Crossover methods and mutation of GA

5.4.5 three parent crossover
in this crossover technique, three parents are randomly chosen. each bit of the first parent is compared with the bit of the second parent. if both are the same, the bit is taken for the offspring otherwise the bit from the third parent is taken for the
offspring. this concept is illustrated in fig.11

fig.11 three parent crossover

5.4.6 precedence preservative crossover (ppx)
ppx was independently developed for vehicle routing problems by blanton and wainwright (1993) and for scheduling problems by bierwirth et al. (1996). the operator passes on precedence relations of operations given in two parental permutations
to one offspring at the same rate, while no new precedence relations are introduced. ppx is illustrated in below, for a problem consisting of six operations a–f.

the operator works as follows:
• a vector of length sigma, sub i=1to mi, representing the number
of operations involved in the problem, is randomly filled with elements of the set {1, 2}.
• this vector defines the order in which the operations are successively drawn from parent 1 and parent 2.
• we can also consider the parent and offspring permutations as lists, for which the operations ‘append’ and ‘deleting’ are defined.
• first we start by initializing an empty offspring.
• the leftmost operation in one of the two parents is selected in accordance with the order of parents given in the vector.
• after an operation is selected it is deletingd in both parents.
• finally the selected operation is appended to the offspring.
• this step is repeated until both parents are empty and the offspring contains all operations involved.
• note that ppx does not work in a uniform-crossover manner due to the ‘deletion append’ scheme used.
example is shown in fig.12


fig.12 ppx crossover