Über die Analyse randomisierter Suchheuristiken und den Entwurf spezialisierter Algorithmen im Bereich der kombinatorischen Optimierung

Dieser Beitrag ist eine Zusammenfassung der gleichnamigen Dissertation. Der Schwerpunkt der Arbeit liegt auf der theoretischen Analyse randomisierter Suchheuristiken wie evolutionarer Algorithmen, insbesondere in Bezug auf ihre Laufzeit bei der Losung kombinatorischer Optimierungsprobleme. Neben einfachen randomisierten Suchheuristiken, die zu jedem Zeitpunkt nur einen Suchpunkt betrachten, werden auch evolutionare Algorithmen mit groseren Populationen untersucht. Dabei werden jeweils neue und allgemeine Methoden zur Analyse randomisierter Suchheuristiken entwickelt. Abschliesend wird ein spezialisierter Algorithmus fur ein aktuelles kombinatorisches Optimierungsproblem vorgestellt.

[1]  Shang-Hua Teng,et al.  Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time , 2001, STOC '01.

[2]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[3]  Anton V. Eremeev,et al.  A Study on Performance of the (1+1)-Evolutionary Algorithm , 2002, FOGA.

[4]  Serge A. Plotkin,et al.  Fast approximation algorithm for minimum cost multicommodity flow , 1995, SODA '95.

[5]  Martin Raab,et al.  "Balls into Bins" - A Simple and Tight Analysis , 1998, RANDOM.

[6]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[7]  Jens Jägersküpper,et al.  Analysis of a Simple Evolutionary Algorithm for Minimization in Euclidean Spaces , 2003, ICALP.

[8]  Susanne Albers,et al.  Minimizing Stall Time in Single and Parallel Disk Systems Using Multicommodity Network Flows , 2001, RANDOM-APPROX.

[9]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[10]  J. Crutchfield,et al.  Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory , 1998, Machine Learning.

[11]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[12]  Günter Rudolph,et al.  Takeover Times and Probabilities of Non-Generational Selection Rules , 2000, GECCO.

[13]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[14]  T. Lindvall.  Lectures on the Coupling Method , 1992 .

[15]  Carsten Witt,et al.  An Analysis of the (µ+1) EA on Simple Pseudo-Boolean Functions , 2004, GECCO.

[16]  Stefan Droste,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Analysis of the (1+1) Ea for a Dynamically Bitwise Changing Onemax Analysis of the (1+1) Ea for a Dynamically Bitwise Changing Onemax , 2003 .

[17]  Tobias Storch,et al.  On the Choice of the Population Size , 2004, GECCO.

[18]  Laszlo A. Belady,et al.  A Study of Replacement Algorithms for Virtual-Storage Computer , 1966, IBM Syst. J..

[19]  Stefan Droste.  Zu Analyse und Entwurf evolutionärer Algorithmen , 2000 .

[20]  Xin Yao,et al.  From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms , 2002, IEEE Trans. Evol. Comput..

[21]  Ingo Wegener,et al.  Real Royal Road Functions for Constant Population Size , 2003, GECCO.

[22]  Stefan Droste,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Analysis of the (1+1) EA for a Noisy OneMax , 2004 .

[23]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[24]  E. G. Coffman,et al.  A Note on Expected Makespans for Largest-First Sequences of Independent Tasks on Two Processors , 1984, Math. Oper. Res..

[25]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[26]  Michel Loève,et al.  Probability Theory I , 1977 .

[27]  Anna R. Karlin,et al.  A study of integrated prefetching and caching strategies , 1995, SIGMETRICS '95/PERFORMANCE '95.

[28]  Martin Dietzfelbinger,et al.  The analysis of a recombinative hill-climber on H-IFF , 2003, IEEE Trans. Evol. Comput..

[29]  Ingo Wegener,et al.  Real royal road functions--where crossover provably is essential , 2001, Discret. Appl. Math..

[30]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[31]  Carsten Witt,et al.  UNIVERSITY OF DORTMUND REIHE COMPUTATIONAL INTELLIGENCE COLLABORATIVE RESEARCH CENTER 531 Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Worst-Case and Average-Case Approximations by Simple Randomized Search Heuristics , 2004 .

