Revisiting the big valley search space structure in the TSP

D R Hains (), L D Whitley and A E Howe
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D R Hains: Colorado State University
L D Whitley: Colorado State University
A E Howe: Colorado State University

Journal of the Operational Research Society, 2011, vol. 62, issue 2, 305-312

Abstract: Abstract The solution space of the travelling salesman problem under 2-opt moves has been characterized as having a big-valley structure, in which the evaluation of a tour is positively correlated to the distance of the tour from the global optimum. We examine the big-valley hypothesis more closely and show that while the big-valley structure does appear in much of the solution space, it breaks down around local optima that have solutions whose evaluation is very close to that of the global optimum; multiple funnels appear around local optima with evaluations close to the global optimum. The appearance of multiple funnels explains why certain iterated local search heuristics can quickly find high-quality solutions, but fail to consistently find the global optimum. We then investigate a novel search operator, which is demonstrated to have the ability to escape funnels at evaluations close to the global optimum.

Keywords: combinatorial optimization; local search; travelling salesman problem (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1057/jors.2010.116

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