Davaatseren Baatar

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In this paper we consider the problem of decomposing an integer matrix into a weighted sum of binary matrices that have the strict consecutive ones property. This problem is motivated by an application in cancer radiotherapy planning, namely the sequencing of multileaf collimators to realize a given intensity matrix. In addition we also mention another(More)
We consider the problem of decomposing an integer matrix into a positively weighted sum of binary matrices that have the consecutive-ones property. This problem is well-known and of practical relevance. It has an important application in cancer radiation therapy treatment planning: the sequencing of multileaf collimators to deliver a given radiation(More)
K e y w o r d s E q u i t a b i l i t y , Pareto efficiency, Multiobjective programming, Preference structure. 1. I N T R O D U C T I O N Traditionally, multiobjective programming (MOP) and multicriteria decision making (MCDM) have been based on the concept of Pareto efficiency (optimality). Yu [1] develops a convexcone theory for modeling preferences in(More)
This paper tackles the di cult but important task of objective algorithm performance assessment for optimization. Rather than reporting average performance of algorithms across a set of chosen instances, which may bias conclusions, we propose a methodology to enable the strengths and weaknesses of di erent optimization algorithms to be compared across a(More)
We consider the problem of decomposing an integer matrix into a positively weighted sum of binary matrices that have the consecutive-ones property. This problem is well-known and of practical relevance. It has an important application in cancer radiation therapy treatment planning: the sequencing of multileaf collimators to deliver a given radiation(More)
delivery of cancer radiation treatment using multileaf collimators Davaasteren Baatar, Natashia Boland, Robert Johnston Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia, {d.baatar@ms.unimelb.edu.au, natashia@unimelb.edu.au, , rj@unimelb.edu.au} Horst W. Hamacher Department of Mathematics, University of(More)
The Maximal Independent Set (MIS) formulation tackles the graph coloring problem (GCP) as the partitioning of vertices of a graph into a minimum number of maximal independent sets as each MIS can be assigned a unique color. Mehrotra and Trick [5] solved the MIS formulation with an exact IP approach, but they were restricted to solving smaller or easier(More)
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