where c quanti es the degree of attraction of an unexplored branch, and is the bias in .NET framework

Printer Quick Response Code in .NET framework where c quanti es the degree of attraction of an unexplored branch, and is the bias
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17 Ant Algorithms
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Figure 172 Shortest Path Selection by Forager Ants to using pheromone deposits in the decision process The larger the value of , the higher the probability that the next ant will follow the path with a higher pheromone concentration even if that branch has only slightly more pheromone deposits The larger the value of c, the more pheromone deposits are required to make the choice of path non-random It was found empirically that 2 and c 20 provide a best t to the experimentally observed behavior Using the probability de ned in equation (171), the decision rule of an ant that arrives at the binary bridge is expressed as follows: if U (0, 1) PA (t + 1) then follow path A otherwise follow path B Goss et al [330] extended the binary bridge experiment, where one of the branches of the bridge was longer than the other, as illustrated in Figure 172 Dots in this gure indicate ants Initially, paths are chosen randomly with approximately the same number of ants following both paths (as illustrated in Figure 172(a)) Over time, more and more ants follow the shorter path as illustrated in Figure 172(b) Selection is biased towards the shortest path, since ants that follow the shortest path return to the nest earlier than ants on the longer path The pheromone on the shorter path is therefore reinforced sooner than that on the longer path Goss et al [330] found that the probability of selecting the shorter path increases with the length ratio between the two paths This has been referred to as the differential path length e ect by Dorigo et al [210, 212] To summarize the ndings of the studies of real ants, the emergence of shortest path selection behavior is explained by autocatalysis (positive feedback) and the di erential
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171 Ant Colony Optimization Meta-Heuristic path length e ect [210, 212]
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Although an ant colony exhibits complex adaptive behavior, a single ant follows very simple behaviors An ant can be seen as a stimulus response agent [629]: the ant observes pheromone concentrations and produces an action based on the pheromonestimulus An ant can therefore abstractly be considered as a simple computational agent An arti cial ant algorithmically models this simple behavior of real ants The logic implemented is a simple production system with a set of production rules as illustrated in Algorithm 171 This algorithm is executed at each point where the ant needs to make a decision Algorithm 171 Arti cial Ant Decision Process Let r U (0, 1); for each potential path A do Calculate PA using, eg, equation (171); if r PA then Follow path A; Break; end end While Algorithm 171 implements a simple random selection mechanism, any other probabilistic selection mechanism (as overviewed in Section 85) can be used, for example, roulette wheel selection
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Stigmergy and Arti cial Pheromone
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Generally stated, stigmergy is a class of mechanisms that mediate animal-to-animal interactions [840] The term stigmergy was formally de ned by Grass [333] as a e form of indirect communication mediated by modi cations of the environment This de nition originated from observations of the nest-building behavior of the termite species Bellicositermes natalensis and Cubitermes Grass observed that coordination e and regulation of nest-building activities are not on an individual level, but achieved by the current nest structure The actions of individuals are triggered by the current con guration of the nest structure Similar observations have been made by Marais [558], with respect to the Termes natalensis The word stigmergy is aptly constructed from the two Greek words [341], stigma, which means sign, and ergon, which means work Individuals observe signals, which trigger a speci c response or action The action may reinforce or modify signals to in uence the actions of other individuals Two forms of stigmergy have been de ned [341, 871, 902]: sematectonic and signbased Sematectonic stigmergy refers to communication via changes in the physical
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