Quadratic Assignment Problem     > QAPLIB - A Quadratic Assignment Problem Library     > Freeware           The Quadratic Assignment Problem (QAP) is one of the most challenging combinatorial optimization problems. We want to assign n facilities to n locations with the cost being proportional to the flow between the facilities multiplied by the distances between the locations, plus eventually costs for placing the facilities at their respective locations. The objective is to allocate each facility to a location such that the total cost is minimized.           Mathematical model:     We are given three n x n matrices: the flow matrix A=(aij), the distance matrix B=(bkl) and matrix C=(cik), where cik is the cost of placing facility i at location k. Let:       1  if facility i is assigned to location j, xij =     0  otherwise     QAP can be modeled as:      min  n  ∑    i = 1  n  ∑    j = 1  n  ∑    k = 1  n  ∑    l = 1  aikbjlxijxkl   +  n  ∑    i = 1  n  ∑    j = 1  cijxij   s.t.        n  ∑    j = 1  xij = 1      (i = 1,2,...n),                 n  ∑    i = 1  xij = 1      (j = 1,2,...n),                  xij {0,1}     (i, j = 1,2,...n)              To get more, read the Introduction