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positive, negative or not correlated, as well as at
various strengths. The type of correlation between
two target-functions is determined by the correla-
tions between their constitutive requirements. In
this respect, the rest of the n -1 target-functions
can be sorted on three categories: the group of
those target-functions that are positive correlated
with PTF , the group of those target-functions
that are not correlated with PTF and the group
of those target-functions that are negative cor-
related with PTF .
Further, the algorithm asks to order the target-
functions inside each of the three groups. Con-
sidering that the PTF is the k -th target-function
in the set TF from step 2, for the target-functions
that are positive or negative correlated with PTF
an index will be calculated; index denoted with
H j ( t ), j = 1, …, n , j k , as the product between
the value weight W j ( t ), j = 1, …, n, j k and the
correlation coefficient C jk , j = 1, …, n , j k . This
formula is shown below:
a. The solution corresponding to the PTF will
be taken and analyzed together with the solu-
tion corresponding to the first target-function
in the group of the target-functions that are
positive correlated with PTF . Because the
two target-functions are positive correlated,
the best ideas from the local solutions will
be combined, resulting an improved hybrid
solution.
b. The hybrid solution from (a) will be then
analyzed against the local solution corre-
sponding to the second target-function in
the group of the target-functions that are
positive correlated with PTF . The new vari-
ant will result as a combination of the best
ideas from the hybrid solution generated at
phase (a) and from the current local variant.
c. The process will go on in the manner above
described until all target-functions from the
group of target-functions that are positive
correlated with PTF are consumed. After
that, the group of no correlated target-func-
tions is taken into account and the process is
continued until all of these target-functions
are consumed. At the end, the group of target-
functions that are negative correlated with
PTF will be taken into account. Because at
this phase potential conflicts could occur,
they have to be solved without compromises,
if possible. In this respect, it is firstly required
to identify pairs of conflicting problems
between the compared variants. Afterwards,
innovative solutions have to be formulated.
Methods like TRIZ could offer a real support
in this respect. At the end of this process, the
complete overall solution will be defined.
H t W t C j
( )
=
( )
,
=
1
,
n j
,
k C
,
0 .
j
j
jk
jk
(4)
In the group of target-functions that are positive
correlated with PTF, the target-functions will be or-
dered starting with the one having the highest H and
ending with the one having the lowest H . The same
rule is kept for the group of target-functions that are
negative correlated with PTF . It is highlighted the
fact that C jk < 0 in the group of negative correlated
target-functions, so the one with the highest H will
have the lowest magnitude in absolute value, too.
The target-functions that are not correlated with
PTF will be ordered starting with the one having
the highest value weight W and ending with the
one having the lowest value weight W .
In the last stage, the aggregated solution is
generated following an iterative approach. The
aggregated solution will result as a “compromise
& combination” of the set of n local solutions. In
this respect, the following rule is applied:
Step 9
The result is reviewed with respect to the most
relevant performance characteristics of each tar-
get-functions and with respect to a cost-objective.
Relevance of the performance characteristics for
each target-function TF j , j = 1, …, n , is given by
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