Glover and Punnen (1997) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!=p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P=NP, the answer to this question is negative. We prove that the answer to this question is, in fact, positive. A generalization of the TSP, the quadra...

The quadratic assignment problem aims to find an optimal assignment of a set of facilities to a set of locations that minimizes an objective function depending on the flow between facilities and the distance between locations. In this paper we investigate a Genetic Algorithm (GA) using new crossover operators to guide the search towards unexplored regions of the search space. First we define a ...

Since crossover operator plays a vital role in genetic algorithms (GAs), several crossover operators have been proposed for the travelling salesman problem, which are then modified for the quadratic assignment problem (QAP). In this paper, we modify the sequential constructive crossover (SCX) operator for a simple GA to find heuristic solution to the QAP. Efficiency of the proposed GA using SCX...

Tabu search (TS) algorithms are among the most efficient heuristic techniques in combinatorial optimization. Within these algorithms, it is important that the proper policies for maintaining the tabu tenure (tabu list size) are applied. In this paper, we discuss the mechanisms of defining the tabu tenure for the famous combinatorial optimization problem − the quadratic assignment problem (QAP)....

On-line parameter adaptation schemes are widely used in metaheuristics. They are sometimes preferred to off-line tuning techniques for two main reasons. First, they promise to achieve good performance even on new instance families that have not been considered during the design or the tuning phase of the algorithm. Second, it is assumed that an on-line scheme could adapt the algorithm’s behavio...

A typical example of the quadratic assignment problem (QAP) is the facility location problem, in which a set of n facilities are to be assigned, at minimum cost, to an equal number of locations. Between each pair of facilities, there is a given amount of flow, contributing a cost equal to the product of the flow and the distance between locations to which the facilities are assigned. Proving op...

In this work we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two differe...