126 Agent-Based Modeling and Simulation with Swarm
FIGURE 5.12: A scene of building a living bridge by army ants (photo
courtesy of Prof. Salvacion P. Angtuaco [4]).
5.8 Emergent cooperation of army ants
This section presents a multi-agent simulation inspired by army ant behav-
ior. Such cooperation in a multi-agent sys tem can be ve ry valuable for engi-
neering applications. The purpo se of this section is to model and c omprehend
this biological behavior by computer simulation. The following description is
mainly based on our previous resear ch results [60].
5.8.1 Altruism of army ants
Altruism refers to behavior that prioritizes b e nefits to others rather than
self and sometimes involves acts of self-sac rifice in order to aid others. Some
army ants construct living bridges with their own bodies when they find holes
or gullies as obstacles to their marching routes, as shown in [1] (se e Fig. 5.12).
Such philanthropic acts are different from the regular be havior of the ants,
e.g., foraging for and transport of food. However, if more ants participate
in bridge construction than is required or if they construct bridges at sites
where those are unnecessary, they may actually hamper the food gathering
performance of the whole colony. But, in nature, the ants are very keen to
balance these actions as per requirements, and it has been c onfirmed that
because of such altruistic activity performance is improved for the group as a
whole. In an experiment by Powell and Franks, it was fo und that the foraging
capacity of the army ant colony increased by up to 26% due to this altruistic
behavior [98]. In this section, this altruism of ants is mo deled and examined
in a multi-agent simulation e nvironment (see Fig . 5.1 3).
Ant Colony–Based Simulation 127
FIGURE 5.13: Simulation environment.
5.8.2 Defining the problem
This se c tion e xplains the problems handled in the multi-agent simulation.
The present simulatio n serves as a model fo r the foraging behavior and the
altruism of ants. The simulation was performed using the Swarm library. Fig-
ure 5.14 shows a screenshot of the simulation screen where an agent repr e sents
an ant move ment.
The actions include foraging for and transport of food and communications
with neighboring ants using pheromone. The nest is the starting point of the
agents and also the po int to which the agents return with food. The pheromone
is released by an agent when it finds food. J ust as in nature, once secreted, the
pheromone attenuates and disp e rses, thus disseminating information among
the ants a bout the food locations. A gully hinders movement of agents and
fundamentally prevents the agents from passing over it. However, if an age nt
shows altruism and forms a living bridge over the gully, other agents can
pass over the gully. The agents move in accordance with the state transition
diagram shown in Fig. 5.15. The behavior of agents in different states is shown
in Table 5.3.
The problem is to determine the conditions that induce the transition to
the altruism state. But it is not concretely known how ants decide the site and
timing of living-bridge construction and when they cease the bridge forma-
tion. Therefore, in this section, several hypothese s are proposed as altruism
initiation conditions, and expe riments were performed for verification.
5.8.3 Judgment criteria for entering the altruism state
5.8.3.1 Hypotheses
Two hypotheses have been proposed as the judgment criter ia for altruistic
activity by army ants.
128 Agent-Based Modeling and Simulation with Swarm
FIGURE 5.14: Swarm-based simulation of army ants.
Model 1: Based on the presence of neighboring ants
An ant will start the formation of a living bridge over a gully only when
neighboring ants are present. Hypothetically, this approach will be more effi-
cient compared to forming a bridge blindly be c ause when there are neighboring
ants the probability is high that they will utilize the shortcut.
Model 2: Based on the presence of pheromone
As described earlier, agents secrete pheromone when they find food, and
this pheromone is used to disseminate information among ants ab out the
location of the food source. The places where phero mone concentrations are
higher than a fixed level are the locations that many ants have passed a nd/or
will pass through in the future. Therefo re, a living bridge can be formed by
judging the pheromone concentration.
In both models, agents leave the bridge after a fixed amount of time passes.
We a c tually used fixed properties optimized by genetic algorithms (shown in
Ant Colony–Based Simulation 129
Altruism
Search Return
???
Discover
Stock
FIGURE 5.15:
State transition of agents.
FIGURE 5.16: Maps for experiment.
Table 5.4, [60]). In order to judge their validity, these hypotheses were fed into
the simulation and their usefulness was verified empirica lly.
5.8.3.2 Experiment to verify the hypotheses
The two scenarios shown in Fig. 5 .16 were used in the experiment. In
these experiments, performance was mea sured using the number of food items
collected within a fixed period of time. Each experiment was repeated 10 times
with 20 to 180 agents, increased by 20 at a time, and the mean values were
compared.
The experimental results fr om the simple map are shown in Fig. 5.17.
The numbers of agents is s hown along the horizontal axis and the number of
fo od items collected within a fixed amount of time is shown along the vertical
axis. In the simple map, Model 1 showed slightly higher performance, but
130 Agent-Based Modeling and Simulation with Swarm
TABLE 5.3: States and b e haviors of agents.
State Behavior
Search This is the initial condition of the ag e nt and it continues ra ndom
work until food is found. When food is found, there is a transition
to the Return sta te. Transition to the Altruism state is also p os-
sible under “certain” conditions. When pheromone is sensed, the
ants are drawn to the higher concentrations.
Return The food is r e turned to the nest. In this state the agent moves
toward the nest secreting pheromone. After reaching the nest, the
agent tr ansits to the Search s tate. An age nt in the Return state
knows the position of the nest.
Altruism A bridge is constructed acro ss the gully. While in this state, move-
ment is impossible for an agent. When certa in conditions are met,
the bridge is abandoned and the agents transit to the Search state.
TABLE 5.4: Properties used in Models 1 and 2.
Model 1 Model 2
Number of Steps 700 700
Time 10 150
Radius 2 -
Pheromone Thre shhold - 30
the differences were small and almost no difference in overall efficiency was
observed.
Exper imental results using the difficult map ar e shown in Fig. 5.18 and
Fig. 5.19. On the whole, Model 2 performed better in the difficult map. Fig-
ure 5.19 shows exp e rimental observations for the difficult map on a different
scale. Just as before, the horizontal axis represents the number of agents; how-
ever, the vertical axis represents the ratio of the total number of times agents
crossed bridges to the total number of times agents helped to form bridges.
This ratio indicates how useful the bridges formed were. From the data, it was
found that Model 2 yielded higher values than Model 1. For Model 1, the ra-
tio was usually about one. This means that even though a bridge was formed,
neighboring agents would not have used it efficiently. This was because in the
difficult map, unlike the simple map, gullies were present at various locations,
causing bridges to be formed at unnecessary sites with Model 1. With Model 2
higher ratios were found compared to that found with Model 1. Although it is
not evident from the g raph, in Model 2 the bridges were formed only at those
sites that were necessar y for bringing food to the nest. This was because the
pheromone was secreted along the way from the food source to the nest. The
concentration of pheromone indicated the optimal sites for bridge construc-
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