The geometric maximum traveling salesman problem

The traveling salesman problem

The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is perhaps the most studied discrete optimization problem. Its popularity is due to the facts that TSP is easy to formulate, difficult to solve, and has a large number of applications. It appears that K. Menger [31] was the first researcher to consider the Traveling Salesman Problem (TSP). He observed that the problem can be solved by examining all permutati...

Tabu Search on the Geometric Traveling Salesman Problem

I Abstract The Traveling Salesman Problem (TSP) is probably the most well-known problem of its genre: Combinatorial Optimization. New heuristics, built on the concept of local search, i.e. continuously to make transitions from one solution to another in the search for better solutions have shown to be successful, especially for medium-to large-scale problems (+1000 cities). This thesis presents...

An Approximation Algorithm for the Maximum Traveling Salesman Problem

We develop a polynomial time approximation algorithm for the maximum traveling salesman problem. It guarantees a solution value of at least r times the optimal one for any given r < 5 7 .

Simpler Approximation of the Maximum Asymmetric Traveling Salesman Problem

We give a very simple approximation algorithm for the maximum asymmetric traveling salesman problem. The approximation guarantee of our algorithm is 2/3, which matches the best known approximation guarantee by Kaplan, Lewenstein, Shafrir and Sviridenko. Our algorithm is simple to analyze, and contrary to previous approaches, which need an optimal solution to a linear program, our algorithm is c...