I'm not sure there is a good statistical test for comparing optimization algorithms. Typically there is a trade off between speed and thoroughness. For a simple optimization problem without multiple local max and min points or discontinuities almost any optimization routine will work and a very simple optimization routine will likely get to the correct answer very efficiently. For more complex problems with the actual optimum point far away from easy to reach local optimum a more complex algorithm is required. If all of the algorithms find the correct optimal solution you could say the one that got there the fastest was the best or you could say they were all equal as long as they all got to the correct optimum point in an acceptable amount of time.
The best choice of optimization algorithm is highly dependent on the optimization problem it is asked to solve.
It depends a lot on the distribution of your variable.
First of all you must to know what is the best fit in the known distributions.
If it behavior is normal-like, ANOVA can be used, and Turkey in sequence to find out where is the difference and how big is it.
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