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

 The field of graph theoryplays important rolein numerous fields.

Graph theory which is used in structural model. This structuralarrangement of different objectsor technologies results in newinventions and modifications withinthe existing setting for improvement in those fields. Theapplications of graph theory in heterogeneous fields to some extent however principally focus on the computer science applications that uses graphtheoretical ideas 1.

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Duringthe last decades, some new algorithms were introduced for national and international search directionsthat depend upon population2.Graph theoretical ideas are extremely utilized by computerscience applications, especially in analysis areasof computer such data processing, image segmentation, clustering,image capturing, networking 3.Application of BeeColony optimization is MANET- RoutingProtocol, Problem finding Mechanism,Engineering optimization, Numerical optimization,Accident identification, Vehicle routing problem,Developing optimization Algorithm, Application to GeneralizedAssignment problem, Job searching arrangement etc.11-13.4-6TheTransportation problem is one in all theforemost significant and most studied issues in OperationsManagement domain. Much of the work on Transportation problem is motivated bylife applications.

The Transportation issue is that the well-known classicalproblem 7.These are several transportation issues ,such as vehicle routingproblem, 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 ofdivision and logistics. The classical TSP can be defined as a completegraph G = (V, A) where V = {0………….

.., N} is a vertexset, and A={(i,j)|i,j?V} is an edge set. Eachvertex represents a city. The distance dij is associated with eachedge (i,j)?A and represents thedistance from city i to city j. The Traveling salesman problemconsist in order visiting a set of cities only once and finally returning tothe original city of exit.

The main goal of TSP is that many cities ought to bevisited by a salesman and return to the starting city along with many possibleshortest ways 8. The purpose to establish a minimum distance of a tourpassing through every city once and only once. The TSP is clearly NP-hardcombinatorial optimization problem and difficult to solve.There are vital advances withinthe development of actual and approximate algorithms. Exactexplanation way can only be used for vary small instances, thus for real –worldissues, researchers should think about and resort to approximate or heuristicmethods in solving the problem 9. Artificial Bee Colony (ABC) algorithm hasverified its significance in solving many problems together with engineeringoptimization problems. ABC algorithm is one of the most well–liked and youngestmembers of the family of population based nature inspired meta- heuristic swarmintelligence method. It has been verify that its superiority over severalNatural Inspired Algorithms (NIA) when applied for both benchmark functions andreal globe problems 10, 11.

The Algorithm is motivated from theintelligent food hunting behavior of honey bee insects. Honey beeswarm is one in all the foremost intelligent swarms exists innature; that follows collective intelligent technique, whereas lookingout the food. The honey bee swarm has several qualities like bees willcommunicate the knowledge, will memorize the atmosphere ,will store and sharethe knowledge and selections supported that per changes within the atmosphere,the swarm updates itself, assign the tasks dynamically and moves additional bysocial learning and teaching. This intelligent behavior of bees motivatesresearchers to simulate on top of search behavior of the beeswarm 12-13. ABC could be a population based mostly optimization algorithmand tries to accomplish worldwide minimum or maximum iteratively. Thetermination conditions for fundamentals oughtto be most cycle figure or acceptable error value. Thepopulation in ABC hive consists of three typesof bees; working bees, viewer bees and scout bees.The working beesand spectator bees exploit nectar sources found roundthe hive and also the scout bee explores the solution spacescout bees 14-15.

The following steps show the original ABC algorithmStep1. The ABC generates arandom distributed initial population..Step2. After initialization, the initial fitness of thepopulation is evaluated.Step3.Working bee phase.

Step4. Observer bee phase.Step 5. Scout bee phaseStep6. Memorize the best solution.Step7. Repeat the cycle till the terminationcondition is fulfilledAims and ObjectivesThe objectives of our proposed researcher work asfollowing:             I.

           To design Artificial Bee Colony algorithm for TravelingSalesman Problem.          II.           To develop an algorithm for TSP using Artificial BeeColonywith Kalman Filter.       III.

           To develop an algorithm that has near optimum solution onTSP benchmarks.       IV.           To showoptimal results through numerical simulations. Plan ofWork After literaturereview study of the previous work done by researchers on basis of thatresearch we will develop an algorithm that solving TSP problem in nearestoptimum solution with the help of proposed ABC algorithm with Kalmanfilter. Our proposed algorithm has the following steps.Step1.

The artificial bee’s initial populationStep 2. After initialization, the fitness of thepopulation is evaluated.Step3.

Working bee phaseStep4. Observer bee phase.Step5.Scout bee phaseStep 6. Apply Kalman Filter for prediction andEstimation.Step7. Memorize the best solution.

