What search method is useful when specifying a number of trials greater than the number of points in the feasible space?

The most suitable search method when specifying a number of trials greater than the number of points in the feasible space is random search. This approach does not limit itself to a structured grid or predetermined paths through the parameter space; rather, it randomly samples parameter values. This characteristic allows for effective exploration, especially in scenarios where the parameter space is vast or complex, and the number of unique configurations (points) is limited.

When trials exceed the number of points in the feasible space, random search can utilize those extra trials to sample the space more thoroughly, potentially discovering optimal configurations that a more systematic search, like grid search, might miss. Grid search operates by evaluating every combination of parameters across a predefined grid, which is computationally expensive as the dimensionality increases and can become infeasible when the number of trials is significantly larger than the number of unique parameter vectors available.

Some other methods, like Bayesian optimization, also rely on a probabilistic approach to search the space but typically focus on exploiting known data to identify promising regions rather than utilizing random sampling across all dimensions. Evolutionary search utilizes strategies inspired by natural selection, like mutation and crossover, but may also lean toward broader sampling strategies when managing high-dimensional spaces.

Overall, random search's inherent flexibility and capacity for