A Set-Based Discrete Differential Evolution Algorithm

The TSP problem is considered as classical discrete optimization grouping problem, which is widely used in practice, but it is real a difficult NP problem. Simultaneously differential evolution (DE) algorithm has been proven to be a powerful optimization algorithm. Since the mutation process of DE contains a series of arithmetic operators operating on continuous space, few algorithms based on DE solve this problem nicely and the advantages of DE in continuous space cannot be used to solve TSP. To take full advantages of the strengths of DE, this paper proposes a set-based DE (S-DE) which completely follows the procedure of the original DE. We present a representation scheme to characterize the discrete problem space and by redefining its basic concept and all related operators in mutation, DE can operate directly on the original set space of the discrete optimization problems instead of performing a space transformation. In that way, the searching features of DE in continuous space is kept. In experiment, we test the performance of our proposed S-DE and the results show it is very promising.