V. Campos, F. Glover, M. Laguna, and R. Martí
Journal of Global Optimization, vol. 21, pp. 397-414 (2001)
Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, such as the surrogate constraint method, 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 goes beyond a simple exercise on applying scatter search, by incorporating 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. Our extensive computational experiments with more than 300 instances establishes the effectiveness of our procedure in relation to those previously identified to be best.
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