Step8. Repeat the cycle until thetermination condition is satisfied for solution.Finally result will becompared with different algorithm test results. Our proposed algorithm istested on the benchmarks problems taken from TSP library (TSPLIB),such asBURMA14, BAYS29, DANTZIG42, BERLIN52, KROA100 and CH130,OLIVER30, EIL51,BERLIN52, PCB442, KROA100 etc.

The algorithm shall be implemented using JAVANetBeans, JAVAAppletandIntel Core i5 computer along with Windows 10. References1.     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 CFaultmodeling on complex plane and tolerance handling methods for analog circuits”IEEETrans. 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 BeeColony Algorithm for Travelling Salesman Problem.” Int. J.

Comput. Appl. 116(14)(2015).

5.      H. E. Kocer, M. R.

Akca “An improved artificial bee colonyalgorithm with local search for traveling salesman problem.” Cybern. Syst. 45(8),635-649 (2014).6.      H. Jiang “Artificial Bee Colony algorithm forTraveling Salesman Problem.

” 4thInternational Conference on Mechatronics, Materials, Chemistry and ComputerEngineering,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 CFaultmodeling on complex plane and tolerance handling methods for analog circuits”IEEETrans. Instrum. Meas. 62(10), 2730–2738(2013).8.     V.

Ungureanu”TravelingSalesman Problem with Transportation.” Comput.Sci.J.Moldova. 14(2), 41(2006).9.     X.

Zhang, Q. Bai,X. Yun “A new hybrid artificial beecolony algorithm for the traveling salesman problem.” 3rdInternational conference on communicationsoftware and networks, Xidian University Xi’an China, May 27–29, 2011; IEEE155-159 (2011).10.

  G.George, K.Raimond “SolvingTravelling 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 optimizationtechniques.” Int. J. Comp. Sci.

Eng. Commun. 3(8),30-37 (2011).12.

  S.Kumar,V. K.Sharma,R. Kumari”Anovel hybrid crossover based artificial bee colony algorithm for optimizationproblem.

” Int. J. Comput. Appl. 82(8),18-25 (2014).13.  H.Nagpure, R.

Raja, “RBGCA-BeeGenetic 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”Animproved 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 beecolony algorithm for continuous optimization problems”. J. Comp.

Sci.Commun. 2(04), 108.(2014).       The field of graph theoryplays important rolein numerous fields.

Graph theory which is used in structural model. This structuralarrangement of different objectsor technologies results in newinventions and modifications withinthe existing setting for improvement in those fields. Theapplications of graph theory in heterogeneous fields to some extent however principally focus on the computer science applications that uses graphtheoretical ideas 1.Duringthe last decades, some new algorithms were introduced for national and international search directionsthat depend upon population2.Graph theoretical ideas are extremely utilized by computerscience applications, especially in analysis areasof computer such data processing, image segmentation, clustering,image capturing, networking 3.Application of BeeColony optimization is MANET- RoutingProtocol, Problem finding Mechanism,Engineering optimization, Numerical optimization,Accident identification, Vehicle routing problem,Developing optimization Algorithm, Application to GeneralizedAssignment problem, Job searching arrangement etc.

11-13.4-6TheTransportation problem is one in all theforemost significant and most studied issues in OperationsManagement domain. Much of the work on Transportation problem is motivated bylife applications. The Transportation issue is that the well-known classicalproblem 7.

These are several transportation issues ,such as vehicle routingproblem, 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 ofdivision and logistics. The classical TSP can be defined as a completegraph G = (V, A) where V = {0………….

.., N} is a vertexset, and A={(i,j)|i,j?V} is an edge set. Eachvertex represents a city. The distance dij is associated with eachedge (i,j)?A and represents thedistance from city i to city j. The Traveling salesman problemconsist in order visiting a set of cities only once and finally returning tothe original city of exit.

The main goal of TSP is that many cities ought to bevisited by a salesman and return to the starting city along with many possibleshortest ways 8. The purpose to establish a minimum distance of a tourpassing through every city once and only once. The TSP is clearly NP-hardcombinatorial optimization problem and difficult to solve.There are vital advances withinthe development of actual and approximate algorithms. Exactexplanation way can only be used for vary small instances, thus for real –worldissues, researchers should think about and resort to approximate or heuristicmethods in solving the problem 9. Artificial Bee Colony (ABC) algorithm hasverified its significance in solving many problems together with engineeringoptimization problems. ABC algorithm is one of the most well–liked and youngestmembers of the family of population based nature inspired meta- heuristic swarmintelligence method.

