In this paper, we present a simple algorithm to obtain mechanically SDP relaxations for any quadratic or linear program with bivalent variables, starting from an existing linear relaxation of the considered combinatorial problem. A significant advantage of our approach is that we obtain an improvement on the linear relaxation we start from. Moreover, we can take into account all the existing th...

— Using an approach that seems to be patterned after that of Yannakakis, Hofman argues that an NP-complete problem cannot be formulated as a polynomial bounded-sized linear programming problem. He then goes on to propose a " construct " that he claims to be a " counterexample " to recently published linear programming formulations of the Traveling Salesman Problem (TSP) and the Quadratic Assign...

It is often difficult to verify the solutions of computationally intensive mathematical optimization problems. Metamorphic testing is a technique to verify software test output even when a complete testing oracle is not present. We apply metamorphic testing to a classic optimization problem, the quadratic assignment problem (QAP). A number of metamorphic relations for the QAP are described in d...

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 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...

Page 55 line 6: replace " among the matched " with " among the unmatched " ; 229 line 13: replace " Palubeckis [544] " with the following (missing) reference: G. Palubeckis. The use of special graphs for obtaining lower bounds in the geometric quadratic assignment problem. 289 eqn (9.27): replace " s ∈ F " with " S ∈ F " ; 308 line 14: replace " approximation algorithms which yield a feasible s...

A striking characteristic of high-tech products is the rapid decrease of their quality-adjusted prices. Empirical studies show that the rate of decrease of QAPs is typically not constant over time; QAPs decrease rapidly at early stages of the product and then the rate of decrease tapers o®. Studies also suggest that the QAP is positively correlated with the rate of product introductions: The fa...