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...ties such as lookahead, local optimization, backtracking, and so on that cannot be found in real ants. In many implementations ants have been hybridized with local optimization procedures (see, e.g., =-=[38, 51, 98]-=-), while, so far, only Michel and Middendorf [78] have used a simple one-step lookahead function and there are no examples of backtracking procedures added to the basic ant capabilities, except for si...

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...gorithm, as it is the case with ACO algorithms, is randomized. Stützle [47] presents computational results for the execution of parallel independent runs on up to ten processors of his MMAS algorithm =-=[48, 49]-=-. His results show that the performance of MMAS improves with the number of processors. 2.7 Ants, pheromones, and solutions evaluation In this section we discuss some of the most characterizing aspect...

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...contributed to the trail update (see [2], [12]). In more recent papers on the TSP, better results were obtained for update rules where only the best ant contributes to the pheromone trails (see [11], =-=[23]-=-). In another paper Bullnheimer et al. [1] suggest to rank the ants according to solution quality and to use only the best ranked ants as well as so-called elitist ants to update the pheromone trails....

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...ted knowledge about the problem). ACS has been improved also by the addition of local search routines that take the solution generated by ants to their local optimum just before the pheromone update. =-=[84,87,88]-=- introduces upper and lower bounds to the values of the pheromone trails, as well as a different initialization of their values. In practice, in the allowed range of the pheromone trail strength is li...

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... GROUPED BY PROBLEM TYPE. Problem type Problem name Authors Year References Routing Traveling salesman Dorigo et al. 1991, 1996 [6], [8] Dorigo & Gambardella 1997 [11] Stützle & Hoos 1997, 2000 [15], =-=[47]-=- Vehicle routing Gambardella et al. 1999 [48] Reimann et al. 2004 [49] Sequential ordering Gambardella & Dorigo 2000 [50] Assignment Quadratic assignment Stützle & Hoos 2000 [15] Maniezzo 1999 [18] Co...

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... set was a singleton containing the best solution within St (if there were several iteration-best solutions, one of them was chosen randomly). For the globalbest update (Dorigo and Gambardella, 1997; =-=Stützle and Hoos, 1997-=-), the reference set contained the best among all the iteration-best solutions (and if there were more than one global-best solution, the earliest one was chosen). In Dorigo, Maniezzo, and Colorni (19...