a multi-objective bisexual reproduction genetic algorithm for ...

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A population is a list of n chromosomes. Starting with an empty population, one
after another we create and add new random chromosomes into this population.
A pseudo code for creating this is given in Figure 3-12.
For each course
n= number of time-slots needed for this class (= number of credits)
Repeat
Randomly select a classroom in list of classrooms that are permissible for this course
Search n free time-slots in the chosen classroom
If (n free time-slots are found)
Book the current course to these time-slots
Until (course is booked)
FIGURE 3-12 Pseudo code for creating a random chromosome
3.6.4 Evaluating Fitness Function
As represented above, each chromosome x has a fitness value f(x). In this
section, we discuss how to find f(x).
Assume that we have m hard constraints. Let Hc i denote the number of
conflicted hard constraints i, where i = 1..m. Each hard constraints i is assigned a
penalty cost Penalty_hc i . We use f 1 (x) to denote the fitness value of hard constraints.
1
f1(
x)
= Eq. 3-1
m
1+
Hc Penalty _ hc
∑
i=
1
i
Similarly assume that we have n soft constraints. Let Sc j denote the number of
conflicted soft constraints j, where j = 0..n. Each soft constraint j is assigned a penalty
cost Penalty_sc j . We use f 2 (x) to denote the fitness value of soft constraints.
∑
j=
1
j
sc j
i
1
f
2
( x)
= Eq. 3-2
n
1+
Sc Penalty _
Thus, if a chromosome has a lower number of conflicts, f 1 (x) and f 2 (x) will have
a higher fitness value. We use f(x) to denote the fitness value of the chromosome x.
f ( x)
= W ( ) ( )
Eq. 3-3
1
f1
x + W2
f
2
x