Cultural Algorithms. Robert G. Reynolds

landscape's generations display a steady maintenance of the discovered maximum in the landscape, while the dynamic landscape's generations show the dramatic drop‐off each time a dynamic update of the landscape occurs.

      Earlier it was mentioned that the homogeneous distribution of agents during the initialization phase of the runs gave a wide breadth of knowledge to the knowledge sources to use during each subsequent step. This could account for rapid early acquisition of a maximum. However, the dynamic landscape's violent landscape changes, which can result in clusters of agents suddenly being on a low‐scoring point in the landscape in unfamiliar terrain, show a more dramatic difference between the scores of the agents immediately after the shift, and several steps later when the maximum is reclaimed.

Figure 2.12 Five steps of the static (left) and dynamic (right) bounding boxes.

Also due to the chaotic nature of the 3.5 value of A of the dynamic landscape's updates, note that the overall possible maximum changes not only its position but also its magnitude with the shifts. This explains the low yet stable fitness values achieved during different points in the dynamic landscape, where plateaus occur in the data.

Figure 2.13 The KS fitnesses for the static (above) and dynamic (below) landscapes.

In addition, as noted in the discussion of bounding boxes, the exploitative and explorative aspects of the knowledge sources can be discerned from their adherence to a found maximum when viewed by the knowledge source fitnesses. Those exploitative knowledge sources, such as Situational and Historical, will tend to achieve a high fitness and then stay at that level. The explorative knowledges source on the other hand, such as Topographical and Domain, will tend to stay away from the maximum as they seek out more information.

In Figure 2.14, we can see the areas of each bounding box produced by each knowledge source. It can be seen in this visualization that the two most exploitative knowledge sources, situational and historical, regularly have the smallest areas of coverage, while the two most explorative knowledge sources, normative and topographical, cover the largest areas. The domain knowledge source straddles the line between these two methodologies of exploration and exploitation, expanding and contracting itself as data come in, focusing on a transitional region between the more extreme knowledge sources.

Figure 2.14 The span of each Knowledge Source's bounding boxes.

      Using this resulting information, it is possible to not only find the solution to a given problem but also to illustrate the in‐depth means by which the solution was found, and how each knowledge source contributed toward a given goal. It is due to this shared responsibility of the knowledge sources to both maintain acquired knowledge and push for the acquisition of new knowledge that the system maintains the balance between all of the knowledge sources as they each assert their influence over the collected individuals of the simulation.

CAT Sample Runs: Other Problems

In addition to the ConesWorld system, the CAT System's optimization abilities can be used on a number of other optimization problems. As the ConesWorld system had two possible input variables with a single output across a relatively small dataset, it was possible to create a three‐dimensional visualization of the data to watch as the system located these optimal values. In these examples, a larger number of variables with wider ranges and finer variations exist, meaning that a visualization of this information in the method previous seen in ConesWorld would quickly become incomprehensible, as the system would attempt to generate images with more than three dimensions.

      Despite being unable to visualize the data range, it is still possible to visualize the means in which the knowledge sources deal with the data they encounter. The additional optimization problems observed by the system include the designs of a Tension Spring, a Welded Beam, and a Pressure Vessel. Each problem sought to minimize the dimensions of a given structure to save on material and space, while still remaining within the constraints rendered necessary by factors, such as precision (for the shaping and rendering of parts) and safety (to reduce the likeliness of critical failure).

The Tension Spring example involves the minimized design of the spring as visualized in Figure 2.15. The four variables that describe the spring itself relate to the diameter of the wire (d), the diameter of the coil (D), and the number of coils in the spring (N). The mass of the spring can be equated as follows:

      where

It can be seen in Figure 2.16 that each knowledge source yields new discoveries, which are then capitalized on by the other knowledge sources. The topographical fitness, the highly explorative knowledge source which searches across bold predictions, leads the system to higher bounds in the fifth generation, after which the situational knowledge source focuses on this latest achievement. While the other, more explorative knowledge sources continue to explore, the exploitative knowledge sources continue to refine, examining only those small variations. Notice that at approximately generation 75, while the explorative knowledge sources had dropped off in terms of new discoveries, the highly exploitative situational knowledge discovered a minor improvement to the arrangement of variables in the design of the tension spring.

Figure 2.15 The tension spring [1].

      Source: Reproduced with permission of Elsevier.

Figure 2.16 The Knowledge Source fitnesses of the tension spring problem.

      This concludes our discussion of the basic conesworld system. In chapters 3 through 5 that follow the system will be used as a vehicle to experiment with varying Cultural Algorithm configurations. The focus of these chapters will be on mechanisms by which knowledge is distributed throughout the population. These mechanisms will include majority voting (wisdom of the crowd, auctions, and games.

Reference

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