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the nonogram ghoostly, Essays (university) of Life Sciences

Universitas Sriwijaya (US)Life Sciences

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2016/2017

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Performance Analysis of a Novel Crossover Technique on Permutation
Encoded Genetic Algorithms
R. Lakshmi, K. Vivekanandan
Assistant Professor, CSE professor, Dept. of Computer Science
Pondicherry University, India pondicherry Engineering College, India
rlakshmiselva@yahoo.co.in k.vivekanandan@pec.edu
Abstract — The Performance of GA is mainly
dependent on two factors are chromosome
representation and the selection of relevant genetic
operators such as selection, crossover and mutation.
Many GA crossover operators have been invented by
researchers because the performance of GA depends on
an ability of these operators. Though there are several
crossover techniques available, these are randomly
removes the duplicate genes in a chromosome lead to
more computation time to converge with optimal
solution. Since most of them do not have stable model.
Removing duplicate genes in a chromosome is a hectic
process in GA. To overcome these difficulties, this
paper uses a novel crossover called Fast Order Mapped
Crossover (FOMX) which does not perform
randomness and gene level comparison to find
duplicate genes in individuals. To prove this technique,
travelling salesperson problem (tsp) has chosen in
order to find the optimal path of a tour. This technique
is applied on different tsp instances and the obtained
results are compared with the existing crossover
techniques.
Keywords — Genetic Algorithm, Fast Order Mapped
Crossover, Alternate Position Crossover, Maximal
Preservative Crossover, Greedy Crossover, Performance
Analysis
I. INTRODUCTION
The architecture of systems that implement Genetic algorithm
(GA) is more able to adapt to a wide range of problems.
Genetic algorithms are basically algorithms based on natural
biological evolution. The Darwin’s theory of “Survival of the
fittest” [3] is followed in GA to get the optimized solutions.
Genetic Algorithm is an optimization strategy where points in
the problem space are analogous to organisms involved in a
process of natural selection. Each organism is represented by a
character string analogous to a chromosome, with each
character position analogous to a gene and each character
value analogous to an allele. If the population size is too
small, the GA without recombination outperforms the GA
with recombination. If the population is large or the search
space is more the GA with crossover outperforms the GA
without crossover. The number of points in crossover is the
number of times the genetic material in an offspring is
inherited from the first parent, second parent and vice versa.
Though, different types of GA, Operators and parameters are
exist, there is a mission for better and better techniques and
algorithms to overcome the difficulties available with the
existing techniques and to improve the performance of genetic
algorithms. Devising of new algorithm, new operators and
new parameters for GA is an additional insight to the field of
genetic algorithm.
GA is composed of operators and genetic parameters.
Crossover operators are the backbone of genetic algorithms.
Crossover is generally applied with higher probability (Pc).
Since performance of GA is the prime factor relying upon
which type of crossover operators can be used for any given
problem whose problem difficulty is known and whose
parameters has been specified by the user and the selection of
available efficiency enhancement techniques like evaluation-
relaxation, etc. When the recombinant operators such as
crossover and mutation are applied on binary information, the
consequences are ignorable. If the same is applied on
permutated encoded information produces replication in
individuals. In order to remove those duplicate genes in
chromosomes, an additional repairing mechanism is required.
Few crossover operators [4] [11] [13] may not lead
duplication in chromosomes but algorithmically they are very
poor. Due to the inefficiencies of these crossover techniques
the performance of genetic algorithm is reduced to some
extent.
In line with the above existing approaches, a novel effective
crossover technique called Fast Order Mapping Crossover
(FOMX) with the features of standard procedure, diversity
pressure, convergence speed and the quality of solution has
been devised to eradicate duplicates in individuals. In this
paper the FOMX method is used to remove the duplicate cities
in a tour which means invalid tour is corrected into a valid tour
in a short time. The proposed crossover technique drastically
IEEE - International Conference on Advances in Engineering and Technology-(ICAET 2014)
ISBN No.: 978-1-4799-4949-6 @ 2014 IEEE
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Performance Analysis of a Novel Crossover Technique on Permutation

Encoded Genetic Algorithms

R. Lakshmi, K. Vivekanandan Assistant Professor, CSE professor, Dept. of Computer Science Pondicherry University, India pondicherry Engineering College, India rlakshmiselva@yahoo.co.in k.vivekanandan@pec.edu

Abstract — The Performance of GA is mainly dependent on two factors are chromosome representation and the selection of relevant genetic operators such as selection, crossover and mutation. Many GA crossover operators have been invented by researchers because the performance of GA depends on an ability of these operators. Though there are several crossover techniques available, these are randomly removes the duplicate genes in a chromosome lead to more computation time to converge with optimal solution. Since most of them do not have stable model. Removing duplicate genes in a chromosome is a hectic process in GA. To overcome these difficulties, this paper uses a novel crossover called Fast Order Mapped Crossover (FOMX) which does not perform randomness and gene level comparison to find duplicate genes in individuals. To prove this technique, travelling salesperson problem (tsp) has chosen in order to find the optimal path of a tour. This technique is applied on different tsp instances and the obtained results are compared with the existing crossover techniques.

