ABC-GSX:Hybrid method to solve TSP

ABC-GSX: A HYBRID METHOD FOR SOLVING

THE TRAVELING SALESMAN PROBLEM

Dept. of CSE, RNSIT 2015

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Guided By

T. satish kumar

Asst Prof, Dept. of

CSE, RNSIT

Dept. of CSE, RNSIT 2015 2

ABSTRACT

• An optimization problem is a problem of finding the best solution from all

possible solutions.

• The decision to select the best solution is not polynomially bounded.

• Heuristics approaches are thus often considered to solve such NP-hard

problems.

• The technique implements the Artificial Bee Colony algorithm, which is

inspired by the decision making process of the honey bees in finding

optimal food sources. The ABC algorithm is extended with Greedy Sub tour

Crossover to improve the precision.

Dept. of CSE, RNSIT 2015 3

overview

• Introduction

• Travelling salesman problem

• Applications of TSP

• Different approaches to solve TSP

• Metaheuristics

• The ABC metaheuristic

• Honey bee foraging behavior

• ABC algorithm

• Mapping ABC-GSX metaheuristic to the TSP

• Results

• Conclusion

• References


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INTRODUCTION

• The Travelling Salesman Problem (TSP) is an example of

combinatorial optimization problems known to be NP-complete.

• It is strongly believed that it cannot be solved to optimality within

polynomial computation time.

• Therefore, in solving TSP, we employ an approximation that finds a

near-optimal solution in a reasonable amount of time rather than a

method that is guaranteed to find the optimal solution in an

exponential time.

• Metaheuristic is one of many approximation methods widely used to

solve practical optimization problems.

• Inspired by the decision making capability of bee swarms ABC-GSX

is applied to solve TSP.


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TRAVELLING SALESMAN PROBLEM

• Travelling salesman problem states that given a set of cities and the

distances between them, determine the shortest path starting from a

given city, passing through all the other cities and returning to the first

city.

• There is (n-1)! Possible routes for n number of cities.

• The Travelling Salesman Problem (TSP) is an example of

combinatorial optimization problems known to be NP-complete.


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Applications of TSP

• Planning

• Logistics

• Manufacture of microchips

• DNA sequencing

• Optimization techniques


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Different approaches to solve TSP

• There are many algorithms to solve travelling salesman problem.

• These algorithms can be divided into two categories.

Exact

Heuristic


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Metaheuristics

• Metaheuristics are strategies that “guide" the search process. The

goal is to efficiently explore the search space in order to find (near-

)optimal solutions.

• Metaheuristic algorithms are approximate and usually non-

deterministic.

• Examples

Genetic algorithm

Simulated annealing algorithm

Ant colony optimization algorithm

Artificial bee colony algorithm


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THE ABC METAHEURISTIC

• Artificial Bee Colony (ABC) is a metaheuristic in which artificial bees

of a colony cooperate in finding good solutions to optimization

problems.

• A characteristic of ABC is that it was inspired by nature, or more

precisely by the behavior of honey bees seeking a quality food

source.

• Honey bee foraging behavior is how honeybees find food sources.


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Honey bee foraging behavior

Types of foraging bee

Employed bees

Unemployed bees

Scout

Onlooker bees


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Hive

Dancing area for A

Dancing area for B

Waggle dances are done by scout

bees in the food source selection

process to exchange information on

new candidate food sources and to

recruit unemployed bees to follow

them to those sources. Through this

kind of information exchanging and

learning, the honeybee swarm

manages to discover quality food

sources.


