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The property analysis of evolutionary algorithms applied to spanning tree problems

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Abstract

The search behavior of an evolutionary algorithm depends on the interactions between the encoding that represents candidate solutions to the target problem and the operators that act on that encoding. In this paper, we focus on analyzing some properties such as locality, heritability, population diversity and searching behavior of various decoder-based evolutionary algorithm (EA) frameworks using different encodings, decoders and genetic operators for spanning tree based optimization problems. Although debate still continues on how and why EAs work well, many researchers have observed that EAs perform well when its encoding and operators exhibit good locality, heritability and diversity properties.

We analyze these properties of various EA frameworks with two types of analytical ways on different spanning tree problems; static analysis and dynamic analysis, and then visualize them. We also show through this analysis that EA using the Edge Set encoding (ES) and the Edge Window Decoder encoding (EWD) indicate very good locality and heritability as well as very good diversity property. These are put forward as a potential explanation for the recent finding that they can outperform other recent high-performance encodings on the constrained spanning tree problems.

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References

  1. Alternberg L (1997) Fitness distance correlation analysis: an instructive counterexample. In: Proceeding of the seventh international conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 57–64

    Google Scholar 

  2. Bean JC (1994) Genetic algorithms and random keys for sequencing and optimization. ORSA J Comput 6(2):154–160

    MATH  Google Scholar 

  3. Chou H, Premkumar G, Chu CH (2001) Genetic algorithms for communications network design-an empirical study of the factors that influence performance. IEEE Trans Evol Comput 5(3):236–249

    Article  Google Scholar 

  4. Chu PC, Beasley JE (1998) A genetic algorithm for the multidimensional knapsack problem. J Heuristics 4:63–86

    Article  MATH  Google Scholar 

  5. Deo N, Kumar N (1996) Computation of constrained spanning trees: a unified approach. In: Lecture notes in economics and mathematical systems, vol 450. Springer, Berlin, pp 194–220

    Google Scholar 

  6. Eckert C, Gottlieb J (2002) Direct representation and variation operators for the fixed charge transportation problem. In: Parallel problem solving in nature VII. Lecture notes in computer science, vol 2439. Springer, Berlin, pp 77–87

    Chapter  Google Scholar 

  7. Gaube T, Rothlauf F (2001) The link and node biased encoding revisited: bias and adjustment of parameters. In: Evo worshop 2001. Lecture notes in computer science, vol 2037. Springer, Berlin, pp 1–10

    Google Scholar 

  8. Gen M, Chen R (1997) Genetic algorithms and engineering design. Wiley, New York. Also see (for Prüfer encoding): http://www.ads.tuwien.ac.at/publications/bib/pdf/gottlieb-01.pdf

    Google Scholar 

  9. Gottlieb J, Eckert C (2000) A comparison of two representations for the fixed charge transportation problem. In: Parallel problem solving in nature VI. Lecture notes in computer science, vol 1917. Springer, Berlin, pp 345–354

    Chapter  Google Scholar 

  10. Gottlieb J, Julstrom BA, Raidl GR, Rothlauf F (2000) Prüfer numbers: a poor representation of spanning trees of evolutionary search. Working papers in information systems. University of Bayreuth

  11. Gottlieb J, Raidl GR (2000) The effects of locality on the dynamics of decoder-based evolutionary search. In: Proceedings of the 2000 genetic and evolutionary computation conference. Morgan Kaufmann, San Francisco, pp 283–290

    Google Scholar 

  12. Jones T, Forrest S (1995) Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings the sixth international conference on genetic algorithm. Morgan Kaufmann, San Francisco, pp 184–192

    Google Scholar 

  13. Julstrom BA (2001) The Bolb code: a better string coding of spanning trees for evolutionary search. In: Genetic and evolutionary computation conference. Morgan Kaufmann, San Francisco, pp 256–261

    Google Scholar 

  14. Krishnamoorthy M, Ernst A, Sharaiha Y (2001) Comparison of algorithms for the DC-MST. J Heuristics 7:587–611

    Article  MATH  Google Scholar 

  15. Kruskal JB (1956) On the shortest spanning tree of a graph and the travelling salesman problem. In: Proceedings of the American mathematical society, vol 7, no 1, pp 48–50

  16. Manderick B, de Weger M, Spiessens P (1991) The genetic algorithm and the structure of the fitness landscape. In: The 4th international conference on genetic algorithms, pp 143–150

  17. Merz P, Freisleben B (2000) Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning. Evol Comput 8(1):61–91

    Article  Google Scholar 

  18. Palmer CC, Kershenbaum A (1995) An approach to a problem in network design using genetic algorithms. Networks 26:151–163

    Article  MATH  Google Scholar 

  19. Palmer CC, Kershenbaum A (1994) Representating trees in genetic algorithms. In: Proceedings of the IEEE conference on evolutionary computation, pp 379–384

