An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem
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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.
Becker, O. (1967), Das Helmstädtersche Reihenfolgeproblem-die Effizienz verschiedener Näherungsverfahren in Computer uses in the Social Sciences, Berichteiner Working Conference, Wien, January 1967.
Chanas, S. and Kobylanski, P. (1996), A new heuristic algorithm solving the linear ordering problem, Computational Optimization and Applications, 6, 191–205.
Crowston, W. B., Glover, F., Thompson, G. L. and Trawick, J. D., (1963), Probabilistic and Parametric Learning Combinations of Local Job Shop Scheduling Rules, ONR Research Memorandum No. 117, GSIA, Carnegie Mellon University, Pittsburgh, PA.
Feo, T. and Resende, M. G. C. (1995), Greedy randomized adaptive search procedures, Journal of Global Optimization, 2, 1–27.
Fisher, H. and Thompson, G. L. (1963), Probabilistic learning combinations of local job-shop scheduling rules, in Industrial Scheduling, J. F. Muth and G. L. Thompson (eds.) Prentice-Hall, pp. 225–251.
Glover, F. (1965), A multiphase dual algorithm for the zero-one integer programming problem, Operations Research 13(6), 879–919.
Glover, F. (1968), Surrogate constraints, Operations Research 16, 741–749.
Glover, F. (1998), A template for scatter search and path relinking, in Artificial Evolution, Lecture Notes in Computer Science 1363, J.-K. Hao, E. Lutton, E. Ronald, M. Schoenauer and D. Snyers (Eds.), Springer, Berlin, pp. 13–54.
Glover, F. and Laguna, M. (1997), Tabu Search, Kluwer Academic Publishers, Boston, MA.
Grotschel, M., Junger, M. and Reinelt, G. (1984), A cutting plane algorithm for the linear ordering problem, Operations Research 32(6), 1195–1220.
Knuth, D. E. (1993), The Stanford GraphBase: A Platform for Combinatorial Computing, Addison-Wesley, New York.
Laguna, M. and Glover, F. (1993), Integrating target analysis and tabu search for improved scheduling systems, Expert Systems with Applications 6, 287–297.
Laguna, M., Martí, R. and Campos, V. (1998), Intensification and diversification with elite tabu search solutions for the linear ordering problem, to appear in Computers and Operations Research.
LOLIB (1997), http://www.iwr.uni-heidelberg.de/iwr/comopt/soft.LOLIB/LOLIB.html.
Reinelt, G. (1985) The Linear Ordering Problem: Algorithms and Applications, Research and Exposition in Mathematics, Vol. 8, H. H. Hofmann and R. Wille (Eds.), Heldermann, Berlin.
- An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem
Journal of Global Optimization
Volume 21, Issue 4 , pp 397-414
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- 1. Dpto. de Estadística e Investigación Operativa, Facultad de Matemáticas, Universitat de Valencia, Dr. Moliner, 50, 46100, Burjassot, Valencia, Spain
- 2. Graduate School of Business and Administration, 419 UCB, University of Colorado, Boulder, CO, 80309-0419, USA