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A Restarting Rule Based on the Schnabel Census for Genetic Algorithms

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Learning and Intelligent Optimization (LION 12 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11353))

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Abstract

A new restart rule is proposed for Genetic Algorithms (GAs) with multiple restarts. The rule is based on the Schnabel Census method, transfered from the biometrics, where it was originally developed for the statistical estimation of a size of animal population. In this paper, the Schnabel Census method is applied to estimate the number of different solutions that may be visited with positive probability, given the current distribution of offspring. The rule consists in restarting the GA as soon as the maximum likelihood estimate reaches the number of different solutions observed at the recent iterations.We demonstrate how the new restart rule can be incorporated into a GA on the example of the Set Cover Problem. Computational experiments on benchmarks from OR-Library show a significant advantage of the GA with the new restarting rule over the original GA. On the unicost instances, the new rule also tends to be superior to the well-known rule, which restarts an algorithm when the current iteration number is twice the iteration number when the best incumbent was found.

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References

  1. Alexandrov, D., Kochetov, Y.: Behavior of the Ant Colony Algorithm for the Set Covering Problem. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds.) Operations Research Proceedings 1999. ORP, vol. 1999, pp. 255–260. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-642-58300-1_38

  2. Balas, E., Niehaus, W.: Optimized crossover-based genetic algorithms for the maximum cardinality and maximum weight clique problems. J. Heuristics 4(2), 107–122 (1998)

    Article  Google Scholar 

  3. Beasley, J.E.: OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41(11), 1069–1072 (1990)

    Article  Google Scholar 

  4. Beasley, J.E., Chu, P.C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2), 394–404 (1996)

    Article  Google Scholar 

  5. Brown, B.W., Hollander, M.: Statistics: A Biomedical Introduction. Wiley, New York (1977)

    Google Scholar 

  6. Caprara, A., Fischetti, M., Toth, P.: Heuristic method for the set covering problem. Oper. Res. 47(5), 730–743 (1999)

    Article  MathSciNet  Google Scholar 

  7. Craig, C.C.: Use of marked specimens in estimating populations. Biometrika 40(1–2), 170–176 (1953)

    Article  Google Scholar 

  8. Erdös, P.: On a combinatorial problem I. Nordisk Mat. Tidskrift 11, 5–10 (1963)

    MathSciNet  MATH  Google Scholar 

  9. Eremeev, A.V.: A genetic algorithm with a non-binary representation for the set covering problem. In: Proceedings of OR’98, pp. 175–181. Springer-Verlag (1999)

    Google Scholar 

  10. Eremeev, A.V., Kovalenko, Y.V.: Genetic algorithm with optimal recombination for the Asymmetric Travelling Salesman Problem. In: Lirkov, I., Margenov, S. (eds.) LSSC 2017. LNCS, vol. 10665, pp. 332–339. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73441-5_36

    Chapter  Google Scholar 

  11. Eremeev, A.V., Reeves, C.R.: Non-parametric estimation of properties of combinatorial landscapes. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoWorkshops 2002. LNCS, vol. 2279, pp. 31–40. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46004-7_4

  12. Fulkerson, D.R., Nemhauser, G.L., Trotter, L.E.: Two computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Math. Program. Stud. 2, 72–81 (1974)

    Article  Google Scholar 

  13. Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of \(NP\)-Completeness. W.H. Freeman and Company, San Francisco (1979)

    Google Scholar 

  14. Garnier, J., Kallel, L.: How to detect all maxima of a function? In: Proceedings of the Second EVONET Summer School on Theoretical Aspects of Evolutionary Computing (Anvers, 1999), pp. 343–370 Springer, Berlin (2001)

    Google Scholar 

  15. Grossman, T., Wool, A.: Computational experience with approximation algorithms for the set covering problem. Eur. J. Oper. Res. 101(1), 81–92 (1997)

    Article  Google Scholar 

  16. Hampson, S., Kibler, D.: Plateaus and Plateau Search in Boolean Satisfiability Problems: When to Give Up Searching and Start Again, pp. 437–456. American Mathematical Society (1996)

    Google Scholar 

  17. Hernando, L., Mendiburu, A., Lozano, J.A.: An evaluation of methods for estimating the number of local optima in combinatorial optimization problems. Evol. Comput. 21(4), 625–658 (2013)

    Article  Google Scholar 

  18. Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  19. Hulin, M.: An optimal stop criterion for genetic algorithms: a Bayesian approach. In: Proceedings of the Seventh International Conference on Genetic Algorithms (ICGA ’97), pp. 135–143. Morgan Kaufmann (1997)

    Google Scholar 

  20. Jansen, T.: On the analysis of dynamic restart strategies for evolutionary algorithms. In: Guervós, J.J.M., Adamidis, P., Beyer, H.-G., Schwefel, H.-P., Fernández-Villacañas, J.-L. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 33–43. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45712-7_4

