Grid Search Optimization

What is grid search optimization?

Grid search is another brute-force optimization algorithm that treats the objective function as a black box and evaluates it on a set of data points just like a random search. Grid search works by dividing the space into a grid and sampling all combinations from that.

Let’s recall the example of the interview process where the task was to find a suitable candidate for a particular role without prescreening. Let’s assume that the objective function $g(x_1, x_2, .., x_m)$ now takes the $m$ inputs—such as CGPA, age, experience, expertise, etc.—and measures the skill difference of the candidate $x$ compared to the desired skills (the lower the objective, the better the candidate).

For each input $x_i$ (for example, CGPA), we will generate $N + 1$ equal distant points in the range $[a_i, b_i]$ (for example, CGPA between 8 and 10, depending upon universities) as follows:

Now, we will evaluate the objective function on the Cartesian product $S = S_1 \times S_2 \times ... \times S_m$, which forms a grid of all possible combinations of the inputs $(x_{}$ ...