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MAINTENANCE SCHEDULING WITH GENETIC ALGORITHMS
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interval, the corresponding bit assumes value 1, otherwise it is 0. For
example, the string 0 1 0 0 presents a schedule for a unit to be
maintained in the second interval. It also shows that the number of
intervals required for maintenance of this unit is equal to 1. Thus, a
complete maintenance schedule for our problem can be represented as
a 28-bit chromosome.
However, crossover and mutation operators could easily create
binary strings that call for maintaining some units more than once
and others not at all. In addition, we could call for maintenance
periods that would exceed the number of intervals really required for
unit maintenance.
A better approach is to change the chromosome syntax. As already
discussed, a chromosome is a collection of elementary parts called
genes. Traditionally, each gene is represented by only one bit and
cannot be broken into smaller elements. For our problem, we can adopt
the same concept, but represent a gene by four bits. In other words, the
smallest indivisible part of our chromosome is a 4-bit string. This
representation allows crossover and mutation operators to act according
to the theoretical grounding of genetic algorithms. What remains
to be done is to produce a pool of genes for each unit:
Unit 1:
Unit 2:
Unit 3:
Unit 4:
Unit 5:
Unit 6:
Unit 7:
1 1 0 0
1 1 0 0
1 0 0 0
1 0 0 0
1 0 0 0
0 1 1 0
0 1 1 0
0 1 0 0
0 1 0 0
0 1 0 0
0 0 1 1
0 0 1 1
0 0 1 0
0 0 1 0
0 0 1 0
0 0 0 1
0 0 0 1
0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
The GA can now create an initial population of chromosomes by filling
7-gene chromosomes with genes randomly selected from the corresponding
pools. A sample of such a chromosome is shown in Figure 7.9.
Step 3:
Define a fitness function to evaluate the chromosome performance
The chromosome evaluation is a crucial part of the GA, because
chromosomes are selected for mating based on their fitness. The fitness
function must capture what makes a maintenance schedule either good
or bad for the user. For our problem we apply a fairly simple function
concerned with constraint violations and the net reserve at each
interval.
Figure 7.9
A chromosome for the scheduling problem