Abstract
Multi-trial Lin-Kernighan-Helsgaun 2 (LKH-2) is widely considered to be the best Interated Local Search heuristic for the Traveling Salesman Problem (TSP) and has found the best-known solutions to a large number of benchmark problems. Although LKH-2 performs exceptionally well on most instances, it is known to have difficulty on clustered instances of the TSP. Generalized Partition Crossover (GPX) is a crossover operator for the TSP that efficiently constructs new solutions by partitioning a graph constructed from the union of two solutions. We show that GPX is especially well-suited for clustered instances and evaluate its ability to improve solutions found by LKH-2. We present two methods of combining GPX with multi-trial LKH-2. We find that combining GPX with LKH-2 dramatically improves the evaluation of solutions found by LKH-2 alone on clustered instances with sizes ranging from 3,000 to 30,000 cities.
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References
Applegate, D., Cook, W., Rohe, A.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS Journal on Computing 15(1), 82–92 (2003)
Helsgaun, K.: General k-opt submoves for the Lin-Kernighan TSP heuristic. Mathematical Programming Computation 1(2), 119–163 (2009)
Johnson, D.S., Mcgeoch, L.A.: The traveling salesman problem: A case study in local optimization. In: Local Search in Combinatorial Optimization, pp. 215–310. John Wiley and Sons (1997)
Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Operations Research 21(2), 498–516 (1973), http://dx.doi.org/10.2307/169020
Lourenço, H., Martin, O., Stützle, T.: Iterated local search. In: Handbook of Metaheuristics, pp. 320–353 (2003)
Möbius, A., Freisleben, B., Merz, P., Schreiber, M.: Combinatorial optimization by iterative partial transcription. Physical Review E 59(4), 4667 (1999)
Neto, D.: Efficient cluster compensation for Lin-Kernighan heuristics. Ph.D. thesis, University of Toronto (1999)
Papadimitriou, C.: The complexity of the Lin-Kernighan heuristic for the traveling salesman problem. SIAM Journal on Computing 21, 450 (1992)
Whitley, D., Hains, D., Howe, A.: Tunneling between optima: partition crossover for the traveling salesman problem. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 915–922. ACM (2009)
Whitley, D., Hains, D., Howe, A.: A Hybrid Genetic Algorithm for the Traveling Salesman Problem Using Generalized Partition Crossover. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 566–575. Springer, Heidelberg (2010)
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Hains, D., Whitley, D., Howe, A. (2012). Improving Lin-Kernighan-Helsgaun with Crossover on Clustered Instances of the TSP. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds) Parallel Problem Solving from Nature - PPSN XII. PPSN 2012. Lecture Notes in Computer Science, vol 7492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32964-7_39
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DOI: https://doi.org/10.1007/978-3-642-32964-7_39
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