Approximate and exact solution methods for the hyperbolic 0-1 knapsack problem

INFOR

Volumn 40, Issue 2, 2002, Pages 97-110

  Billionnet, Alain ^a  

^a IIE   (France)

Author keywords

Approximate solutions; Computational experiments; Exact solutions; Fractional 0 1 programming; Hyperbolic 0 1 knapsack problem; Mixed integer programming

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; INTEGER PROGRAMMING; LINEAR PROGRAMMING; OPTIMIZATION; VECTORS;

HYPERBOLIC KNAPSACK PROBLEM (HKP);

OPERATIONS RESEARCH;

EID: 0036589356     PISSN: 03155986     EISSN: None     Source Type: Journal    
DOI: 10.1080/03155986.2002.11732644     Document Type: Article

References (21)

1. Charnes A. and Cooper W.W., "Programming with linear fractional functionals," Naval Research Logistics Quarterly 9 (1962) 181-186.
2. Dinkelbach W., "On nonlinear fractional programming," Management Science 13 (1967) 492-498.
3. Granot D. and Granot F., "On solving fractional (0,1) programs by implicit enumeration," INFOR 14 (1976) 241-249.
4. Granot D. and Granot F., "On integer and mixed integer fractional programming problems," Annals of Discrete Mathematics 1 (1977) 221-231.
5. Hammer P.L. and Rudeanu S., Boolean Methods in Operations Research (Springer, Berlin, 1968).
6. Hansen P., "Methods of nonlinear 0-1 programming," Annals of Discrete mathematics 5 (1979) 53-70.
7. Hansen P., Poggi de Aragao M.V. and Ribeiro C.C., "Hyperbolic 0-1 programming and query optimization in information retrieval," Mathematical Programming 52 (1991) 255-263.
8. Hashizume S., Fukushima M., Katoh N. and Ibaraki T., "Approximation algorithms for combinatorial fractional programming problems," Mathematical Programming 37 (1987) 255-267.
9. Ishii H., Ibaraki T. and Mine H., "A primal cutting plane algorithm for integer fractional programming problems," J. Oper. Res. Soc. Japan 19 (1976) 228-244.
10. Ishii H., Ibaraki T. and Mine H., "Fractional knapsack problems," Mathematical Programming 13 (1977) 255-271.
11. Isbell J.R. and Marlow W.H., "Attribution games," Naval Research Logistics Quarterly 3 (1956) 71-94.
12. Jagannathan R., "On some properties of programming problems in parametric forms pertaining to fractional programming," Management Science 12 (1966) 609-615.
13. Megiddo N., "Combinatorial optimization with rational objective functions," Mathematics of Operations Research, 4, 1979, 414-424.
14. Nagih A., "Sur la résolution des problèmes fractionnaires en variables 0-1," Thése de Doctorat, Université Paris 13, France, juin 1996.
15. Nagih A. et Plateau G., "Problèmes fractionnaires: tour d'horizon sur les applications et méthodes de résolution," RAIRO Operations research 33 (1999) 383-419.
16. Nagih A. et Plateau G., "A partition algorithm for 0-1 unconstrained hyperbolic programming problems," Investigacion Operativa 9 (2000) 167-178.
17. Nagih A. et Plateau G., "A lagrangean decomposition for the 0-1 hyperbolic programming problem," International Journal of Mathematical Algorithms 1 (2000) 299-314.
18. Radzik T., "Fractional combinatorial optimization," Handbook of Combinatorial Optimization, Edited by Z.-Z. Du and P.M. Pardalos, Kluwer Academic Publishers (1998) 429-478.
19. Schaible S., "Fractional programming: Applications and algorithms," European Journal of Operational Research 7 (1981) 111-120.
20. Schaible S., "Fractional programming" in Handbook of Global Optimization Edited by R. Horst and P. Pardalos, Kluwer Academic Publishers (1995) 495-608.
21. Wolf H., "Parametric analysis in linear fractional programming," Operations research 34 (1986) 930-937.