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close to a global optima is slightly better than a solution
j
in the region close to
another global optima of the problem, the mutated clones of solution
i
tend to
be better than the mutated clones of solution
j
and sometimes even better than
solution
j
at all. Therefore, the solution
i
and probably the most of its mutated
clones are selected to continue in the population while solution
j
, that corre-
sponds to a different optima of the problem, may be discarded. Other important
aspect that lead to the above results is the fact that the Grid procedure analyzes
only the objective space in multi-objective problems to select the most spread
solutions, without considering any information of the spread of these solutions
in the variable space. The obtained results for the ZDT1 and ZDT2 problems
showed that this mechanism seems to be ecient in multi-objective uni-global
problems, but needs improvements to treat multi-objective multi-global opti-
mization problems.
7
Concluding Remarks
This work presented a new immune-inspired algorithm for omni-optimization,
called omni-aiNet, capable of solving single and multi-objective problems, with
a single or multiple global optimal solutions. The proposed algorithm unites the
concepts of omni-optimization proposed by Deb and Tiwari [8] to principles of
Artificial Immune Systems, giving to the algorithm the capabilities of dynami-
cally adjusting its population size and avoiding high levels of redundancy within
the population.
The omni-aiNet was applied to several optimization problems with distinct
characteristics and compared to the performance of the DT omni-optimizer algo-
rithm [8]. The obtained results showed that the proposed approach seems very
promising, once it was even capable of outperforming the DT omni-optimizer
for two of the problems treated in this work. However, further improvements are
still necessary to the omni-aiNet algorithm, specially to its diversity maintenance
mechanism when both the spaces of objectives and variables are considered.
For future work, besides the necessary improvements to the algorithm, a more
rigorous series of tests should also be made, covering a wider range of problems
and comparing the results not only to the Deb and Tiwari's omni-optimizer,
but also to other well known state-of-the-art algorithms. Sensitivity analysis
should also be made to detect the impact of each input parameter on the overall
performance of the algorithm.
Acknowledgment
This work has been supported by grants from Fapesp, Capes and CNPq. The
authors would like to specially thank Prof. Kalyanmoy Deb and Santosh Ti-
wari for providing their omni-optimizer software package and for all the support
given.
