Exploring the runtime of an evolutionary algorithm for themulti-objective shortest path problem

Evolutionary Computation

Volumn 18, Issue 3, 2010, Pages 357-381

  Horoba, Christian ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Approximation algorithms; Combinatorial optimization; Evolutionary optimization; Fully polynomial time randomized approximation scheme (FPRAS); Multi objective optimization; Runtime analysis; Shortest path problem

Indexed keywords

EVOLUTIONARY OPTIMIZATION; MULTI OBJECTIVE; POLYNOMIAL-TIME; RUNTIME ANALYSIS; SHORTEST PATH PROBLEM;

COMBINATORIAL OPTIMIZATION; EVOLUTIONARY ALGORITHMS; FUNCTION EVALUATION; GRAPH THEORY; MULTIOBJECTIVE OPTIMIZATION; POLYNOMIAL APPROXIMATION;

APPROXIMATION ALGORITHMS;

ALGORITHM; ARTICLE; EVOLUTION; STATISTICAL MODEL;

ALGORITHMS; EVOLUTION; MODELS, STATISTICAL; BIOLOGICAL EVOLUTION;

EID: 77956531739     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/EVCO_a_00014     Document Type: Article

References (30)

1. Alon, N., and Spencer, J. H. (2000). The probabilistic method. New York: Wiley.
2. Doerr, B., Happ, E., and Klein, C. (2007). A tight analysis of the (1+1)-EA for the single source shortest path problem. In IEEE Congress on Evolutionary Computation (CEC), pp. 1890-1895.
3. Doerr, B., Happ, E., and Klein, C. (2008). Crossover can provably be useful in evolutionary computation. In Genetic and Evolutionary Computation Conference (GECCO), pp. 539-546.
4. Doerr, B., Hebbinghaus, N., and Neumann, F. (2007). Speeding up evolutionary algorithms through asymmetric mutation operators. Evolutionary Computation, 15(4):401-410.
5. Doerr, B., and Johannsen, D. (2007). Adjacency list matchings-An ideal genotype for cycle covers. In Genetic and Evolutionary Computation Conference (GECCO), pp. 1203-1210.
6. Doerr, B., Klein, C., and Storch, T. (2007). Faster evolutionary algorithms by superior graph representations. In IEEE Symposium on Foundations of Computational Intelligence (FOCI), pp. 245-250.
7. Droste, S., Jansen, T., andWegener, I. (2002). On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science, 276(1-2):51-81.
8. Ehrgott, M. (2005). Multicriteria optimization, 2nd ed. Berlin: Springer.
9. Garey, M. R., and Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: W. H. Freeman.
10. Giel, O. (2003). Expected runtimes of a simple multi-objective evolutionary algorithm. In IEEE Congress on Evolutionary Computation (CEC), pp. 1918-1925.
11. Giel, O., and Wegener, I. (2003). Evolutionary algorithms and the maximum matching problem. In Symposium on Theoretical Aspects of Computer Science (STACS), pp. 415-426.
12. Hansen, P. (1979). Bicriterion path problems. In International Conference onMultiple CriteriaDecision Making (MCDM), pp. 109-127.
13. Horoba, C. (2009). Analysis of a simple evolutionary algorithm for the multiobjective shortest path problem. In Foundations of Genetic Algorithms Workshop (FOGA), pp. 113-120.
14. Horoba, C., and Neumann, F. (2008). Benefits and drawbacks for the use of ε-dominance in evolutionary multi-objective optimization. In Genetic and Evolutionary Computation Conference (GECCO), pp. 641-648.
15. Laumanns, M., Thiele, L., Deb, K., and Zitzler, E. (2002). Combining convergence and diversity in evolutionary multiobjective optimization. Evolutionary Computation, 10(3):263-282.
16. Laumanns M., Thiele, L., and Zitzler, E. (2004). Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions. IEEE Transactions on Evolutionary Computation, 8(2):170-182.
17. Motwani, R., and Raghavan, P. (1995). Randomized algorithms. Cambridge, UK: Cambridge University Press.
18. Müller-Hannemann, M., and Weihe, K. (2006). On the cardinality of the Pareto set in bicriteria shortest path problems. Annals of Operations Research, 147(1):269-286.
19. Neumann, F. (2007). Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem. European Journal of Operational Research, 181(3):1620-1629.
20. Neumann, F. (2008). Expected runtimes of evolutionary algorithms for the Eulerian cycle problem. Computers and Operations Research, 35(9):2750-2759.
21. Neumann, F., and Reichel, J. (2008). Approximating minimum multicuts by evolutionary multiobjective algorithms. In International Conference on Parallel Problem Solving from Nature (PPSN), pp. 72-81.
22. Neumann, F., and Wegener, I. (2006). Minimum spanning trees made easier via multi-objective optimization. Natural Computing, 5(3):305-319.
23. Neumann, F., andWegener, I. (2007). Randomized local search, evolutionary algorithms, and the minimum spanning tree problem. Theoretical Computer Science, 378(1):32-40.
24. Oliveto, P. S., He, J., and Yao, X. (2007). Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results. International Journal of Automation and Computing, 4(3):281-293.
25. Papadimitriou, C., and Yannakakis, M. (2000). On the approximability of trade-offs and optimal access of web sources. In Symposium on Foundations of Computer Science (FOCS), pp. 86-92.
26. Raith, A., and Ehrgott, M. (2009). A comparison of solution strategies for biobjective shortest path problems. Computers and Operations Research, 36(4):1299-1331.
27. Scharnow, J., Tinnefeld, K., and Wegener, I. (2004). The analysis of evolutionary algorithms on sorting and shortest paths problems. Journal of Mathematical Modelling and Algorithms, 3(4):349-366.
28. Tsaggouris, G., and Zaroliagis, C. (2006). Multiobjective optimization: Improved FPTAS for shortest paths and non-linear objectives with applications. In International Symposium on Algorithms and Computation (ISAAC), pp. 389-398.
29. Warburton, A. (1987). Approximation of Pareto optima in multiple-objective shortest path problems. Operations Research, 35(1):70-79.
30. Witt, C. (2005). Worst-case and average-case approximations by simple randomized search heuristics. In Symposium on Theoretical Aspects of Computer Science (STACS), pp. 44-56.