Lower planes for the network design problem

A new class of relaxations for the network design problem based on lower planes, i.e., linear lower approximations of the objective function, is introduced. Such relaxations provide lower bounds much sharper than the bounds used so far in branch and bound algorithms for this problem.

[1]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[2]  Giorgio Gallo,et al.  A new algorithm to find the shortest paths between all pairs of nodes , 1982, Discret. Appl. Math..

[3]  Sang Nguyen,et al.  A dual simplex algorithm for finding all shortest paths , 1981, Networks.

[4]  René Dionne.  Etude Et Extension D’Un Algorithme De Murghland , 1978 .

[5]  Hoang Hai Hoc,et al.  Topological optimization of networks: A nonlinear mixed integer model employing generalized benders , 1980 .

[6]  Jan Karel Lenstra,et al.  The complexity of the network design problem , 1978, Networks.

[7]  A. D. Pearman,et al.  The structure of the solution set to network optimisation problems , 1979 .

[8]  H. Hoc.  Topological optimization of networks: A nonlinear mixed integer model employing generalized benders decomposition , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[9]  R. Weischedel,et al.  Optimal Network Problem: A Branch-and-Bound Algorithm , 1973 .

[10]  Richard T. Wong,et al.  A Survey of Network Design Problems , 1976 .

[11]  F. Glover,et al.  A computational analysis of alternative algorithms and labeling techniques for finding shortest path trees , 1979, Networks.

[12]  Michael Florian,et al.  Exact and approximate algorithms for optimal network design , 1979, Networks.

[13]  Hoang Hai Hoc.  A Computational Approach to the Selection of an Optimal Network , 1973 .

[14]  P. Hammer,et al.  Quadratic knapsack problems , 1980 .