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Tue, 15 Oct 2002 22:29:00 +0200Tue, 15 Oct 2002 22:29:00 +0200A Level Set Method for Multiobjective Combinatorial Optimization: Application to the Quadratic Assignment Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1352
Multiobjective combinatorial optimization problems have received increasing attention in recent years. Nevertheless, many algorithms are still restricted to the bicriteria case. In this paper we propose a new algorithm for computing all Pareto optimal solutions. Our algorithm is based on the notion of level sets and level curves and contains as a subproblem the determination of K best solutions for a single objective combinatorial optimization problem. We apply the method to the Multiobjective Quadratic Assignment Problem (MOQAP). We present two algorithms for ranking QAP solutions and nally give computational results comparing the methods.Matthias Ehrgott; Thomas Stephan; Dagmar Tenfelde-Podehlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1352Tue, 15 Oct 2002 22:29:00 +0200Integrated Scheduling and Location Models: Single Machine Makespan Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1335
Scheduling and location models are often used to tackle problems in production, logistics, and supply chain management. Instead of treating these models independent of each other, as is usually done in the literature, we consider in this paper an integrated model in which the locations of machines define release times for jobs. Polynomial solution algorithms are presented for single machine problems in which the scheduling part can be solved by the earliest release time rule.Holger Hennes; Horst W. Hamacherpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1335Mon, 10 Jun 2002 00:00:00 +0200The continuous stop location problem in public transportation networks
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1284
In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network. The positive effect of new stops is given by the better access of the potential customers to their closest station, while the increasement of travel time caused by the additional stopping activities of the trains leads to a negative effect. The goal is to cover all given demand points with a minimal amount of additional traveling time, where covering may be defined with respect to an arbitrary norm (or even a gauge). Unfortunately, this problem is NP-hard, even if only the Euclidean distance is used. In this paper, we give a reduction to a finite candidate set leading to a discrete set covering problem. Moreover, we identify network structures in which the coefficient matrix of the resulting set covering problem is totally unimodular, and use this result to derive efficient solution approaches. Various extensions of the problem are also discussed.A. Schöbel; H. W. Hamacher; A. Liebers; D. Wagnerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1284Tue, 21 May 2002 00:00:00 +0200Properties of 3-dimensional line location models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1283
We consider the problem of locating a line with respect to some existing facilities in 3-dimensional space, such that the sum of weighted distances between the line and the facilities is minimized. Measuring distance using the l_p norm is discussed, along with the special cases of Euclidean and rectangular norms. Heuristic solution procedures for finding a local minimum are outlined.Jack Brimberg; Henrik Juel; Anita Schöbelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1283Thu, 21 Mar 2002 00:00:00 +0100Minimizing Beam-On Time in Cancer Radiation Treatment Using Multileaf Collimators
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1279
Natashia Boland; Horst W. Hamacher; Frank Lenzenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1279Sun, 10 Feb 2002 00:00:00 +0100