Interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound

European Journal of Operational Research

Volumn 124, Issue 3, 2000, Pages 478-494

  Alves, Maria João ^a   Clímaco, João ^a  

^a INESC COIMBRA   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DECISION MAKING; FUNCTIONS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; SENSITIVITY ANALYSIS;

BRANCH AND BOUND TECHNIQUE; MIXED INTEGER LINEAR PROGRAMMING; MULTICRITERIA ANALYSIS; SCALARIZING PROGRAMS; TCHEBYCHEFF METRIC;

OPERATIONS RESEARCH;

EID: 0343442527     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(99)00183-6     Document Type: Article

References (28)

1. Alves, M.J., Clímaco, J., 1999. Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems. European Journal of Operational Research 117 (3), 565-577.
2. Aksoy Y. An interactive branch-and-bound algorithm for bicriterion nonconvex/mixed integer programming. Naval Research Logistics. 37:1990;403-417.
3. Bitran G.R. Linear multiple objective programs with zero-one variables. Mathematical Programming. 13:1977;121-139.
4. Bowman, V.J., 1976. On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives, In: H. Thiriez, S. Zionts, (Eds.), Multiple Criteria Decision Making, Lecture Notes in Economics and Mathematical Systems 130, Springer, Berlin, pp. 76-86.
5. Coutinho-Rodrigues, J., Current, J., Clímaco, J., Ratick, S., 1997. An interactive spatial decision support system for multiobjective HAZMAT location-routing problems. Transportation Research Board, Record 1602, 101-109.
6. Durso, A., 1992. An interactive combined branch-and-bound/Tchebycheff algorithm for multiple criteria, In: A. Goicoechea, L. Duckstein, S. Zionts, (Eds.), Multiple Criteria Decision Making, Proceedings of the 9th Conference, Springer, Berlin, pp. 107-122.
7. Evans G.W. An overview of techniques for solving multiobjective mathematical programs. Management Science. 30(30):1984;1268-1282.
8. Ferreira C., Santos B.S., Captivo M.E., Clímaco J., Silva C.C. Multiobjective location of unwelcome or central facilities involving environmental aspects: A prototype of a decision support system. Belgian Journal of Operations Research, Statistics and Computer Science. 36(2/3):1996;159-172.
9. Huckert K., Rhode R., Roglin O., Weber R. On the interactive solution to a multicriteria scheduling problem. Zeitschrift für Operations Research. 24:1980;47-60.
10. Karaivanova J.N., Narula S.C., Vassilev V. An interactive procedure for multiple objective integer linear programming problems. European Journal of Operational Research. 68:1993;344-351.
11. Karaivanova J., Korhonen P., Narula S., Wallenius J., Vassilev V. A reference direction approach to multiple objective integer linear programming. European Journal of Operational Research. 81:1995;176-187.
12. Karwan, M.H., Zionts, S., Villarreal, B., Ramesh, R., 1985. An improved interactive multicriteria integer programming algorithm, In: Y.Y. Haimes, V. Chankong (Eds.), Decision Making with Multiple Objectives, Lecture Notes in Economics and Mathematical Systems 242. Springer, Berlin, pp. 261-271.
13. L'Hoir, H., Teghem, J., 1995. Portfolio selection by MOLP using an interactive branch and bound, Foundations of Computing and Decision Sciences 20/3, Institute of Computing Science, Technical University of Poznan, Poland.
14. Narula S.C., Vassilev V. An interactive algorithm for solving multiple objective integer linear programming problems. European Journal of Operational Research. 79:1994;443-450.
15. Osleeb J.P., Ratick S.J. A mixed integer and multiple objective programming model to analyze coal handling in New England. European Journal of Operational Research. 12:1983;302-313.
16. Ramesh R., Zionts S., Karwan M.H. A class of practical interactive branch and bound algorithms for multicriteria integer programming. European Journal of Operational Research. 26:1986;161-172.
17. Ritzel B.J., Eheart J.W., Ranjithan S. Using genetic algorithms to solve a multiple objective groundwater pollution containment problem. Water Resources Research. 30/5:1994;1589-1603.
18. Solanki R. Generating the noninferior set in mixed integer biobjective linear programs: An application to a location problem. Computers and Operations Research. 18(2):1991;1-16.
19. Steuer R., Choo E.-U. An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming. 26:1983;326-344.
20. Steuer, R., 1986. Multiple Criteria Optimization: Theory, computation and application, Wiley, New York.
21. Teghem, J., Kunsch, P.L., 1986. Interactive methods for multi-objective integer linear programming, In: G. Fandel, M. Grauer, A. Kurzhanski, A.P. Wierzbicki (Eds.), Large-Scale Modelling and Interactive Decision Analysis, Lecture Notes in Economics and Mathematical Systems 273, Springer, Berlin, pp. 75-87.
22. Trivedi N.M. A mixed-integer goal programming model for nursing service budgeting. Operations Research. 29(5):1981;1019-1034.
23. Vassilev V., Narula S.C. A reference direction algorithm for solving multiple objective integer linear programming problems. Journal of Operational Research Society. 44(12):1993;1201-1209.
24. Villarreal, M., Karwan, H., Zionts, S., 1980. An interactive branch and bound procedure for multicriterion integer linear programming, In: G. Fandel, T. Gal (Eds.), Multiple Criteria Decision Making Theory and Application, Lecture Notes in Economics and Mathematical Systems 177, Springer, Berlin, pp. 448-467.
25. Weber C.A., Current J.R. A multiobjective approach to vendor selection. European Journal of Operational Research. 68:1993;173-184.
26. White D.J. A bibliography on the applications of mathematical programming multiple-objective methods. Journal of Operational Research Society. 41(8):1990;669-691.
27. Wierzbicki, A., 1980. The use of reference objectives in multiobjective optimization, In: G. Fandel, T. Gal, (Eds.), Multiple Criteria Decision Making, Theory and Application, Lecture Notes in Economics and Mathematical Systems 177. Springer, Berlin, pp. 468-486.
28. Zionts S. Integer Programming with multiples objectives. Annals of Discrete Mathematics. 1:1977;551-562.