In general, "machine learning" means that an algorithm did it, and that the algorithm engages in some analysis of the problem space or the solution space. Usually that analysis involves an iterative or repetitive element: making several tries and modeling what makes a try good or bad, making a try and then changing the solution tiny bits to find a try that's slightly better, etc. And "good" or "bad" is determined according to a human-provided rubric (eg: +1000 points for every sight seen, -1 point for every mile driven, -10 points for every day taken, etc.)

Unless the problem is very constrained, there usually is no guarantee of optimality; here there is probably no guarantee of optimality. It might be "locally" optimal, in that there might be no better trip that differs from this one by only a tiny bit.

And, no, "machine learning" here doesn't mean the enterprise and establishment of "Machine Learning", just some algorithm that the author used.

I'm almost certain it was used incorrectly in this case. The correct term is "combinatorial optimization."

And optimal according to what criteria? Length, safety, sightseeing?