Branch And Bound Assignment Problem Pdf Converter

  • [1]

    E. Balas, D.L. Miller, J.F. Pekny and P. Toth, “A parallel shortest path algorithm for the assignment problem,”Journal of the Association for Computing Machinery 38 (1991) 985–1004.Google Scholar

  • [2]

    E. Balas and P. Toth, “Branch and bound methods,” in: E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, eds.,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley, New York, 1985).Google Scholar

  • [3]

    D.P. Bertsekas and D.A. Castanon, “Parallel synchronous and asynchronous implementations of the auction algorithm,” Working Paper, Department of Electrical Engineering and Computer Science, M.I.T. (Cambridge, MA, 1989).Google Scholar

  • [4]

    B. Carnahan, H.A. Luther and J.O. Wilkes,Applied Numerical Methods (Wiley, New York, 1969).Google Scholar

  • [5]

    G. Carpaneto and P. Toth, “Some new branching and bounding criteria for the asymmetric travelling salesman problem,”Management Science 26 (1980) 736–743.Google Scholar

  • [6]

    G. Carpaneto and P. Toth, “Primal—dual algorithms for the assignment problem,”Discrete Applied Mathematics 18 (1987) 137–153.Google Scholar

  • [7]

    G.B. Dantzig,Linear Programming and Extensions (Princeton University Press, Princeton, NJ, 1963).Google Scholar

  • [8]

    G.B. Dantzig, D.R. Fulkerson and S.M. Johnson, “Solution of a large-scale traveling salesman problem,”Operations Research 2 (1954) 393–410.Google Scholar

  • [9]

    G.B. Dantzig, D.R. Fulkerson and S.M. Johnson, “On a linear-programming, combinatorial approach to the traveling salesman problem,”Operations Research 7 (1959) 58.Google Scholar

  • [10]

    E.W. Dijkstra, “A note on two problems in connexion with graphs,”Numerische Mathematik 1 (1959) 269–271.Google Scholar

  • [11]

    O.I. El-Dessouki and W.H. Huen, “Distributed enumeration on between computers,”IEEE Transactions on Computers C-29 (1980) 818–825.Google Scholar

  • [12]

    M. Fischetti and P. Toth, “An additive bounding procedure for combinatorial optimization problems,”Operations Research 37 (1989) 319–328.Google Scholar

  • [13]

    K. Hwang and F.A. Briggs,Computer Architecture and Parallel Processing (McGraw-Hill, New York, 1984).Google Scholar

  • [14]

    R.M. Karp, “A patching algorithm for the nonsymmetric travelling salesman problem,”Siam Journal on Computing 8 (1979) 561–573.Google Scholar

  • [15]

    G.A.P. Kindervater and J.K. Lenstra, “Parallel algorithms” in: M. O'hEigeartaigh, J.K. Lenstra and A.H.G. Rinnooy Kan, eds.,Combinatorial Optimization: Annotated Bibliographies (Wiley, Chichester, 1985) pp. 106–128.Google Scholar

  • [16]

    T.H. Lai and S. Sahni, “Anomalies in parallel branch-and-bound algorithms,”Communications of the ACM 27 (1984) 594–602.Google Scholar

  • [17]

    T. Lai and A. Sprague, “A note on anomalies in parallel branch-and-bound algorithms with one-to-one bounding function,”Information Processing Letters 23 (1986) 119–122.Google Scholar

  • [18]

    I. Lavallee and C. Roucairol, “Parallel branch and bound algorithms,” MASI Research Report EURO VII (1985).Google Scholar

  • [19]

    E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley, New York, 1985).Google Scholar

  • [20]

    G. Li and B.W. Wah, “Computational efficiency of parallel approximate branch-and-bound algorithms,”International Conference on Parallel Processing (1984) 473–480.Google Scholar

  • [21]

    J.D.C. Little, K.G. Murty, D.W. Sweeney and C. Karel, “An algorithm for the traveling salesman problem,”Operations Research 11 (1963) 972–989.Google Scholar

  • [22]

    S. Martello and P. Toth, “Linear assignment problems,”Annals of Discrete Mathematics 31 (1987) 259–282.Google Scholar

  • [23]

    D.L. Miller and J.F. Pekny, “Results from a parallel branch and bound algorithm for solving large asymmetric traveling salesman problems,”Operations Research Letters 8 (1989) 129–135.Google Scholar

  • [24]

    J. Mohan, “Experience with two parallel programs solving the traveling salesman problem,”IEEE International Conference on Parallel Processing (1983) 191–193.Google Scholar

  • [25]

    M. Padberg and G. Rinaldi, “Optimization of a 532-city symmetric traveling salesman problem by branch and cut,”Operations Research 6 (1987) 1–7.Google Scholar

  • [26]

    C.H. Papadimitrou and K. Steiglitz, “Some examples of difficult traveling salesman problems,”Operations Research 26 (1978) 434–443.Google Scholar

  • [27]

    E.A. Pruul, G.L. Nemhauser and R.A. Rushmeier, “Branch-and-bound and parallel computations: a historical note,”Operations Research 7 (1988) 65–69.Google Scholar

  • [28]

    R. Rettberg and R. Thomas, “Contention is no obstacle to shared memory multiprocessing,”Communications of the ACM 29 (1986) 1202–1212.Google Scholar

  • [29]

    C.C. Ribeiro, “Parallel computer models and combinatorial algorithms,”Annals of Discrete Mathematics 31 (1987) 325–364.Google Scholar

  • [30]

    R.E. Tarjan,Data Structures and Network Algorithms (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983).Google Scholar

  • Cell formation (CF) is the first and the most important problem in designing cellular manufacturing systems. Due to its non-polynomial nature, various heuristic and metaheuristic algorithms have been proposed to solve CF problem. Despite the popularity of heuristic algorithms, few studies have attempted to develop exact algorithms, such as branch and bound (B&B) algorithms, for this problem. We develop three types of branch and bound algorithms to deal with the cell formation problem. The first algorithm uses a binary branching scheme based on the definitions provided for the decision variables. Unlike the first algorithm, which relies on the mathematical model, the second one is designed based on the structure of the cell formation problem. The last algorithm has a similar structure to the second one, except that it has the ability to eliminate duplicated nodes in branching trees. The proposed branch and bound algorithms and a hybrid genetic algorithm are compared through some numerical examples. The results demonstrate the effectiveness of the modified problem-oriented branch and bound algorithm in solving relatively large size cell formation problems.

    0 thoughts on “Branch And Bound Assignment Problem Pdf Converter”


    Leave a Comment

    Your email address will not be published. Required fields are marked *