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Fig. 12 The particles located
in another particle
'
s R
elimination
will be removed using the
dynamic elimination
technique
In which, t stands for the current iteration number and maximum iteration is the
maximum number of allowable iterations.
a
and
b
are positive constants regarding
a
¼
b
¼
as
100 and
10.
5.2.3 Results for Multi-objective Optimization
Five multi-objective benchmark problems are regarded which have similar features
such as the bounds of variables, the number of variables, the nature of Pareto-
optimal front and the true Pareto optimal solutions. These problems which are
unconstrained have two objective functions. The whole features of these algorithms
are illustrated in Table
13
. The contrast of the true Pareto optimal solutions and the
results of the hybrid algorithm is illustrated in Figs.
13
,
14
,
15
,
16
and
17
.Asitis
obtained, the hybrid algorithm can present a proper result in terms of converging to
the true Pareto optimal and gaining advantages of a diverse solution set.
In this comparison, the capability of the hybrid algorithm is contrasted to three
prominent optimization algorithms, that is, NSGA-II (Deb et al.
2002
), SPEA
(Zitzler and Theile
1999
) and PAES (Knowles and Corne
1999
) with respect to the
same test functions. Two crucial facts considered here are the diversity solution of
the solutions with respect to the Pareto optimal front and the capability to gain the
Pareto optimal set. Regarding these two facts, two performance metrics are utilized
in evaluating each of the above-mentioned facts.
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