# The that depend upon population [2]. Graph theoretical ideas

The field of graph theory
plays important role
in numerous fields.
Graph theory which is used in structural model. This structural
arrangement of different objects
or technologies results in new
inventions and modifications within
the existing setting for improvement in those fields. The
applications of graph theory in heterogeneous fields to some extent however principally focus on the computer science applications that uses graph
theoretical ideas 1.During
the last decades, some new algorithms were introduced for national and international search directions
that depend upon population
2.

Graph theoretical ideas are extremely utilized by computer
science applications, especially in analysis areas
of computer such data processing, image segmentation, clustering,
image capturing, networking 3.Application of Bee
Colony optimization is MANET- Routing
Protocol, Problem finding Mechanism,
Engineering optimization, Numerical optimization,
Accident identification, Vehicle routing problem,
Developing optimization Algorithm, Application to Generalized
Assignment problem, Job searching arrangement etc.11-13.4-6

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The
Transportation problem is one in all the
foremost significant and most studied issues in Operations
Management domain. Much of the work on Transportation problem is motivated by
life applications. The Transportation issue is that the well-known classical
problem 7.These are several transportation issues ,such as vehicle routing
problem, travelling salesman problem but travelling salesman is one of  accepted and most studied problem of the globe.
The travelling salesman problem (TSP) has been a vital problem in the field of
division and logistics. The classical TSP can be defined as a complete
graph G = (V, A) where V = {0……………, N} is a vertex
set, and A={(i,j)|i,j?V} is an edge set. Each
vertex represents a city. The distance dij is associated with each
edge (i,j)?A and represents the
distance from city i to city j. The Traveling salesman problem
consist in order visiting a set of cities only once and finally returning to
the original city of exit. The main goal of TSP is that many cities ought to be
visited by a salesman and return to the starting city along with many possible
shortest ways 8. The purpose to establish a minimum distance of a tour
passing through every city once and only once. The TSP is clearly NP-hard
combinatorial optimization problem and difficult to solve.
There are vital advances within
the development of actual and approximate algorithms. Exact
explanation way can only be used for vary small instances, thus for real –world
issues, researchers should think about and resort to approximate or heuristic
methods in solving the problem 9. Artificial Bee Colony (ABC) algorithm has
verified its significance in solving many problems together with engineering
optimization problems. ABC algorithm is one of the most well–liked and youngest
members of the family of population based nature inspired meta- heuristic swarm
intelligence method. It has been verify that its superiority over several
Natural Inspired Algorithms (NIA) when applied for both benchmark functions and
real globe problems 10, 11.The Algorithm is motivated from the
intelligent food hunting behavior of honey bee insects. Honey bee
swarm is one in all the foremost intelligent swarms exists in
nature; that follows collective intelligent technique, whereas looking
out the food. The honey bee swarm has several qualities like bees will
communicate the knowledge, will memorize the atmosphere ,will store and share
the knowledge and selections supported that per changes within the atmosphere,
the swarm updates itself, assign the tasks dynamically and moves additional by
social learning and teaching. This intelligent behavior of bees motivates
researchers to simulate on top of search behavior of the bee
swarm 12-13. ABC could be a population based mostly optimization algorithm
and tries to accomplish worldwide minimum or maximum iteratively. The
termination conditions for fundamentals ought
to be most cycle figure or acceptable error value. The
population in ABC hive consists of three types
of bees; working bees, viewer bees and scout bees.The working bees
and spectator bees exploit nectar sources found round
the hive and also the scout bee explores the solution space
scout bees 14-15.

The following steps show the original ABC algorithm

Step1. The ABC generates a
random distributed initial population..

Step2. After initialization, the initial fitness of the
population is evaluated.

Step3.Working bee phase.

Step4. Observer bee phase.

Step 5. Scout bee phase

Step6. Memorize the best solution.

Step7. Repeat the cycle till the termination
condition is fulfilled

Aims and Objectives

The objectives of our proposed researcher work as
following:

I.
To design Artificial Bee Colony algorithm for Traveling
Salesman Problem.

II.
To develop an algorithm for TSP using Artificial Bee
Colonywith Kalman Filter.

III.
To develop an algorithm that has near optimum solution on
TSP benchmarks.

IV.
To show
optimal results through numerical simulations.

Plan of
Work

After literaturereview study of the previous work done by researchers on basis of that
research we will develop an algorithm that solving TSP problem in nearest
optimum solution with the help of proposed ABC algorithm with Kalmanfilter. Our proposed algorithm has the following steps.

