agents are the bottleneck of performance. However,
in actual applications, it is more difficult to increase
the number of elevators owing to the much higher cost
and effort required for their installation.
Interestingly, we found that the planning time of
double SSS exceeded that of the proposed method
when N
c
≥ 8. Furthermore, the difference in plan-
ning time between SSS and the proposed method be-
came gradually smaller with an increase in the num-
ber of carrier agents N
c
. This occurs because the
baseline methods need to generate a larger number of
lower (child) nodes as the number of carrier agents
increase, and thus, the root node in SSS and double
SSS is required to visit all the nodes before moving
on to the nodes at the next depth level. This discus-
sion also suggests that many messages are necessary
in the baseline methods. Meanwhile, agents using the
proposed method could discriminate better proposals
from appropriate agents through negotiation, and this
resulted in higher efficiency and fewer messages.
5.5 Conclusion
We propose a scheduling and negotiation method for
tasks that require double synchronization between
heterogeneous agents. To achieve efficient task exe-
cutions, our method enables agents to generate their
schedule by determining the effective synchroniza-
tion times and reducing the unnecessary idle time
through a negotiation process, which is an extension
of the CNP. It also decides the appropriate coopera-
tive agents step by step, thus reducing the number of
messages during the negotiation process. We exper-
imentally showed that the proposed method outper-
formed the baseline methods, SSS and double SSS,
for DSMAPD problem instances. It also involved a
reasonable computational cost in environments where
many agents are required to cooperate with other
agents to complete DSMAPD tasks.
In the future, we plan to extend our method to
more complex tasks, such as tasks that need more
synchronization times and locations and tasks that
have their own deadlines. Another extension is that
for tasks in which agents cannot move at a con-
stant speed. We also want to integrate our method
with one of the recent path-finding algorithms for
MAPD (Sharon et al., 2015; Ma et al., 2017; Ya-
mauchi et al., 2022; Okumura et al., 2022; Miyashita
et al., 2023).
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