Stochastic pretty much means randomization in some way. One of the main problems with finding a ray is that it tends to get stuck in local optima instead of a global optimum. To avoid this stochastic search, it gives some (most often small) probability of deciding on the choice of a step that is not optimal at the moment. You can think of it as "adding randomness." A slightly better approach would be simulated annealing , where the likelihood of making a suboptimal choice decreases over time.
A local search, on the other hand, will always choose the best neighbors of K, not allowing you to deviate from the local optimum if you fall into it.