Step1. The artificial bee’s initial population

Step 2. After initialization, the fitness of the
population is evaluated.

Step3. Working bee phase

Step4. Observer bee phase.

Step5.Scout bee phase

Step 6. Apply Kalman Filter for prediction and
Estimation.

Step7. Memorize the best solution.

Step8. Repeat the cycle until the
termination condition is satisfied for solution.

Finally result will be
compared with different algorithm test results. Our proposed algorithm is
tested on the benchmarks problems taken from TSP library (TSPLIB),such as
BURMA14, BAYS29, DANTZIG42, BERLIN52, KROA100 and CH130,OLIVER30, EIL51,
BERLIN52, PCB442, KROA100 etc. The algorithm shall be implemented using JAVA
NetBeans, JAVA
Appletand
Intel Core i5 computer along with Windows 10.

References

1.
S. G. Shirinivas, S.
Vetrivel, N. M. Elango “Applications of graph theory in computer science an overview” Int. J. Eng. Sci. 2(9), 4610-4621 (2010).

2.
C. Yang, S. Tian, Z. Liu, J. Huang, F. Chen CFault
modeling on complex plane and tolerance handling methods for analog circuits”
IEEE
Trans. Instrum. Meas. 62(10), 2730–2738(2013).

3.      R.
J. Trudeau, “Introduction to graph theory” 2nd Edition, Dover Publications Inc, New York, 2013.

4.      A. Shrivastava, M. Gupta, S. Swami “SPV and Mutation based Artificial Bee
Colony Algorithm for Travelling Salesman Problem.” Int. J. Comput. Appl. 116(14)
(2015).

5.      H. E. Kocer, M. R. Akca “An improved artificial bee colony
algorithm with local search for traveling salesman problem.” Cybern. Syst. 45(8),
635-649 (2014).

6.      H. Jiang “Artificial Bee Colony algorithm for
Traveling Salesman Problem.” 4th
International Conference on Mechatronics, Materials, Chemistry and Computer
Engineering,Xian China, December 12-13, 2015;Z. Liang, X. Li, 5(15), 468-472 (2015).

7.
C. Yang, S. Tian, Z. Liu, J. Huang, F. Chen CFault
modeling on complex plane and tolerance handling methods for analog circuits”
IEEE
Trans. Instrum. Meas. 62(10), 2730–2738(2013).

8.
V.Ungureanu”Traveling
Salesman Problem with Transportation.” Comput.
Sci.J.Moldova. 14(2), 41(2006).

9.
X. Zhang, Q. Bai,X. Yun “A new hybrid artificial bee
colony algorithm for the traveling salesman problem.” 3rdInternational conference on communication
software and networks, Xidian University Xi’an China, May 27–29, 2011; IEEE
155-159 (2011).

10.  G.
George, K.Raimond “Solving
Travelling Salesman Problem Using Variants of ABC Algorithm.” Int. J. Comput. 2(01),23-26
(2013).

11.  A.Kaur,S. Goyal”A survey on the applications of bee colony optimization
techniques.” Int. J. Comp. Sci. Eng. Commun. 3(8),
30-37 (2011).

12.  S.Kumar,
V. K.Sharma,R. Kumari”A
novel hybrid crossover based artificial bee colony algorithm for optimization
problem.” Int. J. Comput. Appl. 82(8),18-25 (2014).

13.  H.
Nagpure, R.Raja, “RBGCA-Bee
Genetic Colony Algorithm for Travelling Salesman Problem.”Int.
J. Comput. Sci. Inf. Technol. Adv. Res. 3(6), 5384-5389(2012).

14.  X.
Kong, S.Liu, Z. Wang”An
improved artificial bee colony algorithm and its application.” Int. J. Sig. Pro. Image. Graph.  Pattern.
Recognit.6(6), 259-274(2013).

15.   M. S.Kiran,A Babalik”Improved artificial bee
colony algorithm for continuous optimization problems”. J. Comp. Sci.Commun. 2(04), 108.(2014).

The field of graph theory
plays important role
in numerous fields.
Graph theory which is used in structural model. This structural
arrangement of different objects
or technologies results in new
inventions and modifications within
the existing setting for improvement in those fields. The
applications of graph theory in heterogeneous fields to some extent however principally focus on the computer science applications that uses graph
theoretical ideas 1.During
the last decades, some new algorithms were introduced for national and international search directions
that depend upon population
2.

Graph theoretical ideas are extremely utilized by computer
science applications, especially in analysis areas
of computer such data processing, image segmentation, clustering,
image capturing, networking 3.Application of Bee
Colony optimization is MANET- Routing
Protocol, Problem finding Mechanism,
Engineering optimization, Numerical optimization,
Accident identification, Vehicle routing problem,
Developing optimization Algorithm, Application to Generalized
Assignment problem, Job searching arrangement etc.11-13.4-6

The
Transportation problem is one in all the
foremost significant and most studied issues in Operations
Management domain. Much of the work on Transportation problem is motivated by
life applications. The Transportation issue is that the well-known classical
problem 7.These are several transportation issues ,such as vehicle routing
problem, travelling salesman problem but travelling salesman is one of  accepted and most studied problem of the globe.
The travelling salesman problem (TSP) has been a vital problem in the field of
division and logistics. The classical TSP can be defined as a complete
graph G = (V, A) where V = {0……………, N} is a vertex
set, and A={(i,j)|i,j?V} is an edge set. Each
vertex represents a city. The distance dij is associated with each
edge (i,j)?A and represents the
distance from city i to city j. The Traveling salesman problem
consist in order visiting a set of cities only once and finally returning to
the original city of exit. The main goal of TSP is that many cities ought to be
visited by a salesman and return to the starting city along with many possible
shortest ways 8. The purpose to establish a minimum distance of a tour
passing through every city once and only once. The TSP is clearly NP-hard
combinatorial optimization problem and difficult to solve.
There are vital advances within
the development of actual and approximate algorithms. Exact
explanation way can only be used for vary small instances, thus for real –world
issues, researchers should think about and resort to approximate or heuristic
methods in solving the problem 9. Artificial Bee Colony (ABC) algorithm has
verified its significance in solving many problems together with engineering
optimization problems. ABC algorithm is one of the most well–liked and youngest
members of the family of population based nature inspired meta- heuristic swarm
intelligence method. It has been verify that its superiority over several
Natural Inspired Algorithms (NIA) when applied for both benchmark functions and
real globe problems 10, 11.The Algorithm is motivated from the
intelligent food hunting behavior of honey bee insects. Honey bee
swarm is one in all the foremost intelligent swarms exists in
nature; that follows collective intelligent technique, whereas looking
out the food. The honey bee swarm has several qualities like bees will
communicate the knowledge, will memorize the atmosphere ,will store and share
the knowledge and selections supported that per changes within the atmosphere,
the swarm updates itself, assign the tasks dynamically and moves additional by
social learning and teaching. This intelligent behavior of bees motivates
researchers to simulate on top of search behavior of the bee
swarm 12-13. ABC could be a population based mostly optimization algorithm
and tries to accomplish worldwide minimum or maximum iteratively. The
termination conditions for fundamentals ought
to be most cycle figure or acceptable error value. The
population in ABC hive consists of three types
of bees; working bees, viewer bees and scout bees.The working bees
and spectator bees exploit nectar sources found round
the hive and also the scout bee explores the solution space
scout bees 14-15.

The following steps show the original ABC algorithm

Step1. The ABC generates a
random distributed initial population..

Step2. After initialization, the initial fitness of the
population is evaluated.

Step3.Working bee phase.

Step4. Observer bee phase.

Step 5. Scout bee phase

Step6. Memorize the best solution.

Step7. Repeat the cycle till the termination
condition is fulfilled

Aims and Objectives

The objectives of our proposed researcher work as
following:

I.
To design Artificial Bee Colony algorithm for Traveling
Salesman Problem.

II.
To develop an algorithm for TSP using Artificial Bee
Colonywith Kalman Filter.

III.
To develop an algorithm that has near optimum solution on
TSP benchmarks.

IV.
To show
optimal results through numerical simulations.

Plan of
Work

After literaturereview study of the previous work done by researchers on basis of that
research we will develop an algorithm that solving TSP problem in nearest
optimum solution with the help of proposed ABC algorithm with Kalmanfilter. Our proposed algorithm has the following steps.

Step1. The artificial bee’s initial population

Step 2. After initialization, the fitness of the
population is evaluated.

Step3. Working bee phase

Step4. Observer bee phase.

Step5.Scout bee phase

Step 6. Apply Kalman Filter for prediction and
Estimation.

Step7. Memorize the best solution.

Step8. Repeat the cycle until the
termination condition is satisfied for solution.

Finally result will be
compared with different algorithm test results. Our proposed algorithm is
tested on the benchmarks problems taken from TSP library (TSPLIB),such as
BURMA14, BAYS29, DANTZIG42, BERLIN52, KROA100 and CH130,OLIVER30, EIL51,
BERLIN52, PCB442, KROA100 etc. The algorithm shall be implemented using JAVA
NetBeans, JAVA
Appletand
Intel Core i5 computer along with Windows 10.

References

1.
S. G. Shirinivas, S.
Vetrivel, N. M. Elango “Applications of graph theory in computer science an overview” Int. J. Eng. Sci. 2(9), 4610-4621 (2010).

2.
C. Yang, S. Tian, Z. Liu, J. Huang, F. Chen CFault
modeling on complex plane and tolerance handling methods for analog circuits”
IEEE
Trans. Instrum. Meas. 62(10), 2730–2738(2013).

3.      R.
J. Trudeau, “Introduction to graph theory” 2nd Edition, Dover Publications Inc, New York, 2013.

4.      A. Shrivastava, M. Gupta, S. Swami “SPV and Mutation based Artificial Bee
Colony Algorithm for Travelling Salesman Problem.” Int. J. Comput. Appl. 116(14)
(2015).

5.      H. E. Kocer, M. R. Akca “An improved artificial bee colony
algorithm with local search for traveling salesman problem.” Cybern. Syst. 45(8),
635-649 (2014).

6.      H. Jiang “Artificial Bee Colony algorithm for
Traveling Salesman Problem.” 4th
International Conference on Mechatronics, Materials, Chemistry and Computer
Engineering,Xian China, December 12-13, 2015;Z. Liang, X. Li, 5(15), 468-472 (2015).

7.
C. Yang, S. Tian, Z. Liu, J. Huang, F. Chen CFault
modeling on complex plane and tolerance handling methods for analog circuits”
IEEE
Trans. Instrum. Meas. 62(10), 2730–2738(2013).

8.
V.Ungureanu”Traveling
Salesman Problem with Transportation.” Comput.
Sci.J.Moldova. 14(2), 41(2006).

9.
X. Zhang, Q. Bai,X. Yun “A new hybrid artificial bee
colony algorithm for the traveling salesman problem.” 3rdInternational conference on communication
software and networks, Xidian University Xi’an China, May 27–29, 2011; IEEE
155-159 (2011).

10.  G.
George, K.Raimond “Solving
Travelling Salesman Problem Using Variants of ABC Algorithm.” Int. J. Comput. 2(01),23-26
(2013).

11.  A.Kaur,S. Goyal”A survey on the applications of bee colony optimization
techniques.” Int. J. Comp. Sci. Eng. Commun. 3(8),
30-37 (2011).

12.  S.Kumar,
V. K.Sharma,R. Kumari”A
novel hybrid crossover based artificial bee colony algorithm for optimization
problem.” Int. J. Comput. Appl. 82(8),18-25 (2014).

13.  H.
Nagpure, R.Raja, “RBGCA-Bee
Genetic Colony Algorithm for Travelling Salesman Problem.”Int.
J. Comput. Sci. Inf. Technol. Adv. Res. 3(6), 5384-5389(2012).

14.  X.
Kong, S.Liu, Z. Wang”An
improved artificial bee colony algorithm and its application.” Int. J. Sig. Pro. Image. Graph.  Pattern.
Recognit.6(6), 259-274(2013).

15.   M. S.Kiran,A Babalik”Improved artificial bee
colony algorithm for continuous optimization problems”. J. Comp. Sci.Commun. 2(04), 108.(2014).