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Table 3.25.
Final population with fitness
Fitness
Population
31
1
3
5
2
4
31
5
4
3
2
1
33
4
5
3
1
2
31
2
1
4
3
5
31
3
5
4
2
1
31
2
1
4
3
5
32
4
3
5
1
2
30
2
1
3
5
4
32
2
5
1
4
3
31
5
3
1
2
4
The new solution has a fitness of 30, which is a new fitness from the previous gen-
eration. This population is then taken into the next generation. Since we specified the
G
max
= 1, only 1 iteration of the routine will take place.
Using the above outlined process, it is possible to formulate the basis for most per-
mutative problems.
3.6
Flow Shop Scheduling
One of the common manufacturing tasks is
scheduling
. Often in most manufacturing
systems, a number of tasks have to be completed on every
job
. Usually all these jobs
have to follow the same route through the different
machines
, which are set up in a
series. Such an environment is called a
flow shop
(FSS) [30].
The standard three-field notation [20] used is that for representing a scheduling prob-
lem as
describes the de-
viations from standard scheduling assumptions, and
F
(
C
) describes the objective
C
being optimised. This research solves the generic flow shop problem represented as
n
/
m
/
F
α
|
β
|
F
(
C
),where
α
describes the machine environment,
β
F
(
C
max
).
Stating these problem descriptions more elaborately, the minimization of completion
time (makespan) for a flow shop schedule is equivalent to minimizing the objective
function
||
ℑ
:
n
j
=1
C
m
,
j
ℑ
=
(3.8)
s.t.
C
i
,
j
= max
C
i
−
1
,
j
,
C
i
,
j
−
1
+
P
i
,
j
(3.9)
j
k
=1
C
1
,
k
;
where,
C
m
,
j
= the completion time of job
j
,
C
i
,
j
=
k
(any given value),
C
i
,
j
=
j
k
=1
C
k
,
1
machine number,
j
jobinsequence,
P
i
,
j
processing time of job
j
on
C
i
,
j
=
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