Frantisek Fiala
ABSTRACT
The acceleration algorithm by Hammer and Rudeanu (1) for linear zero-one programming problem was tested with several problems of small and medium size involving up to 300 variables on an IBM 360/67. The problems were chosen at random. Several modifications of the algorithm are discussed and computational experience is collected. The results shown indicate that the algorithm is computationally competitive with the other known algorithms using implicit enumeration. For all problems solved the first feasible solution is optimal. This supports the conjecture that the algorithm can be used as a procedure for finding a near optimal solution.
- 1.Hammer, P. L. and Rudeanu, S., Boolean Methods in Operations Research and Related Areas, 1968, Springer Verlag, New YorkGoogle Scholar
- 2.Gue, R. L. and Liggett, J. C. and Cain, K. C., "Analysis of Algorithms for the Zero-One Programming Problem", Comm. ACM, 11, 837-844, Dec. 1968 Google ScholarDigital Library
- 3.Glover, F., "A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem", Opns. Res., 13, 879-919, 1965Google ScholarDigital Library
- 4.Fiala, F., "Solution of Linear Programming Problems in 0-i Variables" Submitted to Comm. ACM Google ScholarDigital Library
- 5.Fleischman, B., "Computational Experience with the Algorithm of Balas" Opns Res., 15, 153-155, 1967Google ScholarDigital Library
- 6.Freeman, R. J., "Computational Experience with a 'Balasian' Integer Programming Algorithm", Opns. Res., 14, 935-941, 1966Google ScholarDigital Library
- 7.Peterson, C. C., "Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R and D Projects", Mgmt. Sci., 13, 735-750, 1967Google Scholar
- 8.Rao, A., "Balas' and Glover's Algorithm: a Comparison", Paper, 23rd Nat. Meeting. Operations Research Soc. of Amer., Chicago, Nov. 1967Google Scholar
- 9.Balinski, M. L. and Spielberg, K., "Methods for Integer Programming: Algebraic, Combinatorial, and Enumerative", Progress in Operations Research, Vol. III, 195-292, 1969, John Wiley &Sons, Inc., New YorkGoogle Scholar
Index Terms
- Computational experience with a modification of an algorithm by Hammer and Rudeanu for 0-1 linear programming
Recommendations
Linear programming to approximate quadratic 0-1 maximization problems
ACM-SE 35: Proceedings of the 35th Annual Southeast Regional ConferenceMany authors have used the continuous relaxation of linear formulations of quadratic 0-1 optimization problems subject to linear constraints in order to obtain a bound of the optimal value by linear programming. But usually, optimal solutions are non-...
A simplex algorithm for piecewise-linear programming I: Derivation and proof
The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. This three-part paper develops and analyzes a general, computationally practical ...
Comments