T. Stutzle and H.H. Hoos. MAX-MIN Ant System. Journal of Future Generation Computer Systems, Volume 16, 889 - 914, 2000  Home/Search   Document Details and Download   Summary   Related Articles   Check

....version of it that is more particularly dedicated to the car sequencing problem. This new algorithm mainly introduces three new features: rst, it uses an elitist strategy, so that pheromone is used to break the tie between the best cars only; second, it integrates features borrowed from [12] in order to favor exploration; nally, it uses the heuristic functions introduced in section 3 to guide ants. Our new algorithm follows the classical ACO scheme: rst, pheromone trails are initialized; then, at each cycle every ant constructs a sequence, and pheromone trails are updated; the ....

....by c nest 62 C, from which ants start constructing sequences (this extra vertex will be considered as a car that requires no option) The amount of pheromone on an edge (c i ; c j ) is noted (c i ; c j ) and represents the learnt desirability of sequencing c j just after c i . As proposed in [12], and contrary to our previous ACO algorithm, we explicitly impose lower and upper bounds min and max on pheromone trails (with 0 min max ) The goal is to favor a larger exploration of the search space by preventing the relative di erences between pheromone trails from becoming too ....

T. Stutzle and H.H. Hoos. MAX-MIN Ant System. Journal of Future Generation Computer Systems, Volume 16, 889 - 914, 2000

....cycles reached or optimal solution found Pheromone trail initialization: Ants communicate by laying pheromone on the graph edges. The amount of pheromone on edge (v i ; v j ) is noted (v i ; v j ) and represents the learnt desirability for v i and v j to belong to a same clique. As proposed in [9], we explicitly impose lower and upper bounds min and max on pheromone trails (with 0 min max ) The goal is to favor a larger exploration of the search space by preventing the relative di erences between pheromone trails from becoming too extreme during processing. We have considered ....

....processing. We have considered two di erent ways of initializing pheromone trails: 1. Constant initialization to max : such an initialization achieves a higher exploration of the search space during the rst cycles, as all edges nearly have the same amount of pheromone during the rst cycles [9]. 2. Initialization with respect to a preprocessing step: the idea is to rst compute a representative set of maximal cliques without using pheromone thus constituting a kind of sampling of the search space and then to select from this sample set the best cliques and use them to initialize ....

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T. Stutzle and H.H. Hoos. MAX MIN Ant System. Journal of Future Generation Computer Systems, 16:889-914, 2000.

....of the pheromone matrix was initialized is at the same time it s minimum value, since negative updates occur only to cancel out previous positive updates of the same magnitude. The e ect of having a minimum pheromone value has been applied successfully for ACO algorithms by St utzle and Hoos [4, 5]. One motivation for introducing a population based scheme is the planned application to dynamic optimization problems. An ACO approach for a dynamic TSP problem where instances change at certain intervals through the deletion and insertion of cities has been studied in [6, 7] Strategies for ....

....that for every ant n additions respectively subtractions are done (plus a constant number of arithmetic operation to determine the actual amount of pheromone that is added subtracted) To ensure that every pheromone value has a minimum value we do not remove the initial amount of pheromone (cmp. [4, 5]) Otherwise it could happen that pheromone values become zero because there is no solution in the population that puts pheromone on them. But then the ants cannot make the corresponding decision. Another motivation for introducing a population based approach is that it might allow a di erent ....

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T. Stutzle and H.H. Hoos. MAX-MIN ant system. Future Generation Computer Systems Journal, 16(8):889-914, 2000.

....occupied by an ant. The same result have been achieved, for the same data and di erent runs, when using the same parameters and the same number of iterations. The maximum number of cycles was set to 500 for all experiments. The modi ed ACO algorithm have been compared with the MAX MIN algorithm [13], which is the best ACO algorithm. The idea of MAX MIN algorithm is to use min and max , a lower and an upper limit of the pheromone respectively. For max is used the asymptotic upper bound of the pheromone. For lower limit they use min = max =2n, where n is the number of objects. For ....

Stutzle, T., Hoos H.H.: MAX-MIN ant system. In: Dorigo, M., Stutzle, T., Di Caro, G. (eds.): Future Generation Computer System Vol. 16 (2000) 889-914

....j ; w ) Intuitively, this amount of pheromone represents the learnt desirability of assigning value v to variable X i and value w to variable X j simultaneously. Notice that since the graph is not directed, X i ; v ; X j ; w ) X j ; w ; X i ; v ) As proposed in the MAX MIN Ant System [30], we explicitly impose lower and upper bounds min and max on pheromone trails (with 0 min max ) The goal is to favor a larger exploration of the search space by preventing the relative di erences between pheromone trails from becoming too extreme during processing. Also, pheromone ....

....= 2; 0:03, then when = 3; 0:02, then when = 2; 0:02, then when = 3; 0:01, and the worst when = 2; 0:01. rithms for many combinatorial optimization problems are hybrid algorithms that combine probabilistic solution construction by a colony of ants with local search [9] [30]. In this section, we propose to combine local search with AntSolver. In this case, one can view Ant Solver as a way of taking bene t of the di erent locally optimal assignments found previously by local search in order to guide it towards the most promising areas of the search space when ....

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T. Stutzle and H.H. Hoos. MAX MIN Ant System. Journal of Future Generation Computer Systems, 16:889-914, 2000.

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