Advertisement

A Model for Analyzing Black-Box Optimization

  • Vinhthuy Phan
  • Steven Skiena
  • Pavel Sumazin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)

Abstract

The design of heuristics for NP-hard problems is perhaps the most active area of research in the theory of combinatorial algorithms. However, practitioners more often resort to local-improvement heuristics such as gradient-descent search, simulated annealing, tabu search, or genetic algorithms. Properly implemented, local-improvement heuristics can lead to short, efficient programs that yield reasonable solutions. Designers of efficient local-improvement heuristics must make several crucial decisions, including the choice of neighborhood and heuristic for the problem at hand. We are interested in developing a general methodology for predicting the quality of local-neighborhood operators and heuristics, given a time budget and a solution evaluation function.

Keywords

Local Search Tabu Search Travel Salesman Problem Vertex Cover Hill Climbing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aarts, E., Lenstra, J.K.: The Traveling Salesman Problem: A Case Study. Wiley, Chichester (1997)Google Scholar
  2. 2.
    Agrawal, M., Allender, E., Impagliazzo, R., Pitassi, T., Rudich, S.: Reducing the complexity of reductions. In: ACM Symposium on Theory of Computing, pp. 730–738 (1997)Google Scholar
  3. 3.
    Aldous, D., Vazirani, U.V.: Go with the Winners algorithms. In: IEEE Symposium on Foundations of Computer Science, pp. 492–501 (1994)Google Scholar
  4. 4.
    Beame, P., Cook, S., Edmonds, J., Impagliazzo, R., Pitassi, T.: The relative complexity of NP search problems. In: ACM Symposium on Theory of Computing, pp. 303–314 (1995)Google Scholar
  5. 5.
    Carson, T., Impagliazzo, R.: Hill-climbing finds random planted bisections. In: Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 903–909 (2001)Google Scholar
  6. 6.
    Gutin, G., Yeo, A.: TSP heuristics with large domination number. Technical Report PP-1998-13, Odense University, Denmark, August 20 (1998) Google Scholar
  7. 7.
    Gutin, G., Yeo, A., Zverivich, A.: Polynominal restriction approach for the atsp and stsp. The Traveling Salesman Problem (to appear)Google Scholar
  8. 8.
    Hajek, B.: Cooling schedules for optimal simulated annealing. Math. Operations Res. 13, 311–329 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ho, Y., Sreeniva, R., Vakili, P.: Ordinal optimization of discrete event dynamic systems. J. on DEDS 2, 61–68 (1992)zbMATHGoogle Scholar
  10. 10.
    Johnson, D.S., Papadimitriou, C.H., Yannakakis, M.: How easy is local search? In: Proc. 26th Annual Symp. on Foundations of Computer Science, pp. 39–42 (1985); Also J. Computer System Sci. 37(1), 79-100 (1988)Google Scholar
  11. 11.
    Juels, A.: Topics in black box optimization. Ph.D. Thesis, University of California, Berkeley (1996) Google Scholar
  12. 12.
    Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. The Bell system technical journal 49(1), 291–307 (1970)Google Scholar
  13. 13.
    Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling salesman problem. Operations Research 21, 498–516 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Martin, O., Otto, S., Felten, E.: Large-step markov chains for the traveling salesman problem. Complex Systems 5, 299–326 (1991)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Papadimitriou, C.H., Schaffer, A., Yannakakis, M.: On the complexity of local search. In: Proc. 22nd Annual ACM Symp. on Theory of Computing, pp. 438–445 (1990)Google Scholar
  16. 16.
    Phan, V., Sumazin, P., Skiena, S.: A time-sensitive system for black-box combinatorial optimization. In: 4th Workshop on Algorithm Engineering and Experiments, San Francisco, USA (January 2002)Google Scholar
  17. 17.
    Reinelt, G.: TSPLIB. University of Heidelberg, www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95
  18. 18.
    Resende, M.: Max-Satisfiability Data. Information Sciences Research Center, AT&T, www.research.att.com/~mgcr
  19. 19.
    Tovey, C.A.: Local improvements on discrete structures. In: Aarts, E., Lenstra, J.K. (eds.) Local Search and Combinatorial Optimization, pp. 57–89. John Wiley and Sons Ltd., Chichester (1997)Google Scholar
  20. 20.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Vinhthuy Phan
    • 1
  • Steven Skiena
    • 2
  • Pavel Sumazin
    • 3
  1. 1.Computer ScienceSUNY at Stony BrookStony BrookUSA
  2. 2.Computer ScienceState University of New York at Stony BrookStony BrookUSA
  3. 3.Computer SciencePortland State UniversityOregon

Personalised recommendations