# Solving an ordered knapsack problem exactly with a non linear (blackbox) evaluation function

Thanks in advance for the help.

I have the following problem which, for lack of a better description, I'm referring to as the problem I've listed in the title.

Specifically I have a knapsack problem where I must exactly fill the knapsack. Additionally, the order in which I place the elements into the knapsack affects the strength of the solution (but not the volume of the individual elements). The function that is used to evaluate the strength, or goodness, of the packing is non linear and very complex. Because of this, I have a model that I will use to repeatedly simulate my evaluation function to get an idea of the strength of each solution rather than directly evaluating my evaluation function (sort of like a surrogate function).

For example, suppose I have a knapsack of size ten. The following would be possible solutions assuming integers are the elements that I can place into the knapsack (for all intents in purposes my actual problem can be visualized in this manner): [5,5], [3,3,4], [4,3,3], etc.

What I'm interested in is two-fold. First, does this problem reduce to any well studied problems from which I could read up more on how they are solved? I'm currently thinking about using some kind of heuristic search to solve this problem, such as a Genetic Algorithm (I don't have to have the optimal solution, though I would like the best that I can get). Second and somewhat related to the first, what work if any has been done on problems that fit the description that I have given above? The knapsack problem is a very well studied problem and I would find it hard to believe if there hasn't been any work done on problems that fit my current one. Unfortunately though, while I've found work somewhat related to my problem, I haven't been able to find anything that directly reduces to my problem.