We investigate a polytope (the QAP-Polytope) beyond a \natural" integer programming formulation of the Quadratic Assignment Problem (QAP) that has been used successfully in order to compute good lower bounds for the QAP in the very recent years. We present basic structural properties of the QAP-Polytope, partially independently also obtained by Rijal (1995). The main original contribution of th...

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...

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...

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...

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...

This paper presents a simple, yet effective method of enhancing the inherent diversity among packet retransmissions in digital communication systems that employ high-order modulations such as M -PSK and M -QAM through frequency-selective channels. Diversity is enhanced by uniquely redefining the bitto-symbol mapping for each retransmission. Finding the optimal mappings leads to iterative soluti...