This question is related to the subject "Artificial Intelligence" for BS(CS)-- code: CS401

Q- I was studying Local Beam Search in which the book said :

"Local Beam Search begins with k randomly generated states. At each step, all the successors of all k states are generated. If any one is a goal, the algorithm halts. Otherwise, it selects the k best successors from the complete list and repeats."

I understood it and then the book said that:

"In its simplest form, local beam search can suffer from a lack of diversity among the k statesthey can quickly become concentrated in a small region of the state space, making the search little more than an expensive version of hill climbing. A variant called stochastic beam search, analogous to stochastic hill climbing, helps alleviate this problem."

I understood that as well but then the book explained the following about Stochastic beam search that I could not understand:

"Instead of choosing the best k from the the pool of candidate successors, stochastic beam search chooses k successors at random, with the probability of choosing a given successor being an increasing function of its value. Stochastic beam search bears some resemblance to the process of natural selection, whereby the successors (offspring) of a state (organism) populate the next generation according to its value (fitness).

Please help me understand the lines especially marked in BOLD and ITALICS. And please answer only if you are totally sure about it, because this is too much important for me. I shall highly appreciate your help.

Note; I am studying the book--> Artificial Intelligence, a modern approach (3rd edition ,chapter- 4, page 125-126. Topic: Local Beam Search)