The Random Quadratic Assignment Problem
نویسندگان
چکیده
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P . Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for Cmin and Cmax, the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for Cmin and Cmax and their dependence on P only through its mean and standard deviation, independent of the details of P .
منابع مشابه
Effective heuristics and meta-heuristics for the quadratic assignment problem with tuned parameters and analytical comparisons
Quadratic assignment problem (QAP) is a well-known problem in the facility location and layout. It belongs to the NP-complete class. There are many heuristic and meta-heuristic methods, which are presented for QAP in the literature. In this paper, we applied 2-opt, greedy 2-opt, 3-opt, greedy 3-opt, and VNZ as heuristic methods and tabu search (TS), simulated annealing, and pa...
متن کاملRobust Quadratic Assignment Problem with Uncertain Locations
We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the ...
متن کاملA Honey Bee Algorithm To Solve Quadratic Assignment Problem
Assigning facilities to locations is one of the important problems, which significantly is influence in transportation cost reduction. In this study, we solve quadratic assignment problem (QAP), using a meta-heuristic algorithm with deterministic tasks and equality in facilities and location number. It should be noted that any facility must be assign to only one location. In this paper, first o...
متن کاملUsing Greedy Randomize Adaptive Search Procedure for solve the Quadratic Assignment Problem
Greedy randomize adaptive search procedure is one of the repetitive meta-heuristic to solve combinatorial problem. In this procedure, each repetition includes two, construction and local search phase. A high quality feasible primitive answer is made in construction phase and is improved in the second phase with local search. The best answer result of iterations, declare as output. In this stu...
متن کاملOffering a New Algorithm to Improve the Answer-Search Algorithm in Quadratic Assignment Problem
Layout design problem is one of the useful field of study used to increase the efficiency of sources in organizations. In order to achieve an appropriate layout design, it is necessary to define and solve the related nonlinear programming problems. Therefore, using computer in solving the related problems is important in the view of the researchers of this area of study. However, the designs pr...
متن کاملA hybrid CS-SA intelligent approach to solve uncertain dynamic facility layout problems considering dependency of demands
This paper aims at proposing a quadratic assignment-based mathematical model to deal with the stochastic dynamic facility layout problem. In this problem, product demands are assumed to be dependent normally distributed random variables with known probability density function and covariance that change from period to period at random. To solve the proposed model, a novel hybrid intelligent algo...
متن کامل