  20. Paulden T, Smith DK (2006) From the dandelion code to the rainbow code: a class of bijective spanning tree representations with linear complexity and bounded locality. IEEE Trans Evol Comput 10(2):108–123

    Article  Google Scholar 

  21. Picciotto S (1999) How to encode a tree. PhD dissertation, University of California, San Diego

  22. Prim R (1957) Shortest connection networks and some generalisations. Bell Syst Tech J 36:1389–1401

    Google Scholar 

  23. Raidl GR (2000) An efficient evolutionary algorithm for the degree-constrained minimum spanning tree problem. In: Proceedings of the IEEE CEC, pp 104–111

  24. Raidl GR, Gottlieb J (2005) Empirical analysis of locality, heritability and heuristic bias in evolutionary algorithms: a case study for the multidimensional knapsack problem. Evol Comput 13(4):441–475

    Article  Google Scholar 

  25. Raidl GR, Julstrom B (2003) Edge-sets: an effective evolutionary coding of spanning trees. IEEE Trans Evol Comput 7(3):225–239

    Article  Google Scholar 

  26. Reeves CR, Yamada T (1998) Genetic algorithms, path relinking, and the flowshop sequencing problem. Evol Comput 6:45–60

    Article  Google Scholar 

  27. Rothlauf F (2003) Locality, distance distortion, and binary representations of integers. Working papers in information systems, University of Mannheim

  28. Rothlauf F, Goldberg DE, Heinzl A (2002) Network random keys—a tree network representation scheme for genetic and evolutionary algorithms. Evol Comput 10(1):75–97

    Article  Google Scholar 

  29. Rothlauf F, Goldberg DE (2003) Redundant representations in evolutionary computation. Evol Comput 11(4):381–415

    Article  Google Scholar 

  30. Schuter P (1995) Artificial life and molecular evolutionary biology. In: Moran F et al. (eds) Advances in artificial life. Springer, Berlin, pp 3–19

    Google Scholar 

  31. Schindler B, Rothlauf F, Pesch H (2002) Evolution strategies, network random keys, and the one-max tree problem. In: Evoworkshops. Springer, Berlin, pp 143–52

    Google Scholar 

  32. Sendhoff B, Kreutz M, Seelen WV (1997) A condition for the genotype-phenotype mapping: causality. In: Proceedings of the seventh international conference on genetic algorithms. Morgan Kauffman, San Mateo

    Google Scholar 

  33. Soak MS, Corne D, Ahn BH (2004) A powerful new encoding for tree-based combinatorial optimisation problems. In: Parallel problem solving in nature VIII. Lecture notes in computer science, vol 3242. Springer, Berlin, pp 430–439

    Google Scholar 

  34. Soak MS, Corne D, Ahn BH (2006) The edge-window-decoder representation for tree-based problems. IEEE Trans Evol Comput 10(2):124–144

    Article  Google Scholar 

  35. Soak MS (2006) A new evolutionary approach for the optimum communication spanning tree problem. IEICE Trans Fundam Electron, Commun Comput Sci E89-A(10):2882–2893

    Google Scholar 

  36. Soak MS, Corne D, Ahn BH (2004) A new encoding for the degree constrained minimum spanning tree problem. In: KES 2004. Lecture notes in artificial intelligence, vol 3213. Springer, Berlin, pp 952–958

    Google Scholar 

  37. Stadler PF (1996) Towards a theory of landscapes. In: Complex systems and binary networks. Lecture notes in physics, vol 461. Springer, New York, pp 77–163

    Google Scholar 

  38. Thompson E, Paulden T, Smith DK (2007) The dandelion code: a new coding of spanning trees for genetic algorithms. IEEE Trans Evol Comput 11(1):91–100

    Article  Google Scholar 

  39. Watson JP, Barbulescu L, Whitley LD, Howe AE Contrasting structured and random permutation flow-shop scheduling problems: search-space topology and algorithm performance. http://www.cs.colostate.edu/~genitor/Pubs.html

  40. Weinberger ED (1990) Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol Cybern 63:325–336

    Article  MATH  Google Scholar 

  41. Zhou G, Gen M (1998) An effective GA approach to the quadratic minimum spanning tree problem. Comput Oper Res 25(3):229–237

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Information Examination Team, KIPO, Gov. Complex Daejeon Bldg. 4 920 Dunsandong, Seo-gu, Daejeon, Republic of Korea

    Sang-Moon Soak

  2. Department of Information and Communications, Gwangju Institute of Science and Technology, 1 Oryong-dong, Buk-gu, Gwang ju, 500-712, Republic of Korea

    Moongu Jeon

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  1. Sang-Moon Soak
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Correspondence to Moongu Jeon.

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Soak, SM., Jeon, M. The property analysis of evolutionary algorithms applied to spanning tree problems. Appl Intell 32, 96–121 (2010). https://doi.org/10.1007/s10489-008-0137-8

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  • DOI: https://doi.org/10.1007/s10489-008-0137-8

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