In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer. Disclaimer: This article was authored by Craig Alan Feinstein in his private capacity. No official support or endorsement by the U.S. Government is intended or should be inferred. Consider the following well-known NP-hard problem: Traveling Salesman Problem A traveling salesman...

the traveling salesman problem (tsp) is a well-known combinatorial optimization problem and holds a central place in logistics management. the tsp has received much attention because of its practical applications in industrial problems. many exact, heuristic and metaheuristic approaches have been proposed to solve tsp in recent years. in this paper, a modified ant colony optimization (maco) is ...

In the online traveling salesman problem requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman which finishes as early as possible. Performance of algorithms is measured through their competitive ...

Consider a truck running along a road. It picks up a load Li at point βi and delivers it at αi, carrying at most one load at a time. The speed on the various parts of the road in one direction is given by f(x) and that in the other direction is given by g(x). Minimizing the total time spent to deliver loads L1, . . . , Ln is equivalent to solving the Traveling Salesman Problem (TSP) where the c...

Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem is to find the cheapest way of visiting all of the cities and returning to starting point. The simplicity of the statement of the problem is deceptive, the traveling salesman problem is one of the most intensely studied problems in computational mathematics and yet no effective solution...