data visualization is the process of transforming data, information, and knowledge into visual form, making use of humans’ natural visual capabilities which reveals relationships in data sets that are not evident from the raw data, by using mathematical techniques to reduce the number of dimensions in the data set while preserving the relevant inherent properties. in this paper, we formulated d...

Data visualization is the process of transforming data, information, and knowledge into visual form, making use of humans’ natural visual capabilities which reveals relationships in data sets that are not evident from the raw data, by using mathematical techniques to reduce the number of dimensions in the data set while preserving the relevant inherent properties. In this paper, we formulated d...

An instance of the quadratic assignment problem (QAP) with cost matrix Q is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix C such that for each assignment, the QAP and LAP objective function values are identical. The QAP linearization problem can be solved in O(n) time. However, for the special cases of Koopmans-Beckmann QAP and the m...

Quadratic Assignment Problem (QAP) is an NPhard combinatorial optimization problem, therefore, solving the QAP requires applying one or more of the meta-heuristic algorithms. This paper presents a comparative study between Meta-heuristic algorithms: Genetic Algorithm, Tabu Search, and Simulated annealing for solving a real-life (QAP) and analyze their performance in terms of both runtime effici...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadra...

assigning facilities to locations is one of the important problems, which significantly is influence in transportation cost reduction. in this study, we solve quadratic assignment problem (qap), using a meta-heuristic algorithm with deterministic tasks and equality in facilities and location number. it should be noted that any facility must be assign to only one location. in this paper, first o...

It was recently demonstrated that a well-known eigenvalue bound for the Quadratic Assignment Problem (QAP) actually corresponds to a semideenite programming (SDP) relaxation. However, for this bound to be computationally useful the assignment constraints of the QAP must rst be eliminated, and the bound then applied to a lower-dimensional problem. The resulting \projected eigenvalue bound" is on...

In this paper, we consider partial Lagrangian relaxations of continuous quadratic formulations of the Quadratic Assignment Problem (QAP) where the assignment constraints are not relaxed. These relaxations are a theoretical limit for semidefinite relaxations of the QAP using any linearized quadratic equalities made from the assignment constraints. Using this framework, we survey and compare stan...

Semidefinite programming (SDP) bounds for the quadratic assignment problem (QAP) were introduced in: [Q. Zhao, S.E. Karisch, F. Rendl, and H. Wolkowicz. Semidefinite Programming Relaxations for the Quadratic Assignment Problem. Journal of Combinatorial Optimization, 2, 71–109, 1998.] Empirically, these bounds are often quite good in practice, but computationally demanding, even for relatively s...

We consider special cases of the quadratic assignment problem (QAP) that are linearizable in the sense of Bookhold. We provide combinatorial characterizations of the linearizable instances of the weighted feedback arc set QAP, and of the linearizable instances of the traveling salesman QAP. As a by-product, this yields a new well-solvable special case of the weighted feedback arc set problem.