Combinatorics and Graph Theory


New Lower Bounds for Van Der Waerden Numbers Using Genetic Algorithm

Authors: Alexey V. Komkov

Genetic algorithm is a good tool for finding the global minimum in many discrete problems. In particular, it has proven itself in problems where there is no any apriori information about the possibilities of narrowing the search, or the specifics of the problem do not involve such. This work describes the procedure of using a genetic algorithm as applied to the search of van der Waerden numbers. Some new lower bounds of van der Waerden numbers were found using this procedure. Using the genetic algorithm, the author has found the best lower estimates for the Van der Waerden number W (7, 4), W (5, 5), W (6, 5), W (5, 6).

Comments: 114 Pages.

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Submission history

[v1] 2016-11-28 14:44:16
[v2] 2018-10-30 05:38:20

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