Although the algorithmic problem is very generic in nature and there are many (possibly more down to earth) examples of its application, I do not want to suppress the real context of my problem.
I have a large table (matrix) that for a defining polynomial contains a column with the corresponding class number and it contains many (hundreds of) columns with the coefficients of their Dedekind zeta functions (let's call them shortly "zeta coefficients").
A very small section of this table is shown below:
\begin{array}{|c|c|c|c|c|c|c|c|} \hline \small\text{polynomial} & \small\text{class num} & \small\text{zeta coeff 1} & \small\text{zeta coeff 2} & \small\text{zeta coeff 3} & \small\text{zeta coeff 4} & \small\text{zeta coeff 5} & \small\text{zeta coeff 7}\\ \hline \small{x^2-x-1} & 1 & 1 & 0 & 0 & 1 & 1 & 0\\ \hline \small{x^2 - x - 8} & 1 & 1 & 2 & 1 & 3 & 0 & 0\\ \hline \small{x^2 - x - 15} & 1 & 1 & 0 & 2 & 1 & 2 & 0\\ \hline \small{x^2 - 15} & 2 & 1 & 1 & 1 & 1 & 1 & 2 \\ \hline \small{x^2 - x - 16} & 2 & 1 & 2 & 0 & 3 & 1 & 2\\ \hline \small{x^2 - 10} & 2 & 1 & 1 & 2 & 1 & 1 & 0\\ \hline \small{x^2 - x - 327} & 2 & 1 & 0 & 2 & 1 & 2 & 1\\ \hline \end{array}
For the sake of simplicity, we assume that the class number column only contains values $1$ and $2$.
Now I am trying to pick out a triple of zeta coefficients $(\text{zeta coeff}\ \textbf{i},\text{zeta coeff}\ \textbf{j},\text{zeta coeff}\ \textbf{k})$ such that in the ideal case (which obviously will hardly occur) no polynomials of different class number possess the same coefficient values. And if (unfortunately) it does, this overlap should be as small as possible. Hence we are dealing with a kind of minimization algorithm.
For example, a very unfortunate choice is the triple $(\text{zeta coeff}\ \textbf{1},\text{zeta coeff}\ \textbf{2},\text{zeta coeff}\ \textbf{4})$, since it provides two collisions: The polynomials $x^2-x-1$ and $x^2-x-327$ of different class number share the triple $(1,0,1)$ and the polynomials $x^2-x-8$ and $x^2-x-16$ also have a different class number but share the triple $(1,2,3)$.
Now let's choose an example of success: The choice of the triple $(\text{zeta coeff}\ \textbf{2},\text{zeta coeff}\ \textbf{4},\text{zeta coeff}\ \textbf{7})$ is a very good one. In our example no polynomials that have a different class number share these three zeta coefficients.
Note: The original table contains hundred thousands of rows and thousand coefficients, which makes a brute force impossible for searching our collision-free triples.
I am very aware that such a minimization algorithm certainly makes sense in various contexts and is also applied there; and I offer a very exotic case here. Nevertheless, I would already be very grateful for a hint where to look for. I'm not asking for a ready-made solution here - a hint on which keywords to research is quite enough.