Why do chaotic numbers improve evolutionary algorithms such as genetic algorithm? I have implemented a genetic algorithm to solve a problem. In the process of genetic algorithm, instead of random numbers, I have used the chaotic numbers generated by the logistics map. The genetic algorithm that uses chaotic numbers is more efficient than the genetic algorithm that uses random numbers. Why the use of chaotic numbers improves the efficiency of the genetic algorithm?
 A: A number of papers (1, 2, 3, 4, 5) make the same observation as yours, which is usually explained as (e-print)

The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution.

It has also been claimed that a mix of periodic and chaotic search results in a better search strategy:

the convergent behavior leads to exploitation and the chaotic behavior aids to exploration.

Another paper (arxiv) reported a positive effect of using chaos for generating initial populations only, but not when used as a RNG:

The use of chaotic maps for the generation of the initial populations in the genetic algorithm, increases consider-ably the performance of the algorithm in comparison to the tradition stochastic algorithm.
In  addition,  the  proposed  algorithm  was  also  modified using chaotic maps in the mutation and the population processes.  However, the results obtained using these modifications do not show significant improvement.

This same paper also claims to have found a direct link to entropy:

We found a strong relationship between the entropy of the initial populations and the densities of fitness of the solutions. [...] the chaotic maps with higher entropies show an increase in the fitness’s densities in the areas with better solutions: high entropies generated better solutions.

