224 Agent-Based Modeling and Simulation with Swarm
TABLE 7.11: Potential child genotypes [33].
Metab olic rate
Vision m M
v (m, v) (M, v)
V (m, V ) (M, V )
a lower a nd upper breeding age taken from uniform distributions over
these two intervals.
• Reserve: to b e c ome a pare nt, an agent must possess at least as much
sugar in its reserve as at its birth.
In addition, the father and mother of a child each give the child half of the
quantity of sugar that they possessed at birth. In other words, a child is bo rn
with a quantity of sugar equal to the sum of the amounts donate d by its
parents.
In the breeding process, each attribute (e.g., metabolic rate, vision, and
maximum lifespan) is randomly inherited by the child fro m one of its parents.
Therefore, rather than being generated at random, the attributes of a new ly
born agent repr e sent a uniform crossover of the genetic elements of its parent
agents. Taking meta bolic rate and vision as an example, if the genotype of
one parent is (m, v) and the genotype of the other is (M, V ), the child can
obtain one of four genotype combinations with equal probability (Table 7.11):
(m, v), (M, v), (m, V ), and (M, V ). The following rule is adopted fo r breeding
agents [33, p. 56].
Agent breeding rule S:
• Select an adja c e nt agent at random.
• If the selected agent is of the opposite sex and is ca pable of breeding,
and if there is at least one empty position for child next to either agent,
then the agents produce one child.
• Repeat for all agents.
In an experiment where the lifespan was left unchanged and the breeding
rule was substituted for the replacement rule, the agent population initially
decreased in barren regions and then increased rapidly through breeding in
rich regions, before eventually settling at around 700. Here, average values for
both the vision and meta bolic rate of the agents changed; the metabolic rate
decreased e ven more rapidly as compared with the case without crossove rs,
and the vision improved (Fig. 7.35). The reason for this improvement in sight,
in addition to evolution, is that the agents experienced difficulty in finding free
space as the population increased, and therefo re the importa nce of having a
Cellular Automata Simulation 225
(a) Average and std. values
(vision, metabolism)
(b) Numbers of births and deaths
FIGURE 7.35: Features in (G
1
, {M, R
[60,100]
, S}).
(a) Average and std. values (b) Maximum values
FIGURE 7.36: Wealth in (G
1
, {M, R
[60,100]
, S}).
wide field of vision also increase d. Furthermore, the aver age reserve decreased
to 6 as a r e sult of agents donating part of their reserve to their newly born
child, and the maximum reserve decreased to about 15 (Fig. 7.36).
7.10.4 Environmental changes
In this section, we observe the behavior of the agents when their environ-
ment is changed. The basic rules in the following disc ussion are the bre e ding
rule from Section 7.10.3 and the rule that says lifespans are uniformly dis-
tributed over the interval 60–100.
7.10.4.1 Nutritive ratio
Let us lower the nutritive ratio of sugar to 40%; in other words, only 4 out
of 10 collected units of sugar c an be digested, which is equivalent to reducing
the consumption of sugar to 40%. When the exper iment is conducted under
these conditions, the sugar collected by the agents is unable to cover the energy
needs of their metabolisms. As a result, the agents exhaust their reserves, and
226 Agent-Based Modeling and Simulation with Swarm
the entire population perishes at the 25th step. The minimum nutritive ratio
of sugar at which the agents survive is about 50%.
7.10.4.2 Alternating seasons
Next, alternating seasons are introduced as a form o f dynamic environmen-
tal cha nge. Taking the upper half of Sugarscape as the northern hemispher e
and the lower half as the southern hemisphere, the hemispheres alternate be-
tween summer a nd winter every 50 steps such that both hemispheres have
opposing seasons. The sugar yield in winter is 1/8 of that in summer. The
season rule is summarized as follows [33, p. 45].
Rule for season-dependent sugar growth S
αβγ
:
• The sea son is set to summer in the upper (northern) half and winter in
the lower (southern) half of Sugarscape.
• The seasons are swapped after a period of time α (summer bec omes
winter and winter becomes summer).
• Sugar grows at a rate of γ units per step in summer, and a rate of γ
units per β steps in winter.
Conducting the experiment under these conditions, the agents in the win-
ter hemisphere ultimately co nsume all of the s ugar, and their population is
drastically reduced. Only agents located around the equator can survive by
migrating to the summer hemisphere. However, once the seasons are swapped
after 50 steps, the agents that have been consuming generous amounts of sugar
during the summer suddenly face a severe winter (Fig. 7.37), and agents die
in large numbers if they do not reach the summer hemisphere. Agents that
successfully relocate produce offspring and increase in number (Fig. 7.38).
If the seasons are swapped an odd number of times, values of the average
vision and metabolic rate both improve, whereas with an even number of swaps
these attributes degenerate slightly. Agents with supe rior features adapt well
to the change in season and gather together inside the summer hemisphere.
However, since after an odd number of swaps the season in that hemisphere
is winter, a la rge number of agents die, and the remaining agents in the oppo-
site hemisphere produce offspring and increase the population. Therefore , the
effect of location-based selection is stronger tha n that of superior or inferior
features, resulting in an overall degeneration of the attributes. Furthermore,
the average reserve size increases rapidly immediately after the swap, owing to
the small number of agents refilling their reserves in the summer hemisphere
(Fig. 7.39).
7.10.4.3 Generation of pollution
When the climate alternates, the environment exerts a unidirectional in-
fluence on the agents. In contrast, in this section we introduce pollution as an
Cellular Automata Simulation 227
(a) 25 steps later; winter in the
lower hemisphere (south-
ern)
(b) 50 steps later ; winter in the
upper hemisphere (north-
ern)
FIGURE 7.37: Agent aggregation due to sea sonal variation: (S
50,8,1
,
{M, R
[60,100]
, S}).
(a) population (b) numbers of bir ths and dea ths
FIGURE 7.38: Population changes due to seasonal variation: (S
50,8,1
,
{M, R
[60,100]
, S}).
228 Agent-Based Modeling and Simulation with Swarm
(a) aver age and std. values (vi-
sion, metabolism)
(b) average and std. values
(wealth)
FIGURE 7.39: Feature and wealth changes due to seasonal variation:
(S
50,8,1
, {M, R
[60,100]
, S}).
example to show agents affected by their environment. Upon collecting and
digesting s ugar, an agent generates a corresponding amount of pollutant at its
position, which make s it difficult for the agent to continue living there. The
rule for generation of pollution is as follows [33, p. 4 7]:
Pollution g e neration rule P
αβ
:
• Agents generate α ·s units of pollutant upo n collecting s units of sugar
(production waste) and β · m units of pollutant upon digesting m units
of sugar (consumption waste).
• The total amount of pollutant p(t) at time t for a given position is the
sum of the production waste, the consumption waste, and the existing
amount of pollutant, which can be expressed as
p(t) = p(t − 1) + α · s + β · m. (7.15)
The experiment be low is conducted with α = 1 and β = 1, and the move-
ment rule is adjusted as follows [33, p. 48]:
Movement rule M adjusted to account for pollution:
• As vision permits, search for the position with the highest sugar-to-
pollutant ratio and with no o ther agents.
• If more than o ne such position ex ists, choose the nearest.
• Move to the selected position and collect all of the available sugar.
In addition, the p ollutant is dis persed with a fixed ratio in accordance with
the following rule [33, p. 48]:
Pollution dispersal rule D
φ
:
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.