An Algorithmic Package for the Resolution and Analysis of Convex Multiple Objective Problems
• Generation of efficient solutions: both the weighting and the constraint method are developed, through an automatic generation of weights in the former, and of bounds in the latter.
• Goal Programming: We include two versions of the traditional lexicographic algorithms, adapted to the convex case under study, and we also allow the possibility to generate the set of solutions which are satisfying and efficient at the same time. Finally, we also cany out a post-optimal analysis on the target values, so as to find whether they can be improved or not. This analysis, which takes the form of an interactive method, can even lead to an efficient, as well as satisfying, solution for the original problem.
Some computational results are presented, which show the behaviour of the algorithms, in terms of C.P.U. time, on some test problems with different number of variables and constraints. These algorithms have been implemented in FORTRAN language, on a VAX 8530 computer, and with the aid of the NAG subroutine library, mark 15.
Unable to display preview. Download preview PDF.
- Caballero, R, Rey, L., Ruiz, F. Determination of satisfying and efficient solutions in Convex Multi-Objective Programming. Sent to Optimization. 1995.Google Scholar
- Caballero, R, Rey, L., Ruiz, F. Lexicographic Improvement of the Target Values in Convex Goal Programming. Sent to European Journal of Operational Research. 1995.Google Scholar
- Charnes, A., Cooper, W.W. Management Models and Industrial Applications of Linear Programming. John Wiley & Sons. New York. 1961.Google Scholar
- Gill, P.E., Hammarling, S.J., Murray, W., Saunders, M.A., Wright, M.H. User’s Guide for LSSOL. Department of Operations Research. Stanford University. Report SOL 86-1. 1986.Google Scholar
- Hannan, E.L. Nondominance in Goal Programming. INFOR, Canadian Journal of Operational Research and Information Processing 18. 1980. 300–309.Google Scholar
- Ignizio, J.P. Goal Programming and Extensions. Lexington Books. Massachusetts. 1976.Google Scholar
- Lee, S.M. Goal Programming for Decision Analysis. Auerbach Publishers. Philadelphia. 1972.Google Scholar
- N.A.G. (Numerical Algorithms Group Limited), The NAG Fortran Library Introductory Guide, Mark 15. 1991.Google Scholar
- Romero, C. Handbook of critical issues in Goal Programming. Pergamon Press. Oxford. 1991.Google Scholar
- Sawaragi, Y., Nakayama, H., and Tanino, T. Theory of Multiobjective Optimization. Academic Press. Orlando. 1985.Google Scholar
- Steuer, R.E. Manual for ADBASE multiple objective linear programming package. Department of Management Science and Information Technology, University of Georgia, Athens GA, USA. 1992.Google Scholar