Page 226 - Mechatronics for Safety, Security and Dependability in a New Era

Ch43-I044963.fm Page 210 Tuesday, August 1, 2006 3:58 PM
Ch43-I044963.fm
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210 Page 210 Tuesday, August 1, 2006 3:58 PM
Crossover points
Crossover points
Parent1 … J 3 (0) … J 1 (1) … … …
Parent1
Parent2 … … … J 3 (0) … … …
Parent2
(a) Determination of dominance of genes
of genes
of dominance
(a) Determination
Offspring1 … J 1 (1) … J 3 (0) … … - …
Offspring1
…
…
J 3(0)
…
J 1(1)
…
Offspring2
...
... 1
Offspring2 … … ... 1 J 3 (0) … … …
3(0) … -
(b) Exchange of genes
(b) Exchange of genes
Figure 2: Crossover process
STEP2 Creation of initial population
Two cases are considered in the creation of the initial population including the individuals which
represent the production schedules. They are,
(1) First activation of reactive scheduling process at time T\
(2) Second or later activations of reactive scheduling process at time T 2 or later.
For the cases of 1 and 2, the reactive scheduling process creates the initial population through the
STEP2-1 and STEP2-2, respectively.
STEP2-1 First activation of the reactive scheduling process
The reactive scheduling process generates the initial population randomly. The initial population
created here should satisfy the constraint on the schedule of the operations starting before (T] + dt).
STEP2-2 Second or later activations of the reactive scheduling process
In the case 2, the reactive scheduling process can inherit the population created in the previous reactive
scheduling process. Two cases are considered for the inheritance process of the population as shown in
the fallowings.
Case-A No operations start between T x and (T x + dt)
If no operations start between T x and (T x + dt), all the individuals of the last population of the previous
reactive scheduling process are inherited to a new reactive scheduling process between T x and (T x +
dt).

Case-B Some operations start between T x and (T x + dt)
If some operations start between T x and (T x + dt), the production schedules of these operations should
be fixed. Therefore, a new reactive scheduling process can inherit only the individuals, which are
consistent with the schedules of the fixed operations, from the last population created in the previous
reactive scheduling process. The other individuals are deleted, and new individuals are created from
the inherited ones randomly.

STEP3 Application of genetic operators to the population
The fitness value of each individual is calculated. The total tardiness of the production schedule which
has to be minimized is selected as the fitness value. Based on the fitness value, genetic operators, such
as selection, crossover and mutation, are applied to the individuals of the population created in STEP2,
in order to create new individuals of the next population. Crossover is carried out by the following
steps.