Cultural Algorithms. Robert G. Reynolds

initialization step of each run occurs when the system takes the data used to establish the parameters of the simulation, and generates the given number of cones. While the number of cones is set at 150, a number of these cones are not readily visible, as they are absorbed by the larger cones. Whenever two or more cones overlap, the system is designed to take the maximum of those cones at the given points where they overlap. Those cones subsumed by larger cones in the static landscape will remain hidden throughout the entirety of the run, while those hidden cones in the dynamic landscape have a chance of becoming visible when the dynamic landscape is updated and the dimensions of the cones are altered.

      The A‐values fed into the logistics function are used to determine the relative dimensions of each cone. For a given acceptable range of values for the cones to have, each cone will be individually defined based on repeated initial calls of the logistics function as a means of seeding the function, followed by subsequent calls to the function for each newly generated cone. This means that a low A value, which results in the linear results seen in The Cones World section, used for initialization will result in a number of cones that are not terribly dissimilar from one another, the changes in their dimensions being gradual and slight. Using a higher A value, such as 3.5 which was used in these two runs, will result in subsequent calls to the logistics function returning a more chaotic frequency. For this reason, subsequently generated cones can differ dramatically from one another.

A point of interest in Figure 2.9 is the distribution of agents at the time of initialization. They are homogeneously distributed across the landscape, evenly spaced out from one another as well as along the borders of the landscape. With the lBest social network topology visualized, they can be seen connected to one another by a zig‐zagging line and each agent connected to two neighbors. For the purposes of finding a maximum, the early configuration provides a unique sampling of early information for each of the knowledge sources to use. It is for this reason that later we may observe that, once the agents begin to cluster around likely candidates, the dynamic updates can result in a slower ascent back to the maximum. This is because the agents are now tightly clustered and thus yield less relevant data back to their respective knowledge sources.

When viewing the network connections across successive steps, it is possible to see the agents begin to concentrate on a maximum via the convergence of lines. In Figure 2.10, the first two steps depicted on the static landscape on the left indicate that some of the agents have located a local maximum and are investigating it. But as more information is gathered, notice that the large cone towards the right side of the static landscape is abandoned by step 3, as the agents converge more on the overall maximum that has been located. The network takes a denser appearance as more agents gather, and other agents are sent out to explore with the majority remaining with the highest scoring locations.

The shape of the network varies based on the selection made by the user, varying how each agent is able to communicate with its neighbors, and how far information can penetrate the social network. As we can see in Figure 2.11, in a homogeneous topology, all neighbors have an equivalent level of connectedness to all other neighbors. If any given agent has four connections in a homogeneous network topology, then ALL agents have four connections in a homogeneous network topology. Heterogeneity in network topologies can be seen in the uses of subcultures, in which network connections are awarded based on agent merit, and in randomization, in which each agent has access to a random number of others as discussed next in Chapter 3.

Figure 2.9 The initialization stage of the static (above) and dynamic (below) landscape runs.

Figure 2.10 Five steps of the static (left) and dynamic (right) landscape networks.

Figure 2.11 The homogeneous topologies. (a) Ring topology, (b) square topology, (c) global topology, (d) hexagon topology, and (e) octagon topology.

      Meanwhile in the dynamic landscape, it is possible to see in Figure 2.10. that they are just beginning to cluster as the agents in the static landscape did, when the first dynamic change occurs to the landscape. The agent cluster, which had previously begun congregating on the overall maximum for the dynamic landscape, is suddenly clustered near a new overall maximum, although the centroid of the cluster is not on it. But because the loosely clustered group was near the overall maximum, they were able to then cluster on the maximum and send out exploratory agents to investigate the newly changed landscape. As the A‐value for the dynamic landscape is 3.5, this means that each dynamic shift will be a radical update which can result in the total possible maximum being significantly lower as no cone approaches a height similar to those of a pre‐updated landscape. This will be displayed later in the scoring results of the agents working in the static and dynamic landscapes.

The movement of the social clusters, with regards to the network topologies displayed in Figure 2.11, gives us an idea of how the mass of agents moves, with new, more rewarding locations, being disseminated among the other agents at varying rates depending on the shape of the network topology. As the network change will not only produce new information but will make some old information obsolete. For example, overabundance of connections may be both beneficial and detrimental depending on which information is discovered first. Therefore, any poisonous data introduced into a network can take longer to be purged from the system based on how it is able to move through said network (Figure 2.12).

      While continuing the simulation, it is possible to view not only the agents and their network shared network topology, but also the area which each influencing knowledge source encompasses. By identifying each agent with the knowledge source which is influencing it, and then compiling the coordinates of each agent, it is possible to draw a bounding box which contains all agents that adhere to a given knowledge source. The structures of these boxes and their subsequent expansions and contractions can serve to highlight the nature of each knowledge source.

      Boxes that contract over successive steps indicate an exploitative knowledge source, such as the Situational knowledge source. These knowledge sources will tend to focus on a known best example and explore in its immediate vicinity for any possible improvement. Boxes that expand over successive steps or trend toward more encompassing sizes typically represent the explorative knowledge sources, such as the Topographical knowledge source. These knowledge sources tend to send out agents to possibly high‐scoring predicted spots based on calculations made with known data.

      While explorative search suffers from covering massive amounts of ground with limited agents, exploitative suffers from a blindness brought on from agents that only focus on the immediate. With agents sharing information between knowledge sources, however, both types of knowledge source will benefit.

When the CAT system has finished running its generations across the two landscapes, it is possible to view the results of each generation's top scoring results. In Figure 2.13 these results are depicted, with each line indicating the results of one of