A new artificial bee colony algorithm using a gradual weight method for the bi-objective traveling salesman problems

The traveling salesman problem (TSP) is a typical problem in combinatorial optimization. The unique objective of the traditional TSP is to minimize the tour distance. When more than one objective is taken into account to be optimized simultaneously, the problem is known as a multi-objective TSP. In the present paper, a bi-objective traveling salesman problem (BOTSP) is considered, where both the cost and the distance are taken as optimization objectives. We introduce a new algorithm that solves the BOTSP called Gw-ABC. This algorithm is based on an Artificial Bee Colony Algorithm (ABC) and uses a Gradual Weight Generation method. Firstly, we apply a gradual method to prepare the weight vectors. In fact, weight vectors values are gradually distributed in the objective space and change relatively to the optimization process from cycle to another. Secondly, we apply the ABC algorithm with the generated weights to our problem. The proposed algorithm is experimentally tested on well-known benchmark instances of different sizes and compared with other state-of-the-art algorithms. The obtained experimental results show that Gw-ABC is significantly better.