An intelligent algorithm for mixed-integer programming models

Abstract We present an intelligent branch-and-bound algorithm and report preliminary computational results. The conventional approach to use of a particular branching strategy throughout is replaced by a branching algorithm that uses a neural network to direct the branching. The technique is shown to be significantly faster than conventional methods for certain classes of mixed integer linear programming (MILP) models.

[1]  Parviz Ghandforoush,et al.  An advanced dual algorithm with constraint relaxation for all‐integer programming , 1983 .

[2]  Fatemeh Zahedi,et al.  An Introduction to Neural Networks and a Comparison with Artificial Intelligence and Expert Systems , 1991 .

[3]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[4]  Stanley Zionts,et al.  An interactive method for bicriteria integer programming , 1990, IEEE Trans. Syst. Man Cybern..

[5]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[6]  Larry M. Austin,et al.  An advanced start algorithm for all-integer programming , 1985, Comput. Oper. Res..

[7]  Alistair D. C. Holden.  Fast learning in symbolic/neural models using external constraints and automatic re-structuring , 1989, Conference Proceedings., IEEE International Conference on Systems, Man and Cybernetics.

[8]  James R. Burns,et al.  An implicit branch-and-bound algorithm for mixed-integer-linear programming , 1990, Comput. Oper. Res..

[9]  David E. van den Bout,et al.  A traveling salesman objective function that works , 1988, IEEE 1988 International Conference on Neural Networks.

[10]  J. Desrosiers,et al.  Lagrangian relaxation methods for solving the minimum fleet size multiple traveling salesman problem with time windows , 1988 .

[11]  Mauricio G. C. Resende,et al.  An interior point algorithm to solve computationally difficult set covering problems , 1991, Math. Program..

[12]  Rakesh K. Sarin,et al.  Scheduling with multiple performance measures: the one-machine case , 1986 .

[13]  James R. Burns,et al.  Management science : an aid for managerial decision making , 1985 .

[14]  Parviz Ghandforoush,et al.  A primal-dual cutting-plane algorithm for all-integer programming , 1981 .

[15]  Larry M. Austin,et al.  The mixed cutting plane algorithm for all-integer programming , 1986, Comput. Oper. Res..

[16]  H. Szu.  Fast simulated annealing , 1987 .

[17]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[18]  C. A. Trauth,et al.  Integer Linear Programming: A Study in Computational Efficiency , 1969 .

[19]  H. O. Hartley.  Nonlinear Programming by the Simplex Method , 1961 .

[20]  William C. Davidon,et al.  Variable Metric Method for Minimization , 1959, SIAM J. Optim..

[21]  R. J. Dakin,et al.  A tree-search algorithm for mixed integer programming problems , 1965, Comput. J..

[22]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[23]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[24]  D. O. Hebb,et al.  The organization of behavior , 1988 .

[25]  Said Ashour.  Letter to the Editor - An Experimental Investigation and Comparative Evaluation of Flow-Shop Scheduling Techniques , 1970, Oper. Res..

[26]  A. Land,et al.  An Automatic Method for Solving Discrete Programming Problems , 1960, 50 Years of Integer Programming.