Min objective and function evaluations

As I was learning to optimize regression tree, I'm struggling to understand some of the codes and graphs generated in the matlab example ' Optimize Regression Tree'

https://uk.mathworks.com/help/stats/fitrtree.html

load carsmall
X = [Weight,Horsepower];
Y = MPG;
rng default
Mdl = fitrtree(X,Y,'OptimizeHyperparameters','auto',...
    'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName',...
    'expected-improvement-plus'))

As you can see from the above code, they set the 'OptimizeHyperparameters' to 'auto', they struct 'AcquisitionFunctionName' to 'expected-improvement-plus', they also put 'HyperparameterOptimizationOptions' in the bracket.

My first question is that i'm not familiar with all the parameters I could put here, is there a list of those parameters out there for me to familiarize with all the properties I could put in the bracket?

Once you type the above code, the outputs are two graphs shown below.

My second question is that in the first graph, what does 'Min objective' mean? What does 'Number of function Evaluations' mean?

Answer 1

[Don Mathis]

Question 1: https://www.mathworks.com/help/stats/fitrtree.html#bt6cr84_sep_shared-HyperparameterOptimizationOptions

Question 2: As mentioned in the link for Question 1, it's using the 'bayesopt' function. Start here: https://www.mathworks.com/help/stats/bayesopt.html