advance operators. explain about the diploid , dominance, and partial match crossover and the order crossover Technologies Multi objective optimization , knowledge base technologies hibrid, parallel computing

1. Advance operator and
technique in Genetic
algorithm
JMHM Jayamaha
SEU/IS/10/PS/104
PS0372

2. Content
 The low-level operators
 Diploidy, Dominance
 Inversion and Reordering
 Partially Matched Crossover (PMX).
 Order corssover
 Multi-Objective Optimization
 Knowledge Based Techniques
 Summary
 References

3. Diploidy, Dominance
 When nature wants to construct a more complex or animal life to rely upon, a
more complex underlying chromosome structure is needed and this is
achieved by the diploid or double stranded chromosomes
 In the diploid form, a genotype carries one or more pairs of chromosomes,
each containing information for the same function.
 Consider a diploid chromosome structure where different letters represent
different alleles (different gene function values)
 Allele represents the property of a particular gene

4. Diploidy, Dominance (continue)
 Each locus of a letter represents one allele.
 The uppercase and the lowercase letters mentioned above represent the
alternative alleles at that position.
 Originally, in nature each allele may represent different phenotypic
properties. For example Q may represent gray haired gene and q may be
black haired gene.
 a pair of genes exists describing each function; there should be some aspect
to decide which of the two values to choose because,
 for example, the phenotype may not have both gray haired and black haired at the
same time.

5. Diploidy, Dominance(continue)
 The basic approach for eliminating this conflict of redundancy is through a
genetic called dominance.
 At a locus, it has been noted that one allele (called the dominant allele) will
take the precedence over the other alternative allele (called the recessive
allele).
 In the above example, if it is assumed that all uppercase letters are dominant
and all lowercase letters are recessive, the phenotype expressed by the
example chromosome is written as,

6. Diploidy, Dominance(continue)
 The dominant gene is expressed when heterozygote (mixed, Pp→P) or
homozygote (SS→S) and the recessive genes expressed only when homozygote
(tt→t).

7. Diploidy, Dominance(continue)
 Advantages
 Diploid chromosomes lend advantages to individuals where the environment may
change over a period of time
 Disadvantages
 Currently harmful, but potentially useful alleles can still be maintained, but in a
recessive position
 In a GA, diploidy might be useful in an on-line application where the system
could switch between different states.

8. Inversion and Reordering
 Inversion operator is a primary natural mechanism to recode a problem.
 In inversion operator, two points are selected along the length of the
chromosome, the chromosome is cut at those points and the end points of the
section cut, gets reversed (switched, swapped).
 To make it clear, consider a chromosome of length 8 where two inverse points
are selected random (the points are 2 and 6 denoted by ˆ character)
 On using inversion operator, the string becomes,

9. Inversion and Reordering(continue)
 The features of inversion and crossover are combined together to produce a
single operator, which lead to the development of other reordering operators.
On combining inversion and crossover, the reordering operators formulated
are
 1. Partially Matched Crossover (PMX).
 2. Order Crossover (OX).
 3. Cycle Crossover (CX).

10. Partially Matched Crossover (PMX).
 In Partially Matched Crossover, two strings are aligned, and two crossover
points are selected uniformly at random along the length of the strings.
 The two crossover points give a matching selection, which is used to affect a
cross through position by-position exchange operations.
 Consider two strings
 Two crossover points were selected at random, and PMX proceeds by position
wise exchanges.

11. Partially Matched Crossover (PMX).(continue)
 In-between the crossover points the genes get exchanged i.e., the 3 and the
2, the 6 and the 7, the 5 and the 9 exchange places. This is by mapping
parent B to parent A. Now mapping parent A to parent B, the 7 and the 6, the
9 and the 5, the 2 and the 3 exchange places.
 Thus after PMX, the offspring produced as follows

12. Order Crossover (OX)
 The order crossover begins in a manner similar to PMX. But instead of using
point by- point exchanges as PMX does, order crossover applies sliding motion
to fill the left out holes by transferring the mapped positions.
 Consider the parent chromosomes,
 On mapping parent B with parent A, the places 3,6 and 5 are left with holes.

