A note on problem difficulty measures in black-box optimization: Classification, realizations and predictability

Evolutionary Computation

Volumn 15, Issue 4, 2007, Pages 435-443

  He, Jun ^a   Reeves, Colin ^b   Wit, Carsten ^c   Yao, Xin ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b Institute for Clean Growth and Future Mobility   (United Kingdom)

^c TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Black box optimization; Evolutionary algorithm; Problem difficulty measure; Running time; Satisfiability problem

Indexed keywords

ALGORITHM; ARTICLE; COMPUTER SIMULATION; STATISTICAL MODEL; THEORETICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; MODELS, STATISTICAL; MODELS, THEORETICAL;

EID: 38149103197     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/evco.2007.15.4.435     Document Type: Article

References (28)

1. Borenstein, Y. and Poli, R. (2004). Fitness distributions and GA hardness. In Proceedings of the 8th International Conference on Parallel Problem Solving from Nature (PPSN 2004), pages 11-20. Springer.
2. Borenstein, Y. and Poli, R. (2005). Information landscapes and problem hardness. In Proceedings of the 2005 Genetic and Evolutionary Computation Conference (GECCO 2005), pages 1425-1431. ACM Press.
3. Davidor, Y. (1991). Epistasis variance: A viewpoint on GA-hardness. In Rawlins, G. J. E., editor, Foundations of Genetic Algorithms (FOGA), pages 23-35, San Mateo, CA, Morgan Kaufmann.
4. Deb, K. and Goldberg, D. E. (1993). Sufficient conditions for deceptive and easy binary functions. Annals of Mathematics and Artificial Intelligence 10(4):385-408.
5. Droste, S., Jansen, T., and Wegener, I. (2002). On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276, 51-81.
6. Droste, S., Jansen. T., and Wegener, I. (2006). Upper and lower bounds for randomized search heuristics in black-box optimization. Theory of Computing Systems 39(4):525-544.
7. Forrest, S. and Mitchell, M. (1993). What makes a problem hard for a genetic algorithm? Some anomalous results and their explanation. Machine Learning 13:285-319.
8. Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA.
9. Gottlieb, J., Marchiori, E., and Rossi, C. (2002). Evolutionary algorithms for the satisfiability problem. Evolutionary Computation 10(1):35-50.
10. He, J. and Yao, X. (2003). Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artificial Intelligence 145(1-2):59-97.
11. Horn, J. and Goldberg, D. E. (1995). Genetic algorithm difficulty and the modality of fitness landscapes. In Whitley, L. D. and Vose, M. D., editors, Foundations of Genetic Algorithms (FOGA) 3, pages 243-269, San Mateo, CA, Morgan Kaufmann.
12. Horn, J., Goldberg, D. E., and Deb, K. (1994). Long path problems. In Proceedings of the 3rd International Conference on Parallel Problem Solving from Nature (PPSN 1994), pages 149-158, Springer.
13. Jansen, T. (2001). On classifications of fitness functions. In L. Kallel, B. Naudts and A. Rogers (Eds:), Theoretical Aspects of Evolutionary Computing, pages 371-386. Springer.
14. Jones, T. and Forrest, S. (1995). Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In Eshelman, L. J., editor, Proceedings of the 6th International Conference on Genetic Algorithms, pages 184-192, San Mateo, CA, Morgan Kaufmann.
15. Manderick, B., de Weger, M., and Spiessens, P. (1991). The genetic algorithm and the structure of the fitness landscape. In Belew, R. K. and Booker, L. B., editors, Proceedings of the 4th International Conference on Genetic Algorithms, pages 143-150, San Mateo, CA. Morgan Kaufmann.
16. Michalewicz, Z. (1996). Genetic Algorithms + Data Structure = Evolution Programs. Springer Verlag, New York, third edition.
17. Naudts, B. and Kallel, L. (2000). A comparison of predictive measure of problem difficulty in evolutionary algorithms. IEEE Transactions on Evolutionary Computation 4(1):1-15.
18. Papadimitriou, C. H. and Steiglitz, K. (1998). Combinatorial Optimization: Algorithms and Complexity. Dover, Mineola, NY.
19. Radcliffe, N. J. and Surry, P. D. (1995). Formae and the variance of fitness. In Whitley, L. D. and Vose, M. D., editors, Foundations of Genetic Algorithms (FOGA) 3, pages 51-72, San Mateo, CA., Morgan Kaufmann.
20. Reeves, C. R. (1999). Predictive measures for problem difficulty. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC 1999), pages 736-743, IEEE Press.
21. Rudolph, G. (1996). How mutation and selection solve long path problems in polynomial expected time. Evolutionary Computation 4(2):194-205.
22. Smith, T., Husbands, P., Layzell, P. J., and O'Shea, M. (2002). Fitness landscapes and evolvability. Evolutionary Computation 10(1):1-34.
23. Vose, M. D. and Liepins, G. E. (1991). Punctuated equilibria in genetic search. Complex Systems,5:31-44.
24. Vose, M. D. and Wright, A. H. (1995). Stability of vertex fixed points and applications. In Whitley, L. D. and Vose, M. D., editors, Foundations of Genetic Algorithms (FOGA) 3, pages 103-114, San Mateo, CA, Morgan Kaufmann.
25. Wegener, I. (2005). Complexity Theory - Exploring the Limits of Efficient Algorithms, Springer.
26. Wegener, I. and Witt, C. (2005) On the optimization of monotone polynomials by simple randomized search heuristics. Combinatorics, Probability & Computing 14:225-247.
27. Wilson, S. W (1991). GA-easy does not imply steepest-ascent optimizable. In Belew, R. and Booker, L., editors, Proceedings of the 4th International Conference on Genetic Algorithms, pages 85-89, San Mateo, CA. Morgan Kaufmann.
28. Witt, C. (2005). Worst-case and average-case approximations by simple randomized search heuristics. In: Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science (STACS 2005), pages 44-56, LNCS 3404, Springer.