Abstract
Multiple objective linear programming (MOLP) is almost universally implemented within a simplex algorithm and relies on some of its properties, in particular the use of bases. Alternative linear programming methods such as the projective method need not use bases. Yet, their most common approach to post-optimal analysis has been conservative, e.g. reconstructing a basis in order to use the classical framework. A second, less investigated approach, is to adapt the scope of MOLP to the new methods. The simplex and the new methods are affected differently by degeneracy that causes numerical difficulties both in the data representation and the solution process. Symbolic solvers can mitigate such difficulties. Formulating MOLP as disjunctive optimization related to logic programming, the constraint logic program CLP(ℜ) is selected for its symbolic treatment of algebraic constraints seamlessly embedded in a Prolog syntax.
Supported by NSERC Grant OGP0042197 and AUCC Going Global Program.
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Thizy, JM. (1996). Projective and Symbolic Degeneracy-Reducing Techniques for Multiple Objective Linear Programming. In: Tamiz, M. (eds) Multi-Objective Programming and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87561-8_10
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DOI: https://doi.org/10.1007/978-3-642-87561-8_10
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