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 ...

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 ...

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 ...

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) ...

Determining the precise integrality gap for the subtour linear programming (LP) relaxation of the traveling salesman problem is a significant open question, with little progress made in thirty years ...