Search results for "Quadratic assignment problem"
showing 6 items of 6 documents
An Exact Algorithm for the Quadratic Assignment Problem on a Tree
1989
The Tree QAP is a special case of the Quadratic Assignment Problem (QAP) where the nonzero flows form a tree. No condition is required for the distance matrix. This problem is NP-complete and is also a generalization of the Traveling Salesman Problem. In this paper, we present a branch-and-bound algorithm for the exact solution of the Tree QAP based on an integer programming formulation of the problem. The bounds are computed using a Lagrangian relaxation of this formulation. To solve the relaxed problem, we present a Dynamic Programming algorithm which is polynomially bounded. The obtained lower bound is very sharp and equals the optimum in many cases. This fact allows us to employ a redu…
Hybridizing the cross-entropy method: An application to the max-cut problem
2009
Cross-entropy has been recently proposed as a heuristic method for solving combinatorial optimization problems. We briefly review this methodology and then suggest a hybrid version with the goal of improving its performance. In the context of the well-known max-cut problem, we compare an implementation of the original cross-entropy method with our proposed version. The suggested changes are not particular to the max-cut problem and could be considered for future applications to other combinatorial optimization problems.
Applying fuzzy Particle Swarm Optimization to Multi-unit Double Auctions
2010
Abstract In the context of Quadratic Programming Problems, we use a fuzzy Particle Swarm Optimization (PSO) algorithm to analyze a Multi-unit Double Auction (MDA) market. We give also a Linear Programming (LP) based upper bound to help the decision maker in dealing with constraints in the mathematical model. In the computational study, we evaluate our algorithm and show that it is a feasible approach for processing bids and calculating assignments.
A Memetic Algorithm for Binary Image Reconstruction
2008
This paper deals with a memetic algorithm for the reconstruction of binary images, by using their projections along four directions. The algorithm generates by network flows a set of initial images according to two of the input projections and lets them evolve toward a solution that can be optimal or close to the optimum. Switch and compactness operators improve the quality of the reconstructed images which belong to a given generation, while the selection of the best image addresses the evolution to an optimal output.
Branch-and-Bound
2010
We now turn to the discussion of how to solve the linear ordering problem to (proven) optimality. In this chapter we start with the branch-and-bound method which is a general procedure for solving combinatorial optimization problems. In the subsequent chapters this approach will be realized in a special way leading to the so-called branch-and-cut method. There are further possibilities for solving the LOP exactly, e.g. by formulating it as dynamic program or as quadratic assignment problem, but these approaches did not lead to the implementation of practical algorithms and we will not elaborate on them here.
Cotas inferiores para el QAP-Arbol
1985
The Tree-QAP is a special case of the Quadratic Assignment Problem where the flows not equal zero form a tree. No condition is required for the distance matrix. In this paper we present an integer programming formulation for the Tree-QAP. We use this formulation to construct four Lagrangean relaxations that produce several lower bounds for this problem. To solve one of the relaxed problems we present a Dynamic Programming algorithm which is a generalization of the algorithm of this type that gives a lower bound for the Travelling Salesman Problem. A comparison is given between the lower bounds obtained by each ralaxation for examples with size from 12 to 25.