Solving Traveling Salesman Problems by Genetic Differential Evolution with Local Search

To solve traveling salesman problems (TSP), a genetic differential evolution (GDE) was introduced, which was derived from the differential evolution (DE) and incorporated with the genetic reproduction mechanisms, namely crossover and mutation. The Greedy Subtour Crossover (GSX) was employed to generate an offspring to denote the difference of the parents. A modified ordered crossover (MOX) was employed to perform mutation to generate trial vector with a user defined parameter, the parameter were used to control the rates of the target vector components and the mutated vector components in the trial vector. Moreover, a 2-opt local search was implemented to enhance local search performance. GDE was implemented to the well-known TSP with 52, 100 and 200 cities with variable parameters. Based on analysis and discussion on the results, typical values of the parameters were given, with which GDE provided effective and robust performance.