Abstract
Frequently algorithm users can select their solution strategy by choosing from among various options for each of several algorithm factors. If the algorithm will always eventually find a solution, the important question is which combination of options is likely to be “best”. A general statistical approach to answering this question is illustrated in the context of a new integer linear programming algorithm where “best” is quickest.
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References
Balas, E., “An Additive Algorithm for Solving Linear Programs with Zero-One Variables,” Oper. Res., Vol. 13, (1965), pp. 517–546.
Dembo, R.S., “A Set of Geometric Programming Test Problems and Their Solutions,” Math Programming, Vol_. 10, (1976), pp. 192–213.
Geoffrion, A.M., “Integer Programming by Implicit Enumeration and Balas’ Method,” SIAM (Soc. Ind. A.pl. Math.) Rev. 7, (1967), pp. 178–190.
Geoffrion, A.M., “An Improved Implicit Enumeration Approach for Integer Programming,’ Oper. Res., Vol. 17, (1969), pp. 437–454.
Geoffrion, A.M., and Marsten, R.E., “Integer Programming: A Framework and Statement-of-the-Art Survey,” Management Sci., Vol. 18, (1972), pp. 465–491.
Geoffrion, A.M., A Guided Tour of Recent Practical Advances in Integer Linear Programming, Working Paper No. 220, Western Management Science Institute, University of California, Los Angeles (1974).
Gomory, R.E., An Algorithm for the Mixed Integer Problem, RM-2597, Rand Corp., Santa Monica, California (1960).
Haldi, J., 25 Integer Programming Test Problems, Working Paper No. 43, Graduate School of Business, Stanford University (1964).
Hicks, C.R., Fundamental Concepts in the Design of Experiments, Holt, Rinehart and Winston, New York (1973).
Kempthorne, O., The Design and Analysis of Experiments, Robert E. Krieger Publishing Company, Huntington, NY (1979).
Riley, W.J. and R.L. Sielken, Jr., The User’s Guide to SLIP, Texas AandM University, College Station, Texas (1981a).
Riley, W.J., Dissertation, Texas AandM University, College Station, Texas, ( Forthcoming ), (1981b).
Statistical Engineering Laboratory, National Bureau of Standards, Fractional Factorial Experimental Designs for Factors at Two Levels, National Bureau of Standards Applied Math. Series 48, (1957).
Taha, H.A., Integer Programming, Academic Press, New York, (1975).
Tomlin, J.A., “Branch and Bound Methods for Integer and Non-Convex Programming,” In Integer and Nonlinear Programming (J. Abadie, ed.), Amer. Elsevier, New York, pp. 437–450 (1970).
Trauth, C.A., Jr. and R.E. Woolsey, “Integer Linear Programming: A Study in Computational Efficiency,” Management Science, Vol. 15, pp. 481–493 (1969).
Wahi, P.N. and G.H. Bradley, Integer Programming Test Problems,Report NO. 28, Administrative Sciences,Yake Unversity, New Haven, CT (1969).
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© 1982 Springer-Verlag Berlin Heidelberg
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Riley, W.J., Sielken, R.L. (1982). Which Options Provide the Quickest Solutions. In: Mulvey, J.M. (eds) Evaluating Mathematical Programming Techniques. Lecture Notes in Economics and Mathematical Systems, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95406-1_12
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DOI: https://doi.org/10.1007/978-3-642-95406-1_12
Publisher Name: Springer, Berlin, Heidelberg
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