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can see from Fig. 2 (c) that in most cases the clone size is 1. While on the other hand,
VIS and most previous works use a fixed clone size (4 in VIS). This generally leads to
two main problems: 1) in the early stage, a fixed clone size may not be large enough
to speed up the convergence; 2) in the later stage, a fixed clone size may be too large
so that at each iteration step many unnecessary clones are produced.
Δ
Table 4.
Mean and variance values of GD and
for PAIA and VIS
ZDT1
GD
ZDT2
GD
ZDT3
GD
ZDT4
GD
Algorithm
σ
2
σ
2
σ
2
σ
2
VIS
1.32e-4
1.12e-9
1.10e-4
2.2e-12
1.23e-4
1.9e-11
1.23e-3
1.12e-6
PAIA
1.58e-4
2.31e-9
1.06e-4
5.7e-11
1.58e-4
4.6e-10
4.96e-4
1.53e-8
2
2
2
2
Algorithm
σ
σ
σ
σ
Δ
Δ
Δ
Δ
VIS
0.3142
6.31e-4
0.2123
3.12e-3
0.3451
1.22e-3
0.0834
1.12e-4
PAIA
0.3522
1.10e-3
0.3443
1.50e-3
0.4381
1.50e-3
0.3058
1.00e-3
Table 5.
Final population size and evaluation times of PAIA and VIS
Test
suite
Final Population
Evaluation Times
PAIA(mean) VIS
PAIA(mean) VIS
ZDT1
93
100
15844
28523
ZDT2
95
100
15856
29312
ZDT3
94
100
25365
32436
ZDT4
97
100
46899
38956
5 Discussions
5.1 The Differences Between AIS and Population-Based GA
It is clear that the proposed algorithm-PAIA offers significant advantages. However, as al-
ready stated in Section 1, presenting comparative good results is not the main objective of
this study. It was felt that only when the differences between AIS and traditional popula-
tion-based GAs are clarified, can one fully exploit the extra advantages that are exclu-
sively included in AIS. The fundamental differences can be summarized as follows:
1.
Reproduction mechanism:
AIS represents a type of asexual reproduction; while
on the other hand, population-based GA represents the counterpart. Through the
latter, the offspring is produced by crossing the chromosomes of both parents.
Through the former, each Ab copies itself to produce many clones.
2.
Selection scheme:
For population-based GA, good solutions are selected into the
mating pool with high probability. For AIS, good solutions are always selected.
3.
Evolution strategy:
For population-based GA, the whole population evolves by
using crossover. The hypothesis is that if both parents are the good ones their
crossed offspring would have a high probability of becoming even better solutions;
mutation is only used to jump out of the local optima (diversity is very important),
otherwise, GA is likely to lead to premature convergence; for AIS, since clones are
