A hybrid approach to multi-depot multiple traveling salesman problem based on firefly algorithm and ant colony optimization

This study proposed a hybrid approach of firefly algorithm (FA) and ant colony optimization (ACO) for solving multi-depot multiple traveling salesman problem, a TSP with more than one salesman and departure city. The FA is fast converging but easily trapped into the local optimum. The ACO has a great ability to search for the solution but it converges slowly. To get a better result and convergence time, we integrate FA to find the local solutions and ACO to find a global solution. The local solutions of the FA are normalized then initialized to the quantity of pheromones for running the ACO. Furthermore, we experimented with the best parameters in order to optimize the solution. In justification, we used the sea transportation route in Indonesia as a case study. The experimental results showed that the hybrid approach of FA and ACO has superior performance with an average computational time of 26.90% and converges 32.75% faster than ACO.