These routes were comparable to the solutions calculated by a computer algorithm. Currently, when there are many target cities, the best way to tackle the traveling-salesman problem is a tool called ...

We report the solution to optimality of ten large-scale symmetric travelling salesman problems. The travelling salesman problem (TSP) is one of the standard problems of the Operations ...

Dr. James McCaffrey of Microsoft Research uses full code samples to detail an evolutionary algorithm technique that apparently hasn't been published before. The goal of a combinatorial optimization ...

We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long) ...

Is it hopeless to try to compute the shortest route to visit a large number of cities? Not just a good route but the guaranteed shortest. The task is the long-standing challenge known as the traveling ...

Bumblebees can find the solution to a complex mathematical problem which keeps computers busy for days. Scientists in the UK have discovered that bees learn to fly the shortest possible route between ...

The goal of a combinatorial optimization problem is to find a set of distinct integer values that minimizes some cost function. The most famous example is the Traveling Salesman Problem (TSP). There ...