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ABC Algorithm

Procedure ABC Metaheuristic

Initial_Solutions

While (criterion)

Update_Feasible_Solutions (Employed bees)

Select_Feasible_Solutions (Onlooker bees)

Update_Feasible_Solutions (Onlooker bees)

Avoid_ Sub-Optimal_Solutions (Scout bee)

End while

onlookers

Foraging bee

employed bee

Scout


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MAPPING ABC-GSX METAHEURISTIC TO THE TSP

Figure : The ABC-GSX algorithm flowchart for TSP


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a0 a1 a2 ……………………………………

X0

X1

Xn-1

Fitness(x0) = 1/travelling_cost(x0)

Fitness(x1) = 1/travelling_cost(x1)

Fitness(Xn-1)=1/travelling_cost(Xn-1)

Sequence of tour (d)

Fo

od

so

urc

e (n

)

Figure : The mapping between the food sources and the tour sequences

The old

Food source

The neighboring

Food source

The new

Food source

Figure : Example of Greedy Sub tour Crossover method

Add the rest of cities (E, H, J) in the

Random order

MAPPING ABC-GSX METAHEURISTIC TO THE TSP (cont.)


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Figure : The 2opt method.

MAPPING ABC-GSX METAHEURISTIC TO THE TSP (cont.)


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RESULTS

Number of iteration usage

Problem ABC-GSX ACO-PSO BCO

EIL51

BERLIN52

EIL76

KROAI00

KROBI00

CH150

KROB200

LIN318

2000

2000

2000

2000

2000

2000

2000

2000

n/a 50000

2000 n/a

n/a 50000

3500 50000

n/a 50000

4000 n/a

n/a 50000

n/a 50000

TABLE 1: NUMBER OF ITERATIONS USED IN ABC-GSX, ACO-PSO AND BCO ALGORITHMS


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RESULTS (cont.)

• It can be drawn that using ABC-GSX on TSP has produced, on average, nearly optimal

results in each problem instance.

• ABC-GSX also converged substantially faster with a much smaller number of iterations

needed when we focus on the number of iteration usage setting in Table 1.

• Maximum relative error never exceeded 2% except for the LIN318 problem instance and

average relative error was less than 0.8%.


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CONCLUSION

• A hybrid method combining Artificial Bee Colony and Greedy Sub tour

Crossover (ABC-GSX) was proposed.

• The exploitation process in the ABC algorithm is improved by combining

GSX.

• The proposed approach outperformed all other aforementioned approaches.

ABC-GSX managed to find globally optimal solutions on most problem

instances.

• the hybrid method yielded more effective results for TSP, with an average

relative error below 0.8%.

• Many other crossover techniques can be applied to the algorithm to improve

its efficiency and can be tested against the proposed method in future.

• Nature has solution to everything!


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REFERENCES

[I] A. Banharnsakun, T. Achalakul, B. Sirinaovakul, [IEEE 2010 Second World Congress

on Nature and Biologically Inspired Computing (NaBIC 2010)], pp. 978-1-4244-73762.

[2] S. Nonsiri, S. Supratid, "ModifYing Ant Colony Optimization," IEEE Conference on

Soft Computing in Industrial Applications, 2008, pp. 95-100.

[3] W.-L. Zhong, l Zhang, W.-N. Chen, "A Novel Discrete Particle Swarm Optimization to

Solve Travelling Salesman Problem," in Proc. IEEE Int. Conf. Evol. Comput. (CEC),

2007, pp. 3283-3287.

[4] L.-P. Wong, M.Y. Hean Low, C.S. Chong, "A Bee Colony Optimization Algorithm for

Travelling Salesman Problem," Second Asia International Conference on Modelling &

Simulation, 2008, pp. 818-823.

[5] XH. Shi, Y.e. Liang, H.P. Lee, C. Lu, Q.x. Wang, "Particle swarm optimization-based

algorithms for TSP and generalized TSP," Information Processing Letters., vol 103, pp.

169-176,2007.

[6] le. Biesmeijer, T.D. Seeley, "The use of waggle dance information by honey bees

throughout their foraging careers," Behav. Ecol. Sociobiol., vol. 59, pp. 133-142,2005.

[7] http://en.wikipedia.org/wiki/Travelling_salesman_problem

[8] http://www.CleverAlgorithms.com

[9] Clever Algorithms: Nature-Inspired Programming Recipes © Copyright 2011 Jason

Brownlee.


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Engineering

ABC-GSX:Hybrid method to solve TSP