solving traveling salesman problem using artificial bee colony algorithm and greedy sub tour crossover.

1. 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

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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.

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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)
Foodsource(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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