We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is Θ(log n). Moreover, we prove that the same result also holds for graphic, euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the ClarkeWright savings heuristic for the metric Traveling Salesman Problem is Θ(log n). keywor...

This paper describes an effective approach to solve the inspection problem via colored traveling salesman tours. Given an environment with obstacles and regions to be inspected, the approach plans a collision-free and dynamicallyfeasible motion trajectory that enables the vehicle to inspect all the regions of interest while reducing the distance traveled. A key aspect of the approach is the tra...

We consider a generalization of the capacitated vehicle routing problem known as the cumulative vehicle routing problem in the literature. Cumulative VRPs are known be a simple model for fuel consumption in VRPs. We examine four variants of the problem, and give constant factor approximation algorithms. Our results are based on a well-known heuristic of partitioning the traveling salesman tours...

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into so-called clusters, and the salesman has to visit every cluster exactly once. While the GTSP is a very important combinatorial optimization problem and is well stud...

A novel application of the generalized traveling salesman is pro- posed. The practical problem considered optimization different criteria in various models a mixed assembly worksta- tion. Several that give rise to interesting problems are discussed. Keywords: problem, flexible workstation.

In this article we introduce the Quadratic Capacitated Vehicle Routing Problem (QCVRP), a combinatorial optimization problem that arises in practical applications in logistics and transportation. The QCVRP extends two other known problems, the Capacitated Vehicle Routing Problem (CVRP) and the Quadratic Symmetric Traveling Salesman Problem (QSTSP), the former by considering a modified cost matr...

Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in list exactly once and ends in the city where it starts. Despite the Traveling Salesman Problem is NP-Hard, a lot of methods and solutions are proposed to th...

Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in list exactly once and ends in the city where it starts. Despite the Traveling Salesman Problem is NP-Hard, a lot of methods and solutions are proposed to th...

The Generalized Traveling Salesman Problem (GTSP) is an extension of the well known Traveling Salesman Problem (TSP). The GTSP is defined on a graph in which the nodes (customers or vertices) are grouped into a given number of clusters (node sets). Solution procedures for the GTSP are generally focused on transforming the problem to the TSP and applying the exact or heuristic solution methods d...

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...