertainty, Q10,