dear friend,i believe that a branch and bound technique would not be ideal(even simple to implement),I believe that you can you use an A* algorith,and try to think a good (and robust) heuristic function,albeit the inherent combinatorial explotion can be attacked quite efficiently(it is highly dependent on you evaluation function). Another idea is to use a simple technique inspired by physics which is called simulatead annealing(it belongs in the class of hill climbing/gradient descent strategy),which can give quite good results.However in theory to find an global optimum is NP-hard,in practice it can give you good results. I have also some other ideas,that i am going to write in time,i believe that you attack your problem via not only a cs facet,but also try to imitate and engage strategies inspired by nature such as genetic algorithms,etc be in touch
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