A new algorithm based on differential evolution for combinatorial optimization

Differential evolution (DE) was originally designed to solve continuous optimization problems, but recent works have been investigating this algorithm for tackling combinatorial optimization (CO), particularly in permutation-based combinatorial problems. However, most DE approaches for combinatorial optimization are not general approaches to CO, being exclusive for per mutational problems and often failing to retain the good features of the original continuous DE. In this work we introduce a new DE-based technique for combinatorial optimization to addresses these issues. The proposed method employs operations on sets instead of the classical arithmetic operations, with the DE generating smaller sub problems to be solved. This new approach can be applied to general CO problems, not only permutation-based ones. We present results on instances of the traveling salesman problem to illustrate the adequacy of the proposed algorithm, and compare it with existing approaches.