We show that a well-known linearization technique initially proposed for quadratic assignment problems can be generalized to a broader class of quadratic 0-1 mixed-integer problems subject to assignment constraints. The resulting linearized formulation is more compact and tighter than that obtained with a more usual linearization technique. We discuss the application of the compact linearizatio...

Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large...

We investigate special cases of the quadratic assignment problem (QAP) where one of the two underlying matrices carries a simple block structure. For the special case where the second underlying matrix is a monotone anti-Monge matrix, we derive a polynomial time result for a certain class of cut problems. For the special case where the second underlying matrix is a product matrix, we identify t...

The article addresses morphological approaches to design of modular systems. The following methods are briefly described: (i) basic version of morphological analysis (MA), (ii) modification of MA as method of closeness to ideal point(s), (iii) reducing of MA to linear programming, (iv) multiple choice problem, (v) quadratic assignment problem, (vi) Pareto-based MA (i.e., revelation of Pareto-ef...

Smart phone and tablet usage has sharply increased for the last decade. While entering test on these devices, virtual keyboards are generally used instead of conventional hardware keyboards. In this study, a new problem which is two-finger keyboard layout problem and solution approach is presented for increasing user test entrance performance, especially on virtual keyboards. Defined two-finger...

We apply the level-3 Reformulation Linearization Technique (RLT3) to the Quadratic Assignment Problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm, based on this RLT3 formulation. This algorithm is not guaranteed to calculate the RLT3 lower bound exactly, but approximates it very closely and reaches it in some instances. For Nugent problem...

In this study, we present a new tabu search algorithm for the quadratic assignment problem (QAP) that utilizes an embedded neighborhood construction called an ejection chain. Our ejection chain approach provides a combinatorial leverage effect, where the size of the neighborhood grows multiplicatively while the effort of finding a best move in the neighborhood grows only additively. Our results...

We report on the development of algorithms for solving the Quadratic 3-dimensional Assignment Problem (Q3AP). The application is a hybrid ARQ scheme for enriching diversity among multiple packet transmissions by optimizing the mapping of transmission symbols to data. Our current exact algorithm, based on a reformulation linearization technique, solves Q3AP instances of size 13 or smaller. Our f...

We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A,B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along row...

1. Abstract The paper describes a novel technique that allows to reduce by half the number of delta values that were required to be computed with complexity O(N) in most of the heuristics for the quadratic assignment problem. Using the correlation between the old and new delta values, obtained in this work, a new formula of complexity O(1) is proposed. Found result leads up to 25% performance i...