The document discusses research on developing a new crossover operator called XOR for genetic algorithms. It proposes using XOR as the mathematical operator for crossover and mutation. It tests the XOR operator on several test functions and problems and finds it performs better than other crossover operators on most test functions, finding solutions faster. However, it does not work as well on some test cases like the travelling salesman problem. The document concludes the XOR operator shows potential to improve genetic algorithm performance but has limitations and further research is needed to address issues like high mutation rates and inconsistent results on some problems.

1. Made By:
Gyandeep Kansal(9911103464)
F-2

2.  It was indeed difficult to select one topic from the long list hat was
provided to us. I believe that it is technology that binds this entire
society together. Genetic Algorithms have been researched upon and
studied for several years now, surprisingly after all this time most of the
techniques developed are not efficient enough and/or resource intrinsic.
 It was with this basic idea that I chose the topic of research on genetic
algorithms so that I can understand and further the work done on this
particular topic
 In addition genetic algorithms as a technique is interesting and has
applications across various fields, such as secure communication,
optimizing programs, values and hardware etc.

3. Evaluation
When every new population is created each member is evaluated for its fitness by testing
for some attribute. For example in the One’s max problem each member is tested to see
how many of its genes contains the integer 1
Selection
Individuals are selected at random in groups after they are evaluated for their fitness and
the individuals with the highest fitness within these groups are used to populate the new
generation.
Crossover
Once the pool for the new members to be created from is selected crossover is used to
produce the new members a point is chosen at random on a chromosome where it will be
split and joined with the other half of another chromosome split at the same point in
order to make a new chromosome (a new member).

4. Mutation
Mutation to random members and is necessary to produce the randomness
required to prevent a population from becoming identical to previous
generations and in turn to bring about a higher fitness level. A point is picked at
random within a chromosome and the mutation that occurs is random.

5. Here crossover and mutation are shown
diagrammatically. As evident from the
diagrams crossover is the selection of bits for
the purpose of “exploitation” whereas
mutation serves the purpose of “exploration”.

7. The operator called XOR Operates in 3 steps. All of these steps are discussed one by
one.
For Crossover
 Step-1: In this step two parents are selected for the XOR step
 Step-2: The chromosomes of the child are taken from parent 1 if a randomly
generated number is less than or equal to a predefined number known as
Uniformrate.
 Step-3: If the random number generated is greater than Uniformrate, then for that
bit of child’s chromosome a XOR is taken of Parent 1 and Parent 2’s corresponding
bit
For Mutation
 Step-1: The child’s chromosome is run through a loop.
 Step-2: For every bit a random number is generated and if that number is greater
than the predefined MutationRate then the child retains its original bit.
 Step-3: If the number is less than the mutation rate, then the child’s bit is XOR’ed
with a rounded off random number between zero and one. Thus we have a mutated
child.

8. On the basis of test case status, we came to know about the limitations of our
proposed algorithm that our algorithm is not working properly when
 There is a high mutation rate requirement
 For some test cases the algorithm is not functioning as well as it is supposed to.
 The functionality of roll back has not been able to be applied

9. The proposed algorithm has been applied to two test programs:
General Genetic Algorithm: It has been found in the results that the proposed algorithm was
able to find the solution in 16 generations and half the execution time than the common G.A.
Which was used in the previous version of the program
Travelling Salesman Problem: The Proposed algorithm did not work on this problem.
Through this problem we were able to properly analyze the limitations and implementation
issues of our problem

10. Function
Name
Performance
before XOR
Performance
after XOR
Remarks
Generalized
G.A. Problem
21
generations
16
generations
Algorithm
Successfully
applied
TSP 100
generations
N/A Algorithm not
applicable

11. The above project aimed at finding a new approach for genetic algorithms, hence
we arrived at a solution, the XOR approach. However there is plenty of scope for
development in the future. We discuss a few future scope of development
 One of the reasons for choosing XOR as a mathematical operator was to someday
include the feature of “ROLLBACK” in the algorithm. Currently if the algorithms
next generation is not ‘Healthier’ than the parent generation, they are rejected at
the next selection phase. Using a rollback based algorithm will help in going back
to the previous step using reverse xor on children and re-evaluating the children of
that generation until a healthier generation is produced
 Here our algorithm did not work better for some of the test functions, we aim to
remove that discrepancy in the future

12. In this project, a new crossover operator called XOR is proposed and experiments are
conducted. The proposed operator is tested by a number of test functions with various levels
of difficulty. A comparison between the results of this method and the results of other
crossover operators are made. XOR operator gives better results according to other crossover
operators. Although the most of crossover operators showed similar results, XOR operator
had slightly better results than the other crossover for F1, F2, F4, F5 functions. For F3
function, HC operator has slightly better result than XOR operator. However, XOR operator
produces better result than SPC, TPC, IC and AC. For F6 function, the results of this study
are very close to those of AC, but in generally XOR operator performed the best results than
other crossover operators. The most important advantage of the proposed method is that more
variety is presented in possible number of children according to SPC and TPC operators. The
experiments and the results presented in the project clearly reveal the potential capability of
the proposed method in optimization processing based on GA. Moreover, it has the great
potential to improve the performance of GA applications in different area of engineering.
As seen in test programs, only those programs may be optimised by this algorithm whose
objective function and population array can be represented by binary numbers.