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If there is X
j
in a generation, which meets the
condition described as (23), the individual X is called
j
the ideal excellent individual.
r = { r ( X ), r ( X ), r ( X )} = r
(23)
j C j T j Q j g
Similarly, if there is X in a generation, which
j
meets the condition described as (24).
r
j= { rC
( X
j
), rT
( X
j
), rQ
( X
j
)} = r
(24)
b
Thus, for individual X
i
, u ( X ) and u ( )
g i
b
X
i
are defined
as the membership degree of X
i
to the ideal excellent
individual and the ideal inferior individual. Both of them
meet with the conditions described as (25):
⎧0
≤ u
g
( X
i
) ≤ 1
⎪
0 ≤ ub
( X
i
) ≤ 1
(25)
⎨
⎪u
( X ) + u ( X ) = 1
g i b i
⎪
⎩i
= 1,..., M
In order to get the excellent membership degree of X ,
namely u g
(X ) , we set up the optimization rule: the sum
of the square of hamming weighted distance of X to
the ideal excellent individual and the square of hamming
weighted distance of X to the ideal inferior individual
is minimal.
C. Algorithm design
1) Genetic Operators design
The first step in GA is computing the fitness value.
Each chromosome has a selection probability, which is
decided by the distribution of all individual fitness in a
generation. The roulette wheel selection method is
adopted to compute the selection probability in this
paper. Supposing the fitness value for each
chromosome is f k
(, k = 1,2, ⋅⋅⋅,
M)
, and the total fitness
value in a generation is M
∑ f . Then, the selection
k
k=
1
probability for the k -th individual is f k
/ ∑ f ;The
k
k=
1
single point crossover is applied to produce new
individual for next generation. One integer from 0 to
N −1 is decided by random functions, which
expresses the crossover position. The typical crossover
probability P c ranges from 0.6 to 0.9;The mutation
operator has some restriction conditions. The mutation
is carried out at a position in the reasonable integer
range.
2) Selection strategy and ending condition of
algorithm
The M individuals selected from the current
generation and the father generation according to the
fitness value form the next generation. This new
generation reserves the better individuals of the
current generation and the father generation. The
ending condition of GA is the fitness value in a new
generation is convergent. At last, several optimized
individuals, namely several EMP-s, will be exported,
and the decision-maker can select one of them.
V. CONCLUSION
M
To research the networked manufacturing resources
optimization deployment, the idea of LMU and LMP is
put forward, and the information model of networked
manufacturing assignments for a complex part is set up
based on them; For convenience of networked
manufacturing resources optimization deployment, the
manufacturing ability information for PMU is
encapsulated and expressed by LMU; To obtain the
feasible candidate PMU-s, the pre-deployment between
LMU and PMU is implemented by information mapping
in considering the resources manufacturing abilities and
the sub-tasks manufacturing requirements.
To realize networked manufacturing resources
optimization deployment, manufacturing cost, time to
market and manufacturing quality are the most important
factors. In considering these criteria we model the
optimization deployment problem by a multi-objectives
optimization problem. Then, transforming the
multi-objectives optimization problem into a single
objective optimization problem, the mathematics model
and implementing algorithm of manufacturing resources
optimization deployment are studied based on GA. The
recommended GA with a relative fitness function to
decrease the influence of non-standardization on the
optimization result can fast achieve the optimal solution
of the mentioned problems with a probability. A typical
example shows the algorithm has the better synthetic
performance in both computational speed and optimality,
and the computation results show its potential to the
networked manufacturing resources optimization
deployment.
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