This paper deals with the strongly NP-hard minmax regret version of the minimum spanning tree problem with interval costs. The best known exact algorithms solve the problem in reasonable time for rather small graphs. In this paper an algorithm based on the idea of tabu search is constructed. Some properties of the local minima are shown. Exhaustive computational tests for various classes of graphs are performed. The obtained results suggest that the proposed tabu search algorithm quickly outputs optimal solutions for the smaller instances, previously discussed in the existing literature. Furthermore, some arguments that this algorithm performs well also for larger instances are provided.
This paper describes a methodology of automatic genetic algorithm parameters adjustment dedicated to a job-shop problem with a no-wait constraint with a makespan criterion. The numerical results show that in a given problem, the efficiency of an algorithm with auto-tuning is placed at the level of an algorithm steered in a classical way with the best-fit steering parameters.
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