Combinatorial Artificial Bee Colony Optimization with Reinforcement Learning Updating for Travelling Salesman Problem

The Artificial Bee Colony algorithm is originally designed for solving numerical optimization problems, whereas the Travelling Salesman Problem is classified as a combinatorial optimization one. This paper proposes a combinatorial variant of the Artificial Bee Colony algorithm by using reinforcement learning update. Reinforcement values are introduced, and positive reinforcement is given to the selected cities when a better solution is found by an employed bee. On the contrary, negative reinforcement is assigned to the selected cities when a worse solution is found. Onlooker bees then select cities to update their solutions according to these reinforcement values. The performance of the proposed algorithm is tested on six benchmark problems. The results show that the algorithm with the reinforcement learning update provides better solutions than the algorithm without the reinforcement learning update in five out of six benchmark problems. The convergence rates of the algorithm with the reinforcement learning update are also faster than those of the algorithm without the reinforcement learning update.