In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem, in which the object...

Classic multiple traveling salesman problem (MTSP) requires to find the k closed circular paths which minimize the sum of the path lengths, and each vertex is visited only once by a salesman. This paper presents an optimized model for the balanced Multiple-salesman Problem with time and capacity constraints, it requires that a salesman visits each vertex at least once and returns to the startin...

An Eflective Heuristic Algorithm for the Traveling. THE SYMMETRIC traveling-salesman problem is: Given an n by n symmetric matrix of.symmetric traveling salesman problem. However, the design and implementation of an algorithm based on this heuristic is not trivial. There are many.This article is about the heuristic for the travelling salesman problem. An Effective Heuristic Algorithm for the Tr...

Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...