Abstract
HYBRID is a mathematical programming package which includes all the functions necessary for the solution of multicriteria LP problems and single-criteria linear-quadratic problems. HYBRID is specially useful for dynamic problems since the applied algorithm exploits the structure of a dynamic problem and the user has the advantage of handling a problem as a dynamic one which results in an easy way of formulation of criteria and of interpretation of results. HYBRID is oriented towards an interactive mode of operation in which a sequence of problems is to be solved under varying conditions (e.g., different objective functions, reference points, values of constraints or bounds). Criteria for multiobjective problems may be easily defined and updated with the help of the package. Besides that HYBRID offers many options useful for diagnostic and verification of a problem being solved. HYBRID is available in two versions: one for VAX 6210 (running under Ultrix-32) and one for a PC compatible with PC IBM/AT/XT.
on leave from the Systems Research Institute of the Polish Academy of Sciences, Warsaw.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bertsekas, D.P. (1976). Multiplier methods: a survey. Automatica, 12: 133–145.
Curtis, A.R. and J.K. Reid (1972). On the automatic scaling of matrices for Gaussian elimination. Journal of Mathematics and its applications, No. 10, pp. 118–124.
Flecher, R. (1981). Practical methods of optimization, vol II, Constrained optimization, Wiley, New York.
Fourer, R. (1982). Solving staircase linear programs by the simplex method. Mathematical Programming, 23(1982) 274–313, 25 (1983) 251–292.
Gay, D.M. (1986). Electronic Mail Distribution of Linear Programming Test Problems. Numerical Analysis Manuscript, 86–0(1986), ATandT Laboratories, Murray Hill, New Jersey.
Golub, G.H. and C.F. Van Loan (1983). Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland.
Heath, M.T. (1984). Numerical Methods for Large Sparse Linear Least Squares Problems. SIAM J. Sci. Stat. Comput., Vol. 5, No. 3, 1984.
Hestenes, M.R. (1980). Conjugate Gradient Methods in Optimization. Springer Verlag, Berlin.
Hurlimann, T. (1988). Reference manual for the LPL Modeling Language. Research Report, University of Fribourg, Fribourg, Switzerland.
Ho, J.K. and A.S. Hanne (1974). Nested decomposition for dynamic models. Mathematical Programming, 6 (1974) 121–140
Kallio, M., A. Lewandowski and W. Orchard-Hays (1980). An implementation of the reference point approach for multiobjective optimization. WP-80–35, International Institute for Applied Systems Analysis, Laxenburg, Austria.
Kreglewski, T., Lewandowski, A. and T. Rogowski (1985). Dynamic Extension of the DIDAS system and its Application in Flood Control. In M. Grauer, M. Thompson, A.P. Wierzbicki, editors: Plural Rationality and Interactive Decision Processes, Springer Verlag.
Lewandowski, A. and M. Grauer (1982). The reference point optimization approach—methods of efficient implementation. CP-8-S12, IIASA Collaborative Proceedings Series: Multiobjective and Stochastic Optimization Proceedings of an IIASA Task Force Meeting.
Makowski, M. and J. Sosnowski (1981). Implementation of an algorithm for scaling matrices and other programs useful in linear programming, CP-81–37, International Institute for Applied Systems Analysis, Laxenburg, Austria.
Makowski, M. and J. Sosnowski (1984). Hybrid: A mathematical programming package, IIASA, CP-84–9.
Makowski, M. and J. Sosnowski (1985a). A decision support system for planning and controlling agricultural production with a decentralized management structure. In M. Grauer, M. Thompson, A.P. Wierzbicki, editors: Plural Rationality and Interactive Decision Processes, Springer Verlag.
Makowski, M. and J. Sosnowski (1985b). HYBRID 2.1: A mathematical programming package for multicriteria dynamic problems. In A. Lewandowski, A. Wierzbicki, editors: Theory Software and Testing Examples for Decision Support Systems, IIASA, Laxenburg, September 1985.
Makowski, M. and J. Sosnowski (1987). Methodological Guide to HYBRID 3.01: a mathematical programming package for multicriteria dynamic problems. In A. Lewandowski, A. Wierzbicki, editors: Theory Software and Testing Examples for Decision Support Systems, WP-87–26, IIASA, Laxenburg, April 1987.
Makowski, M. and J. Sosnowski (1988a). A Mathematical Programming Package for Multicriteria Dynamic Linear Problems HYBRID. Methodological and User Guide to Version 3.03, WP-88–002, IIASA, Laxenburg, January 1988.
Makowski, M. and J. Sosnowski (1988b). User Guide to a Mathematical Programming Package for Multicriteria Dynamic Linear Problems HYBRID Version 3.1, WP-88–111, IIASA, Laxenburg, December 1988.
Mangasarian, O.L. (1981). Iterative solution of linear programs. SIAM Journal for Numerical Analysis, 18 (4): 606–614.
Murtagh, B.A. (1981). Advanced Linear Programming: Computation and Practice, Mc Graw—Hill, New York.
Murtagh, B.A. and M.A. Sanders (1977). MINOS — A large-scale nonlinear programming system (for problems with linear constraints). User guide. Technical Report, Systems Optimization Laboratory, Stanford University.
Murtagh, B.A. and M.A. Sanders (1982). A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints. Mathematical Programming Study, 16 (1982), 84–117.
Murtagh, B.A. and M.A. Saunders (1983). MINOS 5.0 User’s Guide, Technical Report SOL 83–20, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, December 1983.
O’Leary, D.P. (1980). A generalized conjugate gradient algorithm for solving a class of quadratic problems. Linear Algebra and its Applications, 34: 371–399.
Polyak, B.T. (1969). The conjugate gradient method in extremal problems. Computational Mathematics and Mathematical Physics, 9: 94–112.
Polyak, B.T. and N.V. Tretiyakov (1972). An iterative method for linear programming and its economic interpretation. Economic and Mathematical Methods, 8: 740–751, (in Russian).
Propoi, A. (1976). Problems of Dynamic Linear Programming, IIASA, RM-76–78.
Sosnowski, J.S. (1978). Dynamic optimization of multisectorial linear production model. Systems Research Institute, Warsaw, Ph.D. Thesis, (in Polish).
Sosnowski, J.S. (1981). Linear programming via augmented Lagrangian and conjugate gradient methods. In S. Walukiewicz and A.P. Wierzbicki, editors: Methods of Mathematical Programming, Proceedings of a 1977 Conference in Zakopane. Polish Scientific Publishers, Warsaw.
Tomlin, J.A. (1972). On scaling linear programming problems. Mathematical Programming Study 4, North Holland Publishing Company, Amsterdam.
Wierzbicki, A. (1978). On the use of penalty functions in multiobjective optimization, Institute of Automatics, Technical University of Warsaw.
Wierzbicki, A.P. (1979). A methodological guide to multiobjective decision making, WP-79–122, IIASA.
Wierzbicki, A. (1980). A mathematical basis for satisficing decision making. WP-80–90, IIASA.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Makowski, M., Sosnowski, J.S. (1989). Mathematical Programming Package HYBRID. In: Lewandowski, A., Wierzbicki, A.P. (eds) Aspiration Based Decision Support Systems. Lecture Notes in Economics and Mathematical Systems, vol 331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21637-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-21637-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51213-4
Online ISBN: 978-3-662-21637-8
eBook Packages: Springer Book Archive