We use a branch-and-cut search to solve the Whizzkids’96 vehicle routing problem, demonstrating that the winning solution in the 1996 competition is in fact optimal. Our algorithmic framework combines the LP-based traveling salesman code of Applegate, Bixby, Chvátal, and Cook, with specialized cutting planes and a distributed search algorithm, permitting the use of a computing network located a...

Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized) and travel cost (minimized). Applications of these problems arise in contexts such as traveling salesman ...

The multiple traveling salesmen problem (MTSP) is an extension of the traveling salesman problem with many production and scheduling applications. The TSP has been well studied including methods of solving the problem with genetic algorithms. The MTSP has also been studied and solved with GAs in the form of the vehicle-scheduling problem. This work presents a new modeling methodology for settin...

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the traveling salesman problem with time windows, where additionally generalized precedence constraints have to be respected. The objectiv...

The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...