Note—A Note on “The Formulation of theM-Salesman 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...

An Approach for Solving Traveling Salesman Problem

In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illu...

A note on the prize collecting traveling salesman problem

We study the version of the prize collecting traveling salesman problem, where the objective is to find a tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling s...

Traveling Salesman Problem

In this paper we present a fast approach for solving large scale Traveling Salesman Problems (TSPs). The heuristic is based on Delaunay Triangulation and its runtime is therefore bounded by O(n log n). The algorithm starts by construction the convex hull and successively replaces one edge with two new edges of the triangulation, thus inserting a new city. The decision which edge to remove is ba...