Abstract
There are many alternatives to handle discrete optimization problems in applications. Problem-specific algorithms vs. heuristics, exact optimization vs. approximation vs. heuristic solutions, guaranteed run time vs. expected run time vs. experimental run time analysis. Here, a framework for a theory of randomized search heuristics is presented. After a brief history of discrete optimization, scenarios are discussed where randomized search heuristics are appropriate. Different randomized search heuristics are presented and it is argued why the expected optimization time of heuristics should be analyzed. Afterwards, the tools for such an analysis are described and applied to some well-known discrete optimization problems. Finally, a complexity theory of so-called black-box problems is presented and it is shown how the limits of randomized search heuristics can be proved without assumptions like NP≠P. This survey article does not contain proofs but hints where to find them.
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References
Aldous, D.: Minimization algorithms and random walk on the d-cube. The Annals of Probability 11, 403–413 (1983)
Dietzfelbinger, M., Naudts, B., van Hoyweghen, C., Wegener, I.: The analysis of a recombinative hill-climber on H-IFF. Accepted for publication in IEEE–Trans. on Evolutionary Computation (2002)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276, 51–81 (2002)
Droste, S., Jansen, T., Wegener, I.: Upper and lower bounds for randomized search heuristics in black-box optimization. Accepted for publication in Theory of Computing Systems (2003)
Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press, Piscataway (1995)
Garey, M.R., Johnson, D.B.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Giel, O., Wegener, I.: Evolutionary algorithms and the maximum matching problem. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 415–426. Springer, Heidelberg (2003)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)
Hochbaum, D. (ed.): Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston (1997)
Holland, J.H.: Adaptation in Natural and Artificial Systems. Univ. of Michigan, MI (1975)
Jansen, T., Wegener, I.: Real royal road functions – where crossover is provably essential. In: Proc. of the Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 375–382. Morgan Kaufmann, San Mateo (2001)
Jansen, T., Wegener, I.: The analysis of evolutionary algorithms – a proof that crossover really can help. Algorithmica 34, 47–66 (2002)
Neumann, F., Wegener, I.: Randomized local search, evolutionary algorithms, and the minimum spanning tree problem (2003) (submitted for publication)
Ollivier, Y.: Rate of convergence of crossover operators. Random Structures and Algorithms 23, 58–72 (2003)
Rabani, Y., Rabinovich, Y., Sinclair, A.: A computational view of population genetics. Random Structures and Algorithms 12, 314–330 (1998)
Ranade, A.G.: How to emulate shared memory. Journal of Computer and System Sciences 42, 307–326 (1991)
Rechenberg, I.: Evolutionsstrategie 1994. Frommann-Holzboog, Stuttgart (1994)
Sasaki, G.H., Hajek, B.: The time complexity of maximum matching by simulated annealing. Journal of the ACM 35, 387–403 (1988)
Scharnow, J., Tinnefeld, K., Wegener, I.: Fitness landscapes based on sorting and shortest paths problems. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 54–63. Springer, Heidelberg (2002)
Schwefel, H.-P.: Evolution and Optimum Seeking. Wiley, New York (1995)
Spielman, D.A., Teng, S.-H.: Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. In: Proc. of 33rd ACM Symp. on Theory of Computing (STOC), pp. 296–305 (2001)
Wegener, I., Witt, C.: On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean functions. Accepted for publication in Journal of Discrete Algorithms (2002)
Wegener, I., Witt, C.: On the optimization of monotone polynomials by simple randomized search heuristics. Accepted for publication in Combinatorics, Probability and Computing (2003)
Yao, A.C.: Probabilistic computations: Towards a unified measure of complexity. In: Proc. of 17th IEEE Symp. on Foundations of Computer Science (FOCS), pp. 222–227 (1977)
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Wegener, I. (2004). Randomized Search Heuristics as an Alternative to Exact Optimization. In: Lenski, W. (eds) Logic versus Approximation. Lecture Notes in Computer Science, vol 3075. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25967-1_10
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DOI: https://doi.org/10.1007/978-3-540-25967-1_10
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