Industrial Applications of Genetic Algorithms:Simulation of an Artificial Eco-System Using Genetic Algorithms

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The sum of the criteria produces the fitness value for the organism. The fitness value reflects the innate ability of an individual to survive the effects of environment and predation. For herbivores, this means the ability to avoid predators while successfully competing for limited forage resources. Carnivore fitness is measured by the ability to catch the prey and fend off fellow carnivores. Once determined, a stochastic remainder selection utilizes the fitness values to reproduce and crossover the fittest individuals. A mutation operator randomly modifies alleles during crossover.

The population size will be determined each generation. First, the carrying capacity of the environment is determined for each round - simulating the random effects of sunshine and rainfall. This value, taken in conjunction with the total mass of herbivores from the prior round, will determine the current round’s population size. Reproduction and crossover will fill all of the available slots in the population according to the dictates of the fitness function for herbivores and carnivores.

Because the amount of food available to sustain the population is variable, particularly for carnivores, wild swings in food supply could wipe out a particular food source. A phenotypic speciation operator smoothes fitness functions based upon food source and mass. Animals with different food sources are considered dissimilar. Mass is apportioned with a linear smoothing. This accords well with common sense, since mating individuals that range in size from 5 to 500 kilograms which might be inclined to eat the mate are unlikely at best. The expectation is that species should form based upon food source and mass. Within each species, there should be improvement in the quality of its individuals, with optimizations of prey and predator near the carrying capacity of the environment.

RESULTS

The following parameters were used in all tests:

Initial Population size | 25 |
Generations | 100 |
Prob. of Crossover | .6 |
Prob. of Mutation | .001 |

Two series of tests were conducted. In the first test, the carrying capacity remained constant, which led to a static population size. In the second test, the carrying capacity could vary as much as 66% from one generation to another, with the population size varying as well.

For the first test, the carrying capacity remained constant at 1500 kg, and the population size was 25. For all individuals, the allele values were randomly selected. Figure 18.1 tracks the absolute variance between ideal total mass and actual total mass of herbivore and carnivores over 100 generations. Over succeeding generations, the population converged to approximately 1% variance, while allowing for crossbreeding of herbivores and carnivores.

Figure 18.1 Actual variance from ideal total mass for static environment.

The average fitness value of all generations can be seen in Figure 18.2. A 400% improvement in total fitness occurred over 100 generations, due to maximizations of values for sight, hearing, color and brain size.

Figure 18.2 Average fitness value for static environment.

The speciation algorithm helped to maintain a relatively static number of carnivores and herbivores, with the quantity of either food type fluctuating between 8 and 17 for most of the simulation. At 100 generations, the range of individual’s mass still ran from 160 to 420 kg. The average mass had gone from 260 kg initially, to 320 kg at the end, reflecting the higher mass requirements of the herbivore population. Carnivores, which depended on herbivores for their food, tended to remain at a lower weight.

The average value for vision went from 3.7 to 7. The average value for hearing went from 2.7 to 6.7. Brain size went from 13.4 to 29.2. Color went from an even distribution to varying shades of green. The number of legs per individual went from an even distribution to 90% 2-legged, reflecting greater tool use.

The second series of tests examined various carrying capacities and population sizes. The carrying capacity was allowed to range over 1000-1500 kg for each generation. The population size was incremented or decremented in proportion to the carrying capacity. Again, allele values were selected randomly. Figure 18.3 tracks the absolute variance between ideal total mass and actual total mass of herbivore and carnivores over 100 generations. Over succeeding generations, the variation did evidence some smoothing, but remained overall at approximately the 10% level.

Figure 18.3 Actual variance from ideal total mass for varying environment.

The average fitness value of all generations can be seen in Figure 18.4. A 350% improvement in total fitness occurred over 100 generations, due to near maximizations of values for sight, hearing, color and brain size.

Figure 18.4 Average fitness value for static environment.

The speciation algorithm helped to maintain the relative proportion of carnivores and herbivores, although variances were higher than in the static algorithm. Because the food requirements had a much greater range, the mass of individuals also evidenced a greater range, from 20 to 420 kg. The average mass, which started at 260 kg, finished at 275 kg. The distribution contained substantial accumulation at either extreme.

The values for sight, hearing, brain size and color mimicked the results of the static run, showing good optimization performance.

CONCLUSIONS

The genetic algorithm was able to optimize the static environment’s biomass much better than in the dynamic environment. Because herbivores had a constant amount of food to draw from, the optimization routine narrowed the mass range of the population considerably. This would indicate that less speciation took place in the static environment.

The relatively poor optimization of biomass in the dynamic environment could be expected, because of the additional uncertainty introduced into the herbivore food chain. The algorithm did show robustness by quickly recovering from swings in the food supply, due to the wide range of body mass preserved by the speciation algorithm. This evidence would seem to accord well with observations [5] that changing environmental conditions aggravate the swings of the predator-prey cycle.

Both environments performed well in optimizing attributes unconcerned with food requirements. The values for vision, hearing, and brain size all showed advancement from average initial values to near optimal values.

Genetic algorithms can be a useful method for determining optimal biomasses within a static, and to a lesser extent dynamic, environment. The use of tools such as speciation more closely mimic natural processes, and preserve the diversity necessary for successful response to dynamic environmental changes. At the same time, a GA is able to optimize attributes that relate to an individual’s fitness.

REFERENCES

  1 Rosenberg, R. (1967). Simulation of genetic populations with biochemical properties. New York: McGraw Hill.
  2 Adami, C. T., Brown, M. & Haggerty, J. (1995). Abundance distributions in artificial life and stochastic models: “Age and Area” revisited, Proceedings of ECAL 95.
  3 Ray, T. (1995). Artificial Life. ATR Human Information Processing Research Laboratories.
  4 Kitching, R.L. (1983). Systems ecology - An introduction to ecological modeling. University of Queensland Press.
  5 Smith, M. (1974). Models in ecology. Cambridge University Press, Cambridge.

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