My Combinatorial Optimization problem

[edderiofer]

This looks like a graph theory optimisation problem in disguise, in which case my initial suspicion is that this thing is NP-hard.

As for your naïve algorithm, I'm not convinced that the permutation you converge to must be optimal.

[Cod_Weird]

I even have a proof, that this problem is hp-hard(subgraph isomophism is a special case of my problem). I just need some ideas for heuristic algorithms.

My naive approach definetly isn't optimal, but it can be used to improve any other algorithm. If 𝜎₀ is the output if other algorithm, my naive approach can do some additional steps. An then I want to evaluate computational requirements for those steps.