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Ordering search results, network stability and routing on the Internet are applications of which the performance almost entirely depends of automated solution methods. This dissertation studies fundamental aspects of solution methods for these problems. The simplest solution methods that will always find the best solution is trying each possible solution one by one and selecting the best one. Even on the fastest computer this method takes too much time: years instead of days! Finding a solution method that is both fast and finds the best answer, appears unfortunately not always possible. This dissertation describes solution methods that are very fast, but find a very good answer instead of the best answer. Moreover, for various problems better and simpler solution methods are described.