The travelling salesman problem (TSP) remains one of the most challenging NP‐hard problems in combinatorial optimisation, with significant implications for logistics, network design and route planning ...

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 ...

The Traveling Salesman Problem with Backhauls (TSPB) is defined on a graph G = (V, E). The vertex set is partitioned into V=({v1},L,B), where v1 is a depot, L is a set of linehaul customers, and B is ...

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 ...

The traveling salesman problem is one of the basic problems that many theoretical computer scientists have been working on. Many scientists think that there is no algorithm for the traveling salesman ...

Given a graph whose arc traversal times vary over time, the time-dependent travelling salesman problem (TDTSP) consists in finding a Hamiltonian tour of least total duration covering the vertices of ...

Computers are good at answering questions. What’s the shortest route from my house to Area 51? Is 8,675,309 a prime number? How many teaspoons in a tablespoon? For questions like these, they’ve got ...

Imagine you are a salesperson having to travel between multiple locations. How would you achieve this in the quickest way possible? This is a problem that has stumped mathematicians for decades, and ...

Quantum computing offers the hope of dramatic increases in computational capabilities. That’s the promise of quantum computers that can handle hundreds of thousands or millions of quantum bits or ...