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Fri, 07 Nov 2014 10:55:37 +0100Fri, 07 Nov 2014 10:55:37 +0100A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3911
A new algorithm for optimization problems with three objective functions is presented which computes a representation for the set of nondominated points. This representation is guaranteed to have a desired coverage error and a bound on the number of iterations needed by the algorithm to meet this coverage error is derived. Since the representation does not necessarily contain nondominated points only, ideas to calculate bounds for the representation error are given. Moreover, the incorporation of domination during the algorithm and other quality measures are discussed.Tobias Kuhn; Stefan Ruzikapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3911Fri, 07 Nov 2014 10:55:37 +0100A Survey of Approximation Methods in Multiobjective Programming
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1451
Approaches to approximate the efficient and Pareto sets of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. The survey covers 48 articles published since 1975.Stefan Ruzika; Margaret M. Wiecekpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1451Thu, 13 Nov 2003 11:18:57 +0100Error bounds for the approximative solution of restricted planar location problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/489
Facility location problems in the plane play an important role in mathematical programming. When looking for new locations in modeling real-word problems, we are often confronted with forbidden regions, that are not feasible for the placement of new locations. Furthermore these forbidden regions may habe complicated shapes. It may be more useful or even necessary to use approcimations of such forbidden regions when trying to solve location problems. In this paper we develop error bounds for the approximative solution of restricted planar location problems using the so called sandwich algorithm. The number of approximation steps required to achieve a specified error bound is analyzed. As examples of these approximation schemes, we discuss round norms and polyhedral norms. Also computational tests are included.Stefan Nickel; Barbara Käferpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/489Mon, 03 Apr 2000 00:00:00 +0200