An algorithm of set-based differential evolution for traveling salesman problem

This paper is concerned with combinatorial optimization problems (COPs) for traveling salesman problem (TSP). Differential evolution (DE) is a population-based stochastic technique of evolutionary algorithm (EA), which has been widely used to solve COPs over continuous space in many scientific and engineering fields. Set-based differential evolution (SBDE) is based on a set-based representation scheme that enables differential evolution (DE) to characterize the discrete search space. A parameter ω indicating the possibility is added into the formula for the mutation. All arithmetic operators for elements, individuals, vectors and are replaced by new definitions. In this paper, SBDE is amplified in detail for TSP of COPs in discrete space. The possibility ω is tested and the range allowed of ω is identified. The performance of SBDE with the range allowed of ω is evaluated on TSP. The results of the numerical experiments show that the convergence of SBDE is fast and SBDE is effective in quality for TSP.