Mir Mohammad Alipour

The travelling salesman problem one of the well-known NP-hard problems, and there are various models with respect to its different specifications of the travalling salesman problem. Specially, the symmetric travelling salesman problem is one of the most studied models, which has been applied for routing models. The critical node detection problem has received increasing attention throughout the routing models. It is defined as the node its deletion from the network results in the largest decrease of the optimal cost. The 2-opt heuristic is applied by the critical node in the symmetric traveling salesman problem and the the iterations are reduced significantly. Then, the pseudo-critical node is detected in the approximate solution, whose removal results in the largest decrease of the approximate cost. So, the 2-opt heuristic is applied by the pseudo-critical node and the optimal or nearby optimal solution is obtained.