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Insertion Heuristics for Central Cycle Problems

By John Douglas Lamb

Abstract

A central cycle problem requires a cycle that is\ud reasonably short and keeps a the maximum distance\ud from any node not on the cycle to its nearest\ud node on the cycle reasonably low. The objective\ud may be to minimise maximumdistance or cycle\ud length and the solution may have further constraints.\ud Most classes of central cycle problems\ud are NP-hard. This paper investigates insertion\ud heuristics for central cycle problems, drawing on\ud insertion heuristics for p-centres [7] and travelling\ud salesman tours [21]. It shows that a modified\ud farthest insertion heuristic has reasonable worstcase\ud bounds for a particular class of problem.\ud It then compares the performance of two farthest\ud insertion heuristics against each other and\ud against bounds (where available) obtained by integer\ud programming on a range of problems from\ud TSPLIB [20]. It shows that a simple farthest insertion\ud heuristic is fast, performs well in practice\ud and so is likely to be useful for a general problems\ud or as the basis for more complex heuristics\ud for specific problems

Topics: tour, cycle, centre, eccentricity, cyclelength
Year: 2006
OAI identifier: oai:aura.abdn.ac.uk:2164/96

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Citations

  1. (1996). A review of extensive facility location in networks, doi
  2. (1985). A simple heuristic for the p-centre problem doi
  3. (1977). An analysis of several heuristics for the traveling salesman problem, doi
  4. An analysis of several heuristics for the travelingsalesmanproblem, doi
  5. (2006). An exact algorithm for the capacitated vertex p-center problem, doi
  6. (1998). An O(log ∗ n) approximation algorithm for the asymmetric p-centre problem, doi
  7. (1998). An O(log∗ n) approximation algorithm for the asymmetric p-centre problem, doi
  8. (1998). Combinatorial optimization, doi
  9. (2003). Dominant, an algorithm for the p-center problem, doi
  10. (1979). Easy and hard bottleneck location problems, doi
  11. (1997). Generalized p-center problems: complexity results and approximation algorithms, doi
  12. (2005). k-center problems with minimum coverage, doi
  13. (2004). Large-scale local search heuristics for the capacitated vertex p-center problem, doi
  14. (2003). Lexicographic local search and the p-center problem, doi
  15. (1982). Locating central paths in a graph, doi
  16. (2005). Locating median cycles in networks, doi
  17. (2004). Modelling and solving central cycle problems with integer programming, doi
  18. (1964). Optimum location of switching centers and the absolute centers and medians of a graph, doi
  19. (2003). Solving the p-center problem with tabu search and variable neighbourhood search, doi
  20. The boost graph library, doi
  21. (1994). The median tour and maximal covering tour problems: formulations and heuristics, doi
  22. (1984). The p-centre problem—heuristic and optimal algorithms, doi
  23. (1985). The traveling salesman problem, doi
  24. (1976). Worst-case analysis of a new heuristic for the travelling salesman problem,

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