Keywords — Genetic Algorithm, Fast Order Mapped Crossover, Alternate Position Crossover, Maximal Preservative Crossover, Greedy Crossover, Performance Analysis

I. I NTRODUCTION

The architecture of systems that implement Genetic algorithm (GA) is more able to adapt to a wide range of problems. Genetic algorithms are basically algorithms based on natural biological evolution. The Darwin’s theory of “Survival of the fittest” [3] is followed in GA to get the optimized solutions. Genetic Algorithm is an optimization strategy where points in the problem space are analogous to organisms involved in a process of natural selection. Each organism is represented by a character string analogous to a chromosome, with each character position analogous to a gene and each character value analogous to an allele. If the population size is too small, the GA without recombination outperforms the GA

with recombination. If the population is large or the search space is more the GA with crossover outperforms the GA without crossover. The number of points in crossover is the number of times the genetic material in an offspring is inherited from the first parent, second parent and vice versa. Though, different types of GA, Operators and parameters are exist, there is a mission for better and better techniques and algorithms to overcome the difficulties available with the existing techniques and to improve the performance of genetic algorithms. Devising of new algorithm, new operators and new parameters for GA is an additional insight to the field of genetic algorithm.

GA is composed of operators and genetic parameters. Crossover operators are the backbone of genetic algorithms. Crossover is generally applied with higher probability (Pc). Since performance of GA is the prime factor relying upon which type of crossover operators can be used for any given problem whose problem difficulty is known and whose parameters has been specified by the user and the selection of available efficiency enhancement techniques like evaluation- relaxation, etc. When the recombinant operators such as crossover and mutation are applied on binary information, the consequences are ignorable. If the same is applied on permutated encoded information produces replication in individuals. In order to remove those duplicate genes in chromosomes, an additional repairing mechanism is required. Few crossover operators [4] [11] [13] may not lead duplication in chromosomes but algorithmically they are very poor. Due to the inefficiencies of these crossover techniques the performance of genetic algorithm is reduced to some extent.

In line with the above existing approaches, a novel effective crossover technique called Fast Order Mapping Crossover (FOMX) with the features of standard procedure, diversity pressure, convergence speed and the quality of solution has been devised to eradicate duplicates in individuals. In this paper the FOMX method is used to remove the duplicate cities in a tour which means invalid tour is corrected into a valid tour in a short time. The proposed crossover technique drastically

increases the convergence speed of a GA without compromising the diversity in the population. Thus, in this paper, an effective FOMX technique has been developed for GA to solve TSP effectively. Experimentation results shows that more than 80% of convergence speed of a GA can be attained at the crossover stage. The FOMX and the existing crossover techniques are experimented on different tsp instances taken from TSPLIB database which is a standard library for tsp problem. The experimental results proved that the FOMX technique outperforms the existing crossover techniques in a considerable amount of time.

II. R ELATED C ROSSOVER O PERATORS

The crossover operator is a genetic operator that combines (mates) two chromosomes (parents) to produce a new chromosome (offspring). The idea behind the crossover operator is that the new chromosome may be better than both parent if it takes the best characteristics from each of the parents or an it may be worse than their parent. Crossover occurs during evolution according to a user-definable crossover probability. For the purpose of this work, only crossover operators that operate on two parents and have no self- adaptation properties will be considered. This paper uses two point crossover (tpc), Alternate Position Crossover (AX), Maximal Preservative Crossover (MPX), Greedy Crossover (GX) and Heuristics Crossover (HX) to solve Travelling salesman problem of different instances.

A. Two Point Crossover

When performing crossover, both parental chromosomes are split at a randomly determined crossover points. Subsequently, a new child genotype is created by appending the first part of the first parent with the second part of the second parent [3].

B. Alternate Position Crossover (AX) Alternate position crossover [ ] simply creates an offspring by selecting alternate allele from parents. In alternate position crossover selects the first allele from one parent and the second allele from other parent and allele which are already present there in offspring will be omitted. For example

Parrent1:- 1 2 3 4 5 6 7 8

Parrent2:- 3 7 5 1 6 8 2 4

Offspring1:- 1 3 2 7 5 4 6 8

Offspring2:- 3 1 7 2 5 4 6 8

In offspring1 first allele is selected from parrent1 and the second allele is selected from parrent2 and so on. The same mechanism is followed for creating offspring2 also.

C. Maximal Preservative Crossover(MPX) In 1988 Muhlenbein et al introduce new crossover operator named Maximal Preservative Crossover [1]. In maximal preservative crossover, a sub string of a string is selected which length must be greater than 10 except for less number of genes in a chromosome. The length of the sub string must be less or equal to the size of a string when the length of the string is small. After that a selected sub tour is removed from the second parent and copied in first part of offspring1 and the remaining cities of second parent is as in order. This process is continued to breed children for the next generation.

