Solving Dynamic Multicriteria Linear Problems with HYBRID
The purpose of the paper is to describe methods used for formulation, solution and analysis of dynamic multiobjective linear programming problems with HYBRID package (see Makowski and Sosnowski, 1987). The method adopted in HYBRID for formulation and solution of a multicriteria problem is based on the reference point approach introduced by Wierzbicki (1980). In this approach a piecewise linear scalarizing function is defined. The function parameters are aspiration level for each criterion (reference points) and — possibly — weights. Minimization of the scalarizing function subject linear constraints is substituted by solution of an equivalent single-objective linear programming problem.
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- Chow, G.C. (1975). Analysis and Control of Dynamic Economic Systems. Wiley, New York.Google Scholar
- Fourer, R. (1982). Solving staircase linear programs by the simplex method. Mathematical Programming 23, pp. 274–313, 25, pp. 251–292.Google Scholar
- Kreglewski, T., Lewandowski, A. and Rogowski, T. (1985). Dynamic Extension of the DIDAS system and its Application in Flood Control. In M. Grauer, M. Thompson, A.P. Wierzbicki, eds., Plural Rationality and Interactive Decision Processes, Springer-Verlag.Google Scholar
- Lewandowski, A. and Grauer, M. (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.Google Scholar
- Lewandowski, A. and Wierzbicki, A. eds (1987). Theory, Software and Testing Exam- ples for Decision Support Systems. WP-87–26, IIASA, Laxenburg, Austria.Google Scholar
- Makowski, M. and Sosnowski, J. (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.Google Scholar
- Makowski, M. and Sosnowski, J. (1987). A Mathematical Programming Package for Multicriteria Dynamic Linear Problems HYBRID; Methodological and User Guide to version 3.03. WP-87–00, IIASA, Laxenburg, Austria.Google Scholar
- Murtagh, B.A. (1981). Advanced Linear Programming: Computation and Practice, Mc Graw-Hill, New York.Google Scholar
- Polyak, B.T. and Tretiyakov, N.V. (1972). An iterative method for linear programming and its economic interpretation. Economic and Mathematical Methods, 8, pp. 740–751, (in Russian).Google Scholar
- Propoi, A. (1978). Problems of Dynamic Linear Programming. RM-76–78, IIASA.Google Scholar
- Sosnowski, J. (1981). Linear programming via augmented Lagrangian and conjugate gradient methods. In S. Walukiewicz and A.P. Wierzbicki, eds., Methods of Mathematical Programming, Proceedings of a 1977 Conference in Zakopane. Polish Scientific Publishers, Warsaw.Google Scholar
- Tamura, H. (1977). Multistage Linear Programming for Discrete Optimal Control with Distributed Lags. Autonomica, vol. 13, pp. 369–376, Pergamon Press.Google Scholar