Ant Colony Optimization for Quadratic Assignment Problem

THE quadratic assignement problem (QAP) can be described as an optimizing the assignment a set of facilities to a set of locations with given costs between the locations and given flows between the facilities in order to minimize the sum of the product between flows and distances. A concrete example, would be a hospital planning optimization the location of various medical facilities in order to minimize the overall travel distance of patients inside the hospital. Formally, given n facilities and n locations, two n × n matrices, A = [aij ] and B = [brs], where aij is the distance between locations i and j and brs is the flow between facilities r and s, the QAP can be stated as follows: