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).

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).