[32]  Oliver Giel,et al.  Expected runtimes of a simple multi-objective evolutionary algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[33]  Simon Fischer.  A Polynomial Upper Bound for a Mutation-Based Algorithm on the Two-Dimensional Ising Model , 2004, GECCO.

[34]  Marco Laumanns,et al.  Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions , 2004, IEEE Transactions on Evolutionary Computation.

[35]  René Beier,et al.  Typical properties of winners and losers in discrete optimization , 2004, STOC '04.

[36]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[37]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[38]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[39]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[40]  George S. Lueker.  Exponentially small bounds on the expected optimum of the partition and subset sum problems , 1998 .

[41]  Hans-Paul Schwefel,et al.  How to analyse evolutionary algorithms , 2002, Theor. Comput. Sci..

[42]  Susanne Albers,et al.  Integrated Prefetching and Caching with Read and Write Requests , 2003, WADS.

[43]  C. Witt.  Population size vs. runtime of a simple EA , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[44]  Thomas Jansen,et al.  Exploring the Explorative Advantage of the Cooperative Coevolutionary (1+1) EA , 2003, GECCO.

[45]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[46]  I. Wegener,et al.  Dynamic Parameter Control in Simple Evolutionary Algorithms , 2001 .

[47]  Ingo Wegener,et al.  On the utility of populations in evolutionary algorithms , 2001 .

[48]  Anna R. Karlin,et al.  Implementation and performance of integrated application-controlled file caching, prefetching, and disk scheduling , 1996, TOCS.

[49]  Angelika Steger,et al.  Diskrete Strukturen 2 , 2002 .

[50]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[51]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .

[52]  René Beier,et al.  Random knapsack in expected polynomial time , 2004, J. Comput. Syst. Sci..

[53]  Jim Zelenka,et al.  Informed prefetching and caching , 1995, SOSP.

[54]  Xin Yao,et al.  Drift analysis and average time complexity of evolutionary algorithms , 2001, Artif. Intell..

[55]  X. Yao,et al.  An analysis of evolutionary algorithms for finding approximation solutions to hard optimisation problems , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[56]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[57]  Nancy L. Garcia,et al.  On mixing times for stratified walks on the d-cube , 2002, Random Struct. Algorithms.

[58]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[59]  Thomas Jansen,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Evolutionary Algorithms-How to Cope With Plateaus of Constant Fitness and When to Reject Strings of the Same Fitness , 2001 .

[60]  Heinz Mühlenbein,et al.  How Genetic Algorithms Really Work: Mutation and Hillclimbing , 1992, PPSN.

[61]  Carsten Witt,et al.  Runtime Analysis of the ( μ +1) EA on Simple Pseudo-Boolean Functions , 2006 .

[62]  John N. Tsitsiklis,et al.  Introduction to Probability , 2002 .

[63]  Ingo Wegener,et al.  The Ising Model on the Ring: Mutation Versus Recombination , 2004, GECCO.

[64]  Anna R. Karlin,et al.  Near-Optimal Parallel Prefetching and Caching , 2000, SIAM J. Comput..

[65]  B. Hajek.  Hitting-time and occupation-time bounds implied by drift analysis with applications , 1982, Advances in Applied Probability.

[66]  Ingo Wegener,et al.  Fitness Landscapes Based on Sorting and Shortest Paths Problems , 2002, PPSN.

[67]  Jim Griffioen,et al.  Reducing File System Latency using a Predictive Approach , 1994, USENIX Summer.

[68]  Frank Neumann,et al.  Expected runtimes of evolutionary algorithms for the Eulerian cycle problem , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[69]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[70]  Susanne Albers,et al.  Integrated prefetching and caching in single and parallel disk systems , 2003, SPAA '03.

[71]  Bruce E. Hajek,et al.  The time complexity of maximum matching by simulated annealing , 1988, JACM.

[72]  Thomas Jansen.  On the utility of populations , 2004 .

[73]  I. Wegener,et al.  On the Optimization of Monotone Polynomials by the (1+1) EA and Randomized Local Search , 2003, GECCO.

[74]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[75]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[76]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[77]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .