zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A heuristic algorithm for the multidimensional zero-one knapsack problem. (English) Zbl 0532.90070
Summary: Computational and theoretical aspects of a new heuristic for the multidimensional zero-one knapsack problem are studied. Its computational efficiency is compared with two other well-known heuristics.

90C09Boolean programming
65K05Mathematical programming (numerical methods)
90C10Integer programming
Full Text: DOI
[1] Balas, E.; Martin, C. H.: Pivot and complement--A heuristic for 0--1 programming. Management sci. 26, No. 1, 86-96 (1980) · Zbl 0442.90060
[2] Balas, E.; Zemel, E.: Solving large zero-one knapsack problems. Operations res. 28, 1130-1154 (1980) · Zbl 0449.90064
[3] Dembo, R. S.; Hammer, P. L.: A reduction algorithm for knapsack problems. Department of combinatorics and optimization research report CORR 75-6 (1975)
[4] Iii, H. Everett: Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Operations res. 2, 399-417 (1963) · Zbl 0113.14202
[5] Fulkerson, D. R.; Nemhauser, G. L.; Trotter, L. E.: Two computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Mathematical programming study 2 (1974) · Zbl 0353.90060
[6] Garey, M.; Johnson, D.: Computers and intractability: A guide to the theory of NP-completeness. (1979) · Zbl 0411.68039
[7] Geoffrion, A. M.: Lagrangian relaxation for integer programming. Mathematical programming study 2 (1974) · Zbl 0395.90056
[8] Hillier, F. S.: Efficient procedures for integer linear programming with an interior. Operations res. 17, No. 4, 637-679 (1969) · Zbl 0176.49902
[9] Ingargiola, G. P.; Korsch, J. F.: Reduction algorithm for zero-one single knapsack problems. Management sci. 20, No. 4 (1974)
[10] Kaplan, S.: Solution to the lorie-savage and similar integer programming problems by the generalized Lagrange multiplier method. Operations res. 14, No. 6 (1966) · Zbl 0158.38406
[11] Kochenberger, G. A.; Mccarl, B. A.; Wyman, F. P.: A heuristic for general integer programming. Decision sci. 5, No. 1 (1974)
[12] Lorie, J.; Savage, L. J.: Three problems in capital rationing. J. business (October, 1955)
[13] Nemhauser, G.; Ullman, Z.: A note on the generalized Lagrange multiplier solution to an integer programming problem. Operations res. 16 (1968)
[14] Nemhauser, G.; Ullman, Z.: Discrete dynamic programming and capital allocation. Management sci. 15, 494-505 (1979)
[15] Petersen, C. C.: Computational experience with variants of the balas algorithm applied to the selection of C&D projects. Management sci. 13, 736-750 (1967)
[16] Senju, S.; Toyoda, Y.: An approach to linear programming with 0--1 variables. Management sci. 15, B196-207 (1968)
[17] Toyoda, Y.: A simplified algorithm for obtaining approximate solutions to zero-one programming problems. Management sci. 21, No. 12, 1407-1417 (1975) · Zbl 0307.90056
[18] Weingartner, H. M.: Mathematical programming and the analysis of capital budgeting problems. (1967)
[19] Weingartner, H. M.; Ness, D. N.: Methods for the solution of the multi-dimensional 0--1 knapsack problem. Operations res. 15, No. 1, 83-103 (1967)
[20] Zanakis, S. H.: Heuristic 0--1 linear programming: comparisons of three methods. Management sci. 24, No. 1 (1977) · Zbl 0369.90086