Sure, but my question is what does evolution try? If it is full random, then it will TRY much better and much worse mutations as well, so will go back and forth, and will take a lot of time. If it is not fully random, e.g. it is not not able to try big changes, then what is the thing that actually determines what is "feasible", BEFORE trying it out.

IIRC, the rate is somewhat dynamic.

That said, my experiments in silico say that what matters most is the pressure from the utility function, more so than the rate of mutation.

So if some organism is in an environment where only a few mutations help, then evolution progresses slowly; and when most possible changes are improvements, then evolution progresses faster.

Both environments can happen even without any dynamic change to the rate of mutations themselves.

Environment. You seem to be missing the "natural selection" part of evolution. The optimization process works like this:

- Life reproduces; between imperfections in reproduction and environmental mutagenic factors, there is a certain amount of random mutations;

- The churn happens. Organisms compete for resources; winners reproduce, losers starve. Environment throws curveballs - spills, seasons, volcanos, radiation, oxygen, and a million different things. A lot of organisms are killed, some survive and reproduce. Now, mutations can make organisms better or worse at surviving the challenges. This is the asymmetry you're looking for, the driver of evolution. Helpful mutations propagate, unhelpful mutations die. Where "helpful" means, of course, "helpful locally, at a given moment".

Rinse and repeat. The randomness isn't the driver - it's just jitter preventing evolution from getting stuck in a local minimum. The life cycle of birth and death is what drives evolution, specifically because it depends on both how the organism is built, and on the environment.

Full random. Something like 50% of human babies have random mutations which make them unable to develop past the stage of being invisible to the naked eye. Such miscarriages seem like normal menstruation.

There's a knack to optimizing the mutation rate. If you mutate too much, 99.9999% of offspring can't develop and in the end there's too little reproduction. If you don't mutate enough, you don't evolve. Evolution has already optimized this hyperparameter.

It will try much better and much worse, those that are much better will produce a lot of offspring while those that are a lot worse will produce few to none, and so in the next generation there will be a lot more starting from "much better" than "much worse."