Linear programming insights into solvable cases of the quadratic assignment problem

Quadratic Assignment Problem: Linearizations and Polynomial Time Solvable Cases

The bipartite unconstrained 0-1 quadratic programming problem: polynomially solvable cases

We consider the bipartite unconstrained 0–1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0–1 quadratic programming problem (QP01). BQP01 has numerous applications and the problem is known to be MAX SNPhard.We show that if the rank of an associatedm×n costmatrixQ = (qij) is fixed, then BQP01 can be solved in polynomial time. When Q is of rank ...

Robust Quadratic Assignment Problem with Uncertain Locations

 We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the ...

Equality of complexity classes P and NP: Linear programming formulation of the quadratic assignment problem

In this paper, we present a first linear programming formulation of the Quadratic Assignment Problem (QAP). The proposed linear program is a network flow-based model with 0(n9) variables and 0(n7) constraints, where n is the number of assignments. Hence, it provides for the solution of the QAP in polynomial-time and represents therefore, a proof of the equality of the computational complexity c...

A O(n8)×O(n7) Linear Programming Model of the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is the problem of making exclusive assignments of n indivisible entities to n other indivisible entities in such a way that a total quadratic interaction cost is minimized. The problem can be interpreted from a wide variety of perspectives. The perspective adopted in this paper is that of the generic facilities location/layout context, as in the seminal wo...