    Chapter  Google Scholar 

  21. Johnson, N.L., Kotz, S.: Discrete Distributions. Wiley, New York (1969)

    Google Scholar 

  22. Luke, S.: When short runs beat long runs. In: Proceedings of he Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 74–80. Morgan Kaufmann (2001)

    Google Scholar 

  23. Marti, L., Garcia, J., Berlanga, A. and Molina, J. M.: An approach to stopping criteria for multi-objective optimization evolutionary algorithms: the MGBM criterion. In: Proceedings of 2009 IEEE Congress on Evolutionary Computation, Trondheim, pp. 1263–1270. IEEE (2009)

    Google Scholar 

  24. Van Nimwegen, E., Crutchfield, J.P., Mitchell, M.: Finite populations induce metastability in evolutionary search. Phys. Lett. A 229(2), 144–150 (1997)

    Article  MathSciNet  Google Scholar 

  25. Ostrowski, J., Linderoth, J.T., Rossi, F., Smriglio, S.: Solving Steiner triple covering problems. Oper. Res. Lett. 39, 127–131 (2011)

    Article  MathSciNet  Google Scholar 

  26. Paixao, T., Badkobeh, G., Barton, N., et al.: Toward a unifying framework for evolutionary processes. J. Theor. Biol. 383, 28–43 (2015)

    Article  MathSciNet  Google Scholar 

  27. Pledger, S.: The performance of mixture models in heterogeneous closed population capture-recapture. Biometrics 61(3), 868–876 (2005)

    Article  MathSciNet  Google Scholar 

  28. Reeves, C.R.: The “crossover landscape” and the Hamming landscape for binary search spaces. In: Foundations of Genetic Algorithms, vol. 7, pp. 81–98. Morgan Kaufmann, San Francisco (2003)

    Google Scholar 

  29. Reeves, C.R.: Fitness landscapes and evolutionary algorithms. In: Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M., Ronald, E. (eds.) AE 1999. LNCS, vol. 1829, pp. 3–20. Springer, Heidelberg (2000). https://doi.org/10.1007/10721187_1

  30. Reeves, C.R.: Landscapes, operators and heuristic search. Ann. Oper. Res. 86, 473–490 (1999)

    Article  MathSciNet  Google Scholar 

  31. Reeves, C.R.: Direct statistical estimation of GA landscape properties. In: Foundations of Genetic Algorithms, vol. 6, pp. 91–108. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  32. Reeves, C.R.: Estimating the number of optima in a landscape, part II: experimental investigations. Coventry University Technical Report SOR#01-04 (2001)

    Google Scholar 

  33. Schnabel, Z.E.: The estimation of the total fish population of a lake. Am. Math. Mon. 45, 348–352 (1938)

    MathSciNet  MATH  Google Scholar 

  34. Seber, G.A.F.: The Estimation of Animal Abundance. Charles Griffin, London (1982)

    Google Scholar 

  35. Vose, M.D.: The Simple Genetic Algorithm: Foundations and Theory. MIT Press, Cambridge (1999)

    Google Scholar 

  36. Vose, M.D., Wright, A.H.: Stability of vertex fixed points and applications. In: Foundations of Genetic Algorithms, vol. 3, pp. 103–114. Morgan Kaufmann, San Mateo, CA (1995)

    Google Scholar 

  37. Wright, A.H., Rowe, J.E.: Continuous dynamical systems models of steady-state genetic algorithms. In: Foundations of Genetic Algorithms, vol. 6, pp. 209–226. Morgan Kaufmann, San Francisco, CA (2001)

    Google Scholar 

  38. Yagiura, M., Kishida, M., Ibaraki, T.: A 3-flip neighborhood local search for the set covering problem. Eur. J. Oper. Res. 172, 472–499 (2006)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This research is supported by the Russian Science Foundation grant 17-18-01536.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Omsk, Russia

    Anton V. Eremeev

  2. Institute of Scientific Information on Social Sciences RAS, Moscow, Russia

    Anton V. Eremeev

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  1. Anton V. Eremeev
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Correspondence to Anton V. Eremeev .

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Editors and Affiliations

  1. University of Trento, Trento, Italy

    Roberto Battiti

  2. University of Trento, Trento, Italy

    Mauro Brunato

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

  4. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Eremeev, A.V. (2019). A Restarting Rule Based on the Schnabel Census for Genetic Algorithms. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 12 2018. Lecture Notes in Computer Science(), vol 11353. Springer, Cham. https://doi.org/10.1007/978-3-030-05348-2_29

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  • DOI: https://doi.org/10.1007/978-3-030-05348-2_29

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