This chapter proposes a combination of estimation of distribution algorithm (EDA) and the 2-opt local search algorithm (EDA/LS) for the quadratic assignment problem (QAP). In EDA/LS, a new operator, called guided mutation, is employed for generating new solutions. This operator uses both global statistical information collected from the previous search and the location information of solutions ...

This paper introduces a new path relinking algorithm for the well-known quadratic assignment problem (QAP) in combinatorial optimization. The QAP has attracted considerable attention in research because of its complexity and its applicability to many domains. The algorithm presented in this study employs path relinking as a solution combination method incorporating a multistart tabu search algo...

The quadratic assignment problem (QAP ) is arguably one of the hardest of the NP-hard discrete optimization problems. Problems of dimension greater than 20 are considered to be large scale. Current successful solution techniques depend on branch and bound methods. However, it is difficult to get strong and inexpensive bounds. In this paper we introduce a new semidefinite programming (SDP ) rela...

We describe a branch-and-bound algorithm for the quadratic assignment problem (QAP) that uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The QP subproblems are approximately solved using the Frank-Wolfe algorithm, which in this case requires the solution of a linear assignment problem on each iteration. Our branching strategy makes extensive use of dual infor...

The quadratic assignment problem (QAP) is one of the great challenges in combinatorial optimization. Linearization for QAP is to transform the quadratic objective function into a linear one. Numerous QAP linearizations have been proposed, most of which yield mixed integer linear programs (MILP). Kauffmann and Broeckx’s linearization (KBL) is the current smallest one in terms of the number of va...

In this paper we present an algorithm for generating quadratic assignment problem (QAP) instances with known provably optimal solution. The flow matrix of such instances is constructed from the matrices corresponding to special graphs whose size may reach the dimension of the problem. In this respect, the algorithm generalizes some existing algorithms based on the iterative selection of triangl...

The goal of this paper is to discuss the tabu search (TS) meta-heuristic and its enhancement for combinatorial optimization problems. Firstly, the issues related to the principles and specific features of the standard TS are concerned. Further, a promising extension to the classical tabu search scheme is introduced. The most important component of this extension is a special kind of diversifica...

The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P . Surprisingly, the QAP has not b...

This article introduces a new method for statistically comparing pairs of aggregate data series. Aggregate data series refers to a set of values, each of which is averaged or otherwise aggregated across respondents. Themotivating problem is the comparison of aggregate proximity matrices, such as those obtained from pile sort exercises. The standard approach to this problem uses the nonparametri...

The graph edit distance (GED) is a flexible and widely used dissimilarity measure between graphs. Computing the GED between two graphs can be performed by solving a quadratic assignment problem (QAP). However, the problem is NP complete hence forbidding the computation of the optimal GED on large graphs. To tackle this drawback, recent heuristics are based on a linear approximation of the initi...