Computational Complexity
The problem is NP-hard, so there is no known algorithm for solving this problem in polynomial time, and even small instances may require long computation time. The Travelling salesman problem may be seen as a special case of QAP if one assumes that the flows connect all facilities only along a single ring, all flows have the same non-zero (constant) value. Many other problems of standard combinatorial optimization problems may be written in this form.
Read more about this topic: Quadratic Assignment Problem
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