The Sequential Ordering Problem (SOP) is a version of the Asymmetric Traveling Salesman Problem (ATSP) where precedence constraints on the vertices must also be observed. The SOP has many real life applications and it has proved to be a great challenge (there are SOPs with 40-50 vertices which have not been solved optimally yet with significant computational effort). We use novel branch&bound s...

This paper presents a new constructive approach based on simulated annealing for the large scope of scheduling problem can be assumed as traveling salesman problem (TSP). The main contribution of this research is developing a new definition of TSP. We solve the TSP when there are no roads between some cities. This leads us to incomplete graph constructed based on TSP. We demonstrate this realit...

Pheromone trails are the main media for gathering collective knowledge about a problem, and have a central role in all ant colony optimization algorithms. Setting appropriate trail limits for the MAX-MIN ant system (MMAS) is important for good performance of the algorithm. We used rigorous analysis to develop expressions that model the influence of trail limits on MMAS behavior. Besides the gen...

Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSP-TW) from such a point of view. The real–world applic...

A simple lexisearch algorithm that uses path representation method for the asymmetric traveling salesman problem ATSP is proposed, along with an illustrative example, to obtain exact optimal solution to the problem. Then a data-guided lexisearch algorithm is presented. First, the cost matrix of the problem is transposed depending on the variance of rows and columns, and then the simple lexisear...