It has been verify that its superiority over severalNatural Inspired Algorithms (NIA) when applied for both benchmark functions andreal globe problems 10, 11.The Algorithm is motivated from theintelligent food hunting behavior of honey bee insects. Honey beeswarm is one in all the foremost intelligent swarms exists innature; that follows collective intelligent technique, whereas lookingout the food. The honey bee swarm has several qualities like bees willcommunicate the knowledge, will memorize the atmosphere ,will store and sharethe knowledge and selections supported that per changes within the atmosphere,the swarm updates itself, assign the tasks dynamically and moves additional bysocial learning and teaching. This intelligent behavior of bees motivatesresearchers to simulate on top of search behavior of the beeswarm 12-13. ABC could be a population based mostly optimization algorithmand tries to accomplish worldwide minimum or maximum iteratively. Thetermination conditions for fundamentals oughtto be most cycle figure or acceptable error value. Thepopulation in ABC hive consists of three typesof bees; working bees, viewer bees and scout bees.

The working beesand spectator bees exploit nectar sources found roundthe hive and also the scout bee explores the solution spacescout bees 14-15.The following steps show the original ABC algorithmStep1. The ABC generates arandom distributed initial population.

.Step2. After initialization, the initial fitness of thepopulation is evaluated.Step3.Working bee phase.

Step4. Observer bee phase.Step 5.

Scout bee phaseStep6. Memorize the best solution.Step7. Repeat the cycle till the terminationcondition is fulfilledAims and ObjectivesThe objectives of our proposed researcher work asfollowing:             I.           To design Artificial Bee Colony algorithm for TravelingSalesman Problem.

          II.           To develop an algorithm for TSP using Artificial BeeColonywith Kalman Filter.       III.           To develop an algorithm that has near optimum solution onTSP benchmarks.       IV.           To showoptimal results through numerical simulations. Plan ofWork After literaturereview study of the previous work done by researchers on basis of thatresearch we will develop an algorithm that solving TSP problem in nearestoptimum solution with the help of proposed ABC algorithm with Kalmanfilter. Our proposed algorithm has the following steps.

Step1. The artificial bee’s initial populationStep 2. After initialization, the fitness of thepopulation is evaluated.Step3. Working bee phaseStep4. Observer bee phase.Step5.Scout bee phaseStep 6.

Apply Kalman Filter for prediction andEstimation.Step7. Memorize the best solution.Step8. Repeat the cycle until thetermination condition is satisfied for solution.Finally result will becompared with different algorithm test results. Our proposed algorithm istested on the benchmarks problems taken from TSP library (TSPLIB),such asBURMA14, BAYS29, DANTZIG42, BERLIN52, KROA100 and CH130,OLIVER30, EIL51,BERLIN52, PCB442, KROA100 etc. The algorithm shall be implemented using JAVANetBeans, JAVAAppletandIntel Core i5 computer along with Windows 10.

 References1.     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 CFaultmodeling on complex plane and tolerance handling methods for analog circuits”IEEETrans. 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 BeeColony Algorithm for Travelling Salesman Problem.

” Int. J. Comput. Appl.

 116(14)(2015).5.      H. E. Kocer, M. R.

Akca “An improved artificial bee colonyalgorithm with local search for traveling salesman problem.” Cybern. Syst. 45(8),635-649 (2014).6.      H. Jiang “Artificial Bee Colony algorithm forTraveling Salesman Problem.

” 4thInternational Conference on Mechatronics, Materials, Chemistry and ComputerEngineering,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 CFaultmodeling on complex plane and tolerance handling methods for analog circuits”IEEETrans. Instrum. Meas. 62(10), 2730–2738(2013).

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

9.     X. Zhang, Q.

Bai,X. Yun “A new hybrid artificial beecolony algorithm for the traveling salesman problem.” 3rdInternational conference on communicationsoftware and networks, Xidian University Xi’an China, May 27–29, 2011; IEEE155-159 (2011).10.  G.George, K.Raimond “SolvingTravelling 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 optimizationtechniques.” Int. J. Comp. Sci.

Eng. Commun. 3(8),30-37 (2011).

12.  S.Kumar,V. K.Sharma,R. Kumari”Anovel hybrid crossover based artificial bee colony algorithm for optimizationproblem.” Int. J.

Comput. Appl. 82(8),18-25 (2014).13.  H.Nagpure, R.Raja, “RBGCA-BeeGenetic 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”Animproved 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 beecolony algorithm for continuous optimization problems”. J. Comp.

Sci.Commun. 2(04), 108.(2014).