Providing a method for selecting the constrained shortest path problem using logical cuts

Shortest path problem is one of the practical issues in optimization, and there are many efficient algorithms in this area. In this issue, a network of some nodes and arcs is considered in which, each arc has a specific parameter such as distance or cost. The main objective is to find the shortest or least costly route between two distinct points. By considering an additional parameter and adding a new limitation, as a capacity constraint, the problem will be closer to the real world condition. This extended issue is known as the constrained shortest path problem and has a higher complexity order and practical algorithms are needed to solve it. In this study, an effective algorithm is presented that obtains the optimal solution within a short time. In this method, a repetitive pattern is used so that, in each iteration, the relaxed model, after adding a logical cut, is solved. The results of the implementation of the proposed algorithm on different networks show its efficiency.