Quantitative stability analysis for vector problems of 0-1 programming

Discrete Optimization

Volumn 7, Issue 1-2, 2010, Pages 48-63

  Emelichev, Vladimir ^a   Podkopaev, Dmitry ^b  

^a BELARUSIAN STATE UNIVERSITY   (Belarus)

^b SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

0 1 programming; Stability radius; Vector optimization

Indexed keywords

0-1 PROGRAMMING; 0-1 PROGRAMMING PROBLEM; ABSOLUTE VALUES; LINEAR CONSTRAINTS; MULTIPLE OBJECTIVES; NONLINEAR OBJECTIVE FUNCTIONS; OBJECTIVE FUNCTIONS; QUANTITATIVE CHARACTERISTICS; QUANTITATIVE STABILITY ANALYSIS; STABILITY ANALYSIS; STABILITY RADIUS; VECTOR PROBLEM;

OPTIMIZATION;

STABILITY;

EID: 77950520631     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2010.02.001     Document Type: Article

References (17)

1. Ehrgott M., and Gandibleux X.A. Survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectrum 22 (2000) 425-460
2. Greenberg H.J. An annotated bibliography for post-solution analysis in mixed integer programming and combinatorial optimization. In: Woodruff D.L. (Ed). Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search (1998), Kluwer Academic Publishers, Boston, MA 97-148
3. Sotskov Yu.N., Leontiev V.K., and Gordeev E.N. Some concepts of stability analysis in combinatorial optimization. Discrete Appl. Math. 58 (1995) 169-190
4. Sotskov Yu.N., Tanaev V.S., and Werner F. Stability radius of an optimal schedule: A survey and recent developments. In: Yu G. (Ed). Industrial Applications of Combinatorial Optimization (1998), Kluwer Academic Press, Boston, MA 72-108
5. Sotskov Yu.N., Dolgui A., and Portmann M.-C. Stability analysis of an optimal balance for an assembly line with fixed cycle time. European J. Oper. Res. 168 (2006) 783-797
6. Emelichev V.A., Girlich E., Nikulin Yu.V., and Podkopaev D.P. Stability and regularization of vector problems of integer linear programming. Optimization 51 (2002) 645-676
7. Libura M., Van der Poort E.S., Sierksma G., and Van der Veen J.A.A. Stability aspects of the traveling salesman problem based on k-best solutions. Discrete Appl. Math. 87 (1998) 159-185
8. Chakravarti N., and Wagelmans A. Calculation of stability radius for combinatorial optimization problems. Oper. Res. Lett. 23 (1999) 1-7
9. Van Hoesel S., and Wagelmans A. On the complexity of postoptimality analysis of 0-1 programs. Discrete Appl. Math. 91 (1999) 251-263
10. Leontiev V.K., and Mamutov K.X. Stability of solutions in problems of linear Boolean programming. Jurn. Vychisl. Matematiki i Matem. Fiziki 28 (1988) 1475-1481
11. Emelichev V.A., and Krichko V.N. On the stability radius of a Pareto optimum of the vector problem of Boolean programming. Izv. AN Respubliki Moldova. Matematika. 1 (1999) 79-84
12. Emelichev V.A., and Krichko V.N. On stability of a Pareto optimum of a vector Boolean programming problem. Discrete Math. Appl. 9 (1999) 607-613
13. Emelichev V.A., and Krichko V.N. Stability radius of a Pareto optimal solution to a vector quadratic problem of Boolean programming. Comput. Math. Math. Phys. 41 (2001) 322-326
14. Emelichev V.A., Krichko V.N., and Podkopaev D.P. On the radius of stability of a vector problem of linear Boolean programming. Discrete Math. Appl. 10 (2000) 103-108
15. Gordeev E.N., and Leontiev V.K. Applying stability analysis to solving choice problems. Mathematical Methods of Image Recognition and Discrete Optimization (1987), VC AN SSSR, Moscow 36-51 (in Russian)
16. Tanino T., and Sawaragi Y. Stability of nondominated solutions in multicriteria decision-making. J. Optim. Theory Appl. 30 (1980) 229-253
17. V. Emelichev, D. Podkopaev, Quantitative stability analysis in vector problems of 0-1 programming, Research Report IBS PAN RB/44/2008, 33 p.