I have an assignment problem. So typically I need to find the optimal combination between two sets of parameters P, M. I know that the Hungarian Algorithm is often privileged for this kind of problem but there is few key points making this technique probably not well appropriated.
My matrix is not really a cost matrix. It contains values evaluated for each combination of my two parameters. It does not represent a cost but a normalized distance. The minimal or maximal distance does not represent an optimal value.
My objective is the minimization of the standard deviation. So I want to find the combination of Pi,mi minimizing the standard deviation of their values. i.e. the minimal standard deviation of the distances.
Hungarian algorithm work with squared matrix and I would like a technique working on m*n matrix. ( it is not a strong constraint for me)
The matrix size will not exceed 10*10 and most of the pairs can be already associated. (i.e. other criteria indicates that distance value is 0 or out of bounds leading to a single P,M combination). But I would like the find the solution in the worst case: None of the pairs are formed.
What kind of technique could you recommend ?
Thank you very much for your help.