A Novel Algorithm for Solving the Prize Collecting Traveling Salesman Problem Based on DNA Computing

DNA computing is a new pattern of computing that combines biotechnology and information technology. As a new technology born in less than three decades, it has developed at an extremely rapid rate, which can be attributed to its advantages, including high parallelism, powerful data storage capacity, and low power consumption. Nowadays, DNA computing has become one of the most popular research fields worldwide and has been effective in solving certain combinatorial optimization problems. In this study, we use the Adleman-Lipton model based on DNA computing for solving the Prize Collecting Traveling Salesman Problem (PCTSP) and demonstrate the feasibility of this model. Then, we design a simulation experiment of the model to solve some open instances of PCTSP. The results illustrate that the model can satisfactorily solve these instances. Finally, the comparison with the results of the Clustering Search algorithm and the Greedy Stochastic Adaptive Search Procedure/Variable Neighborhood Search method reveals that the optimal solutions obtained by this simulation experiment are significantly superior to those of the other two algorithms in all instances. This research also provides a method for proficiently solving additional combinatorial optimization problems.