Cultural Algorithms. Robert G. Reynolds
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Название: Cultural Algorithms

Автор: Robert G. Reynolds

Издательство: John Wiley & Sons Limited

Жанр: Программы

Серия:

isbn: 9781119403104

isbn:

СКАЧАТЬ at a set rate, while a third aspect should predictably variate between one extreme to the next (Figure 2.4).

      As the topography of ConesWorld is subject to change if the user defines multiple landscapes for it to generate during a given run, it is entirely possible that new maximum values for the function would be created. At the same time past maximum values might vanish as the cones lower in height. Due to this process of vanishing and reappearing maximums, agents need to adjust their movements and mechanisms to explore the environment for new viable maximum points. This can result in a dramatic downturn in the scoring for a group of agents during an update cycle.

      To control this shift, a logistics function is utilized, which produces a change variable that fluctuates between a range of 0 and 1, and this rate of fluctuation may be controlled by the earlier described A‐values that may be set by the user.

Graph of KS fitnesses versus tick displaying five fluctuating curves for best topographical fitness, best situational fitness, best domain fitness, best normative fitness, and best historical fitness. Graph of KS fitnesses versus tick displaying five fluctuating curves for best topographical fitness, best situational fitness, best domain fitness, best normative fitness, and best historical fitness.

      Given an A value between 0 and 4, successive iterations of the logistics function will generate a fluctuation between the values of 0 and 1. The frequency of this fluctuation is dependent on the size of the A value. Due to the recursive nature of the function, low values of A will result in subsequent values of Y(n) approaching a steady output that will cease to fluctuate after a sufficient number of iterations. For this reason, using lower values of A in the ConesWorld simulation will result in the appearance of smooth, predictable, near‐linear transitions from one update to the next.

      However, as the A value approaches 3, the resulting fluctuations becomes more self‐sufficient and will maintain a steady, regular frequency between two absolutes, which its peaks and valleys will trend toward. For these cases, it is possible to have subsequent steps of the logistics function vary, but in predictable ways. As each cone in the ConesWorld simulation freshly calculates the logistics function with the next iteration of Y(n), alternating cones querying it for their rate of change will receive alternating high and low rates from it.

      In those rows of the graph beyond 3.33, the pattern becomes erratic, with each subsequent iteration of the logistics function taking a dramatic, seemingly unpredictable movement that bears little relation to the patterns produced by lower values of A. It should also be noted that even with this erratic fluctuation the resulting Y(n) values are still within the range of 0 and 1. However, should the A value exceed 4, then the system will destabilize and quickly break out of the given range.

Equation of the CAT system logistics function. Three-dimensional visualization of successive iterations of the logistics function across increasing values of A, with curves for 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.33, 3.5, 3.75, and 4.

      The following data are the result of two separate runs of the CAT system's ConesWorld simulation. Both runs use similar parameters for their initializations. The population consists of 50 agents in each of them; the social topology between them is represented by lBest (each agent having a connection to 2 agents, resulting in a circular chain); the influence is calculated by Majority; the number of cones is 150 (it must be noted that some smaller cones can be consumed by larger cones and not be visible during the simulation); and the A‐values for height, radius, and position are all 3.5

      The difference between the two runs is the usage of СКАЧАТЬ