Journal of Global Optimization

, Volume 43, Issue 2–3, pp 357–372 | Cite as

Branch and bound algorithm for multidimensional scaling with city-block metric

  • Antanas Žilinskas
  • Julius ŽilinskasEmail author


A two level global optimization algorithm for multidimensional scaling (MDS) with city-block metric is proposed. The piecewise quadratic structure of the objective function is employed. At the upper level a combinatorial global optimization problem is solved by means of branch and bound method, where an objective function is defined as the minimum of a quadratic programming problem. The later is solved at the lower level by a standard quadratic programming algorithm. The proposed algorithm has been applied for auxiliary and practical problems whose global optimization counterpart was of dimensionality up to 24.


Multidimensional scaling City-block metric Branch and bound 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Vilnius Gediminas Technical UniversityVilniusLithuania

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