Algorithmen kurz gefasst by Uwe Schöning

By Uwe Schöning

In kompakter shape macht das Buch mit den wesentlichen Themen vertraut, die in einer Vorlesung ?ber Algorithmen behandelt werden. Im Mittelpunkt stehen dabei die verschiedensten sequentiellen Algorithmen, deren Komplexit?tsanalyse und allgemeine Algoithmen-Paradigma. Prof. Sch?ning gelingt es, kurz, konkret und verst?ndlich die wichtigsten algorithmischen Aufgabenstellungen (Selektion, Sortieren, Hashing), Algorithmen auf Graphen, algebraische und zahlentheoretische Verfahren zu behandeln. Hinzu kommen heuristische Algorithmenprinzipien wie z.B. genetisches Programmieren.

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B Set a counter countj to equal the number of partitions within which each wj has an effect. C To each wj add a random number x j , taken from a standard normal distribution with mean zero and variance 1 . If wj is of odd order, add xj to the running sum s u m i , and xj2 to vari. D Repeat for each partition i - 2 , . . , P. E Set the P order K + I Walsh coefficients indicated by the set of P partitions, using the following formula: 1 w, = ~-~ [(R su,n~) + (1 - I R I ) [ a ( 0 , ~ ) 1 ] , where the sum is taken over odd ordered subpartitions, the S is a scale parameter, and R is a correlation parameter, which ranges from -1 to 1.

T h e m i n i m u m n u m b e r of cycles is two, a second pass being required to verify t h a t there are no more changes t h a t lead to an i m p r o v e m e n t . As expected, all N with K - 0 require only two cycles. F u r t h e r m o r e , the n u m b e r of cycles per restart for all N approaches two as K approaches N - 1. As the n u m b e r of local o p t i m a increase, the average a t t r a c t i o n basin gets smaller and shallower. T h e intriguing point is t h a t the m e a s u r e of cycles per restart peak in the same region where C H C - H U X has a competitive advantage, possibly indicating effective complexity.

Addison-Wesley, 1989. [11] Bernard Manderick, Mark de Weger, and Piet Spiessens. The Genetic Algorithm and the Structure of the Fitness Landscape. In L. Booker and R. Belew, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 143-150. Morgan Kauffman, 1991. R. Smith and J. Smith. An Examination of Tunable, Random Search Landscapes. [12] In Wolfgang Banzhaf and Colin Reeves, editors, Foundations of Genetic Algorithms - 5, pages 165-181. Morgan Kaufmann, 1998.

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