III. FAST ORDER MAPPED CROSSOVER (FOMX)

The new crossover technique FOMX removes the bad consequences of gene level comparison and multi point crossover operation on permutated chromosomes. When we apply two point crossover operation as well as multi point crossover operation on permutated chromosomes, the two point chromosomes outperforms the multi point crossover operation. The simple GA uses different crossover techniques stated above and also a novel crossover FOMX to solve travelling salesperson problem which is a popular combinatorial NP problem.

Figure1. FOMX in Two Point Crossover Operation

In two point crossover operation, the two cut points are chosen randomly shown in rectangular boxes in figure 1. The genes between two cut points are swapped and created offspring wherein which the duplicate cities are existed. This removes all duplicate cities occurred in the crossover region. It does repairing operation within the crossover sites. This crossover operator does not worry about what elements apart from cut points are. In this way, this crossover operator presumes most of the properties of previous path/tour. After swapping city/substrings of tour, it is checked that whether duplicity is occurred between cut points. If duplicity is occurred, the position of duplicity is stored in mapping function. According to the mapping function, elements of parent are swapped using the position stored in mapping function. This can be understood from the figure1. It will not perform any other

denotes the different instances and the ‘y’ axis denotes the error rate obtained from each crossover techniques.

Figure3. Comparison of Error Rate of Different Crossover Techniques for all TSP Instances

From the graph it is noticeably revealed that the error rate of novel crossover technique FOMX for all tsp instances is ignorable when compare to the other crossover operators.

V Conclusion In this paper, a new methodology called FOMX is used to remove duplicate genes in offspring. To prove the benefits of FOMX and its efficacy in solving tsp is solved and compared the results with the existing crossover operators proved satisfactory in terms of error rate and the optimal distances obtained. The experimental results show that the minimum distances (optimal solution) for all benchmark instances obtained from FOMX is incomparable to the minimum distances obtained from other existing crossover techniques. From the results it was found that the fast order mapped crossover performed better than the existing crossover techniques in terms of optimal solutions and the convergence speed.

R EFERENCES

[1] Oliver Kramer, Patrick Koch, “Self-Adaptive Partially Mapped Crossover”, proceedings of Genetic and Evolution Computation Conference, pp. 593 – 697, ACM, July 2007. [2] Arthur L. Corcoran, Roger L. Wainwright, “Reducing disruption of superior building blocks in genetic algorithms”, Proceedings of the, ACM SIGAPP Symposium on Applied Computing February, 2003. [3] [4] Ayed A. Salman, Kishan Mehrotra, and Chilukuri K. Mohan, “Adaptive linkage crossover evolutionary computation”, Evolutionary computation, Vol.8 1(3), September 2000. [4] Dr.Sabry M. Abdel-Moetty “Enhanced Traveling Salesman Problem Solving using Genetic Algorithm

Technique with modified Sequential Constructive Crossover Operator”, IJCSNS International Journal of Computer Science and Network Security, VOL.12 No.6, June 2012 [5] Chen, Y.-p., & Goldberg, D. E., “An analysis of a reordering operator with tournament selection on a GA- hard problem”, Lecture Notes in Computer Science (LNCS), 2723, pp. 825–836, 2009. [6] Chen, Y.-p., Peng, W.-C., & Jian, M.-c, “Particle swarm optimization with recombination and dynamic linkage discovery”, IEEE Transactions on Systems, Vol. 37(6): pp.1460–1470, 2012 [7] S.Siva Sathya, S.Kuppuswami, Department of Computer Science, Pondicherry University, “Gene Silencing for Course Time-Tabling with Genetic Algorithm”. [8] P. Larra˜ naga, et. Al, “Genetic algorithms for the Travelling Salesman Problem: A Review of Representations and Operators”, Artificial Intelligence Review, 1999. [9] Davis L. (1991). Handbook of Genetic Algorithms. [10] Hassan Ismkhan et.al, “ Developing Improved Greedy Crossover to solve symmetric Travelling Salesman Problem”, University of Isfahan, Islamic Republic of Iron. [11] Kusum Deep, Manoj Thakur. (2007). A new crossover operator for real coded genetic algorithms. Applied Mathematics and Computation, Science Direct, pp. 895-

[12] Lin W-Y, Hong T-P, Liu S-M. (2004). A new approach to the traveling salesman problem using genetic algorithms with priority encoding On adapting migration parameters for multi-population genetic algorithms. IEEE International Conference, Vol. 6, pp. 5731–5735. [13] Mustafa Kaya. (2011). The effects of two new crossover operators on genetic algorithm performance. Applied Soft Computing, Elsevier, Vol. 11 pp. 881–890.

IEEE - International Conference on Advances in Engineering and Technology-(ICAET 2014)IEEE - International Conference on Advances in Engineering and Technology-(ICAET 2014)