@RodrigodeAzevedo The order of $a,b,c,d,e$ is what I expected by intuition.

@RodrigodeAzevedo Yes. The search space is so big that we could never know the global minimum. At least the solution looks quite convincing to me.

@RodrigodeAzevedo Yes there are $101^5$ possible functions. I have already managed to found the solution using a genetic algorithm after 500+ generations. Evolutionary algorithm is particularly suitable for this type of multifactorial optimization problem, and it is called "evolutionary multi-tasking"

@RodrigodeAzevedo Yes, the parameters are all integers ranging from 0 to 100, so the parameter space is finite. Btw I have already found the name for this type of optimization problem. It's called "multifactorial optimization" or "multitask optimization".

@LSpice Yes I agree the notation is confusing, but you understand it correctly. I have changed the notation from $f(x,z)$ to a function space $\mathcal{C}(x, z)$. As for $f(x_0,z) \le f(x,z)$, I mean for a given fixed interval $[c,d]$ of $z$, the curve of $f(x_0,z)$ is the lowest, i.e., $x_0$ minimizes $\int_c^d f(x, z) dz$

@BrendanMcKay If there are multiple isomorphisms, then the similarity should average over the similarity w.r.t. each isomorphism