Comparative study of artificial bee colony algorithms with heuristic swap operators for traveling salesman problem

Because the traveling salesman problem (TSP) is one type of classical NP-hard problems, it is not easy to find the optimal tour in polynomial time. Some conventional deterministic methods and exhaustive algorithms are applied to small-scale TSP; whereas, heuristic algorithms are more advantageous for the large-scale TSP. Inspired by the behavior of honey bee swarm, Artificial Bee Colony (ABC) algorithms have been developed as potential optimization approaches and performed well in solving scientific researches and engineering applications. This paper proposes two efficient ABC algorithms with heuristic swap operators (i.e., ABC-HS1 and ABC-HS2) for TSP, which are used to search its better tour solutions. A series of numerical experiments are arranged between the proposed two ABC algorithms and the other three ABC algorithms for TSP. Experimental results demonstrate that ABC-HS1 and ABC-HS2 are both effective and efficient optimization methods.