Abstract
The analysis of evolutionary algorithms is up to now limited to special classes of functions and fitness landscapes. It is not possible to describe those subproblems of NP-hard optimization problems where certain evolutionary algorithms work in polynomial time. Therefore, fitness landscapes based on important computer science problems as sorting and shortest paths problems are investigated here. Although it cannot be expected that evolutionary algorithms outperform the well-known problem specific algorithms on these simple problems, it is interesting to analyze how evolutionary algorithms work on these fitness landscapes which are based on practical problems. The following results are obtained:
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Sorting is the maximization of “sortedness” which is measured by one of several well-known measures of presortedness. The different measures of presortedness lead to fitness landscapes of quite different difficulty for EAs.
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Shortest paths problems are hard for all types of EA, if they are considered as single-objective optimization problems, while they are easy as multi-objective optimization problems.
This work was supported by the Deutsche Forschungsgemeinschaft (DFG) as part of the Collaborative Research Center “Computational Intelligence” (SFB 531).
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References
Bäck, T., Fogel, D.B., and Michalewicz, Z. (Eds.) (1997). Handbook of Evolutionary Computation. Oxford University Press.
Droste, S., Jansen, T., and Wegener, I. (1998a). A rigorous complexity analysis of the (1+1) evolutionary algorithm for separable functions with Boolean inputs. Evolutionary Computation 6, 185–196.
Droste, S., Jansen, T., and Wegener, I. (1998b). On the optimization of unimodal functions with the (1+1) evolutionary algorithm. Parallel Problem Solving from Nature— PPSN V, LNCS 1498, 13–22.
Horn, J., Goldberg, D.E., and Deb, K. (1994). Long path problems. Parallel Problem Solving from Nature— PPSN III, LNCS 866, 149–158.
Jansen, T., and Wegener, I. (2001a). Real royal road functions-where crossover provably is essential. Genetic and Evolutionary Computation Conf.— GECCO, 375–382.
Jansen, T., and Wegener, I. (2001b). Evolutionary algorithms-how to cope with plateaus of constant fitness and when to reject strings of the same fitness. IEEE Trans. on Evolutionary Computation 5, 589–599.
Mitchell, M., Holland, J.H., and Forrest, S. (1994). When will a genetic algorithm outperform hill climbing. In J. Cowan, G. Tesauro, and J. Alspector (Eds.): Advances in Neural Information Processing Systems. Morgan Kaufman.
Petersson, O., and Moffat, A. (1995). A framework for adaptive sorting. Discrete Applied Mathematics 59, 153–179.
Rudolph, G. (1997). How mutations and selection solve long path problems in polynomial expected time. Evolutionary Computation 4, 195–205.
Wegener, I. (2001). Theoretical aspects of evolutionary algorithms. Int. Colloq. on Automata, Languages, and Programming— ICALP, LNCS 2076, 64–78.
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Scharnow, J., Tinnefeld, K., Wegener, I. (2002). Fitness Landscapes Based on Sorting and Shortest Paths Problems. In: Guervós, J.J.M., Adamidis, P., Beyer, HG., Schwefel, HP., Fernández-Villacañas, JL. (eds) Parallel Problem Solving from Nature — PPSN VII. PPSN 2002. Lecture Notes in Computer Science, vol 2439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45712-7_6
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DOI: https://doi.org/10.1007/3-540-45712-7_6
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