How can we conclude that an optimization algorithm is better than another one When we test a new optimization algorithm, what the process that we need to do?For example, do we need to run the algorithm several times, and pick a best performance,i.e., in terms of accuracy, f1 score .etc, and do the same for an old optimization algorithm, or do we need to compute the average performance,i.e.,the average value of accuracy or f1 scores for these runs, to show that it is better than the old optimization algorithm? Because when I read the papers on a new optimization algorithm, I don't know how they calculate the performance and draw the train-loss vs iters curves, because it has random effects, and for different runs we may get different performance and different curves.
See here for a potential way to do it:

http://infinity77.net/global_optimization/#motivation-motivation

http://infinity77.net/global_optimization/#rules-the-rules

You basically test the two (or more) optimization algorithms against known objective functions, with several random (but repeatable) starting points and then analyze the outcome.