A Preliminary Study On Firefly Algorithm Approach For Travelling Salesman Problem - Ismail, Mohd Muzafar; Che Hasan, Mohd Hanif; Mohamad @ Ab Rahman, Syahrul Hisham; Jaafar, Hazriq Izzuan (2013)
Travelling Salesman Problem is a mathematical problem that describes a salesman problem in finding the shortest distance to travel to all the cities given that each city is visited once only. Travelling Salesman Problem is nondeterministic and a polynomial time problem, which makes the conventional mathematical optimization techniques, irrelevant to solve the problem. This paper explores the use of one of swarm intelligence available, Firefly Algorithm in finding the optimal solution of the problem. Each firefly in Firefly Algorithm represents a candidate solution of the Travelling Salesman Problem. The candidate solution is modeled using a voting technique where each dimension of the firefly in search space represents a city that need to be visited by the salesman. The city with largest vote will be the initial city of the salesman, while the city with least vote, will be the second last city visited by the salesman before going back to the first city, he comes from. Each of this candidate solution has a distance that correlates with the fitness value of the firefly. A firefly will try to improve the solution its represents by moving closer to other fireflies with better fitness values, in the search space. This process is repeated until a stopping condition reached. The performance of the proposed approach is benchmark with a case study.