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Leif Peterson - Dec 12, 2021
We have been studying quasi-random number sequences over the last year, and have successfully been able to generate numerous types of random numbers, including Halton sequences, low-discrepancy recursive numbers, multi-dimensional Sobol sequences, and linear congruential-based pseudo-random numbers.  Below is a plot of n=4999 random numbers from each generator. 
Swarm intelligence (derivative-free particle swarm optimization) was used to minimize several complex 2D functions which have multiple local minima and one global minimum.  The image below shows the complex functions which were employed for minimization.
Preliminary results indicate that the 2D whitened quasi-random Sobol numbers outperform Sobol numbers and whitened linear congruential-based pseudo-random numbers, as shown in the plot below.