13. Order Crossover (OX)(continue)
 These holes are now filled with a sliding motion that starts with the second
crossover point.
 The holes are then filled with the matching section taken from the parent A.
Thus performing this operation, the offspring produced using order crossover
is as given below.

14. Multi-Objective Optimization
 Multi-objective optimization problems have received interest form researches
since early 1960s
 In a multi-objective optimization problem, multiple objective functions need
to be optimized simultaneously.
 In the case of multiple objectives, there does not necessarily exist a solution
that is best with respect to all objectives because of differentiation between
objectives.
 A solution may be best in one objective but worst in another.
 Therefore, there usually exist a set of solutions for the multiple-objective
 case, which cannot simply be compared with each other.

15. Multi-Objective Optimization(continue)
 For such solutions, called Pareto optimal solutions or non-dominated
solutions, no improvement is possible in any objective function without
sacrificing at least one of the other objective functions.
 Thus by using the concept of Pareto-optimality we can find a set of solutions
that are all optimal compromises between the conflicting objectives.
 Pareto-optimality is a concept used economics, game theory, etc.
 In the past few years, there has been a wide development in applying genetic
algorithms to solve the multi-objective optimization problem, known as
evolutionary multi-objective optimization or genetic multi-objective
optimization.

16. Multi-Objective Optimization(continue)
 The population-to-population approach is beneficial in the exploration of
Pareto-optimal solutions.
 The main issue in solving multi-objective optimization problems by use of
genetic algorithms is how to determine the fitness value of individuals
according to multiple objectives.

17. Knowledge Based Techniques
 While most research has gone into GAs using the traditional crossover and
mutation operators, some have advocated designing new operators for each
task, using domain knowledge.
 This makes each GA more task specific (less robust), but may improve
performance significantly.
 GA is being designed to tackle a real world problem, and has to compete with
other search and optimization techniques, the incorporation of domain
knowledge often makes sense.
 Domain knowledge may be used to prevent obviously unfit chromosomes,or
those, which would violate problem constraints, from being produced in the
first place.

18. Knowledge Based Techniques(continue)
 This avoids wasting time evaluating such individuals, and avoids introducing
poor performers into the population.
 For example, a researcher designed analogous crossover for his task in robotic
trajectory generation.
 This used local information in the chromosome (i.e., the values of just a few
genes) to decide which crossover sites would be certain to yield unfit offspring.
 Domain knowledge can also be used to design local improvement operators,
which allow more efficient exploration of the search space around good point
 It can also be used to perform heuristic initialization of the population, so
that search begins with some reasonably good points, rather than a random
set.

19. Knowledge Based Techniques(continue)
 The various methods for combining problem specific information with genetic
algorithm are as follows:
 Hybrid schemes
 Parallel computers.

20. Hybrid Schemes
 In hybrid schemes GAs are used to get close to optimum value, then
conventional optimization schemes like greedy search, gradient search or
stochastic hill climbing may be used to become closer to optimum value.
 The hybrid scheme can be represented using scheme as shown in Figure

22. Hybrid Schemes (continue)
 Thus from Figure , it can be noted that the genetic algorithm sorts out peak
and the local search techniques are used for hill climbing. Considering greedy
heuristic crossover for Traveling salesman problem, if chromosomes are
permutations of city numbers, then normal crossover may produce infeasible
chromosomes. This is done by,
 Start at a random city X and go to the closest city to X using the parent’s tours;
repeat.

23. Parallel Computers
 Using parallel computers in Genetic Algorithms, master/slave operation is
performed.
 Master does selection and mating and slaves evaluated fitness of new
chromosomes.
 Master waits for all the slaves to finish or master can hand out new work as
each slave finishes.
 Thus on a parallel machine the conventional optimization can be done on
each species on its own CPU. This is shown in next figure.

25. Summary
 The low-level operators
 Diploidy, Dominance
 Multi-Objective Optimization
 Knowledge Based Techniques

26. References
 Introduction to Genetic Algorithms by S.N.Sivanandam · S.N.Deepa (page 83 –
104)