Asurvey of the results described in the author’s PhD thesis (Montemanni 2001) is presented. The thesis, which was supervised by Prof. Derek H. Smith and Dr. Stuart M. Allen, has been defended in January 2002 at the University of Glamorgan (U.K.). The thesis proposes new heuristic algorithms, based on well-known metaheuristic paradigms, and new lower bounding techniques, based on linear programm...

the problem of pole assignment, also known as an eigenvalue assignment, in linear discrete-time periodic systems in discs was solved by a novel method which employs elementary similarity operations. the former methods tried to assign the points inside the unit circle while preserving the stability of the discrete time periodic system. nevertheless, now we can obtain the location of eigenvalues ...

this paper introduces a new method for incorporating the performance of alternatives into their ultimate ranking in a linear assignment method. this method is one of multi-criteria decision-making methods, in which the weight of criteria is incorporated in ranking the alternatives, and the distance between the performances of alternatives do not affect in ranking the alternatives. in order to m...

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

Semidefinite relaxations of the quadratic assignment problem (QAP ) have recently turned out to provide good approximations to the optimal value of QAP . We take a systematic look at various conic relaxations of QAP . We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look ...

3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...

— 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...

The Quadratic Assignment Problem (QAP) can be solved by linearization, where one formulates the QAP as a mixed integer linear programming (MILP) problem. On the one hand, most of these linearization are tight, but hardly exploited within a reasonable computing time because of their size. On the other hand, Kaufman and Broeckx formulation [1] is the smallest of these linearizations, but very wea...

In this paper we address the Adjacent Quadratic Assignment Problem (AQAP) which is a variant of the QAP where the cost coefficient matrix has a particular structure. Motivated by strong lower bounds obtained by applying Reformulation Linearization Technique (RLT) to the classical QAP, we propose two special RLT representations for the problem. The first is based on a “flow” formulation whose li...