4000
4500
5000
5500
0 100 200 300
Total cost
120
140
160
180
200
0 100 200 300
Maximum cost
0.04
0.06
0.08
0.1
0 100 200 300
Theil index
Figure 2: Anytime curve (gamma92, d = 5, c = 150).
Table 6 compares the execution time of the so-
lution methods for 1000 iterations. The experiment
was performed on a computer with g++ (GCC) 8.5.0,
MPIR 3.0.0, Linux version 4.18, Intel (R) Core (TM)
i9-9900 CPU @ 3.10GHz and 64GB memory. As
the ﬁrst study, the total computation time was evalu-
ated excluding communication delay. Note that there
are opportunities to improve our experimental imple-
mentation. A major common issue is the processing
to handle the sorted objective vectors and the lexi-
max criterion. For each criterion, the parts of the
process of sampling new solution sets were differ-
ently affected by the implementation techniques. Fig-
ure 2 shows several selected anytime curves of solu-
tion quality for gamma92, d = 5 and c = 150. While
the leximax-based criteria took a long execution time,
their results improved in relatively earlier steps of the
search process.
5 CONCLUSIONS
We applied an evolutionary algorithm called AED
to asymmetric multi-objective DCOPs in which opti-
mization is performed on a leximax criterion that im-
proves the worst case and fairness among agents. To
handle asymmetry constraints, we extended the struc-
ture in the algorithm. In addition, we replaced the cri-
teria in the sampling process by one of social welfare
criteria and experimentally investigated the sampling
criteria. Our result shows the effect of sampling based
on leximax-based criteria.
Our future work will include more exact evalu-
ations using improved implementation of the algo-
rithm, a comparison with different classes of algo-
rithms, detailed analysis on the search space of the
problems with leximax criterion, and applications to
practical domains.
ACKNOWLEDGEMENTS
This work was supported in part by JSPS KAKENHI
Grant Number JP19K12117.
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