Journal of Global Optimization

, Volume 21, Issue 4, pp 397–414 | Cite as

An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem

  • Vicente Campos
  • Fred Glover
  • Manuel Laguna
  • Rafael Martí


Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear global optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, such as in generating surrogate constraints, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation designed to find high quality solutions for the NP-hard linear ordering problem, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to combine solutions and to create a balance between quality and diversification in the reference set. We also use a tracking process that generates solution statistics disclosing the nature of combinations and the ranks of antecedent solutions that produced the best final solutions. Extensive computational experiments with more than 300 instances establishes the effectiveness of our procedure in relation to approaches previously identified to be best.


Linear Order Global Optimization Problem Scatter Search High Quality Solution Problem Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Vicente Campos
    • 1
  • Fred Glover
    • 2
  • Manuel Laguna
    • 2
  • Rafael Martí
    • 1
  1. 1.Dpto. de Estadística e Investigación Operativa, Facultad de MatemáticasUniversitat de ValenciaBurjassot, ValenciaSpain
  2. 2.Graduate School of Business and Administration, 419 UCBUniversity of ColoradoBoulderUSA

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