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...

The attempts to use mobile robots in a variety of environments are currently being limited by their navigational capability, thus a set of robots must be configured for one specific environment. The problem of navigating an environment is the fundamental problem in mobile robotic where various methods including exact and heuristic approaches have been proposed to solve the problem. This paper p...

This paper presents a variation of the Euclidean Traveling Salesman Problem (TSP), the Multiple Traveling Salesman Problem (MTSP), and compares a variety of evolutionary computation algorithms and paradigms for solving it. Techniques implemented, analyzed, and discussed herein with regard to MTSP include use of a neighborhood attractor schema (a variation on k-means clustering), the "shrink-wra...

Derived from the well-known Traveling Salesman problem (TSP), the multiple-Traveling Salesman problem (multiple-TSP) with single depot is a straightforward generalization: several salesmen located in a given city (the depot) need to visit a set of interconnected cities, such that each city is visited exactly once (by a single salesman) while the total cost of their tours is minimized. Designed ...

in today’s competitive transportation systems, passengers search to find traveling agencies that are able to serve them efficiently considering both traveling time and transportation costs. in this paper, we present a new model for the traveling salesman problem with multiple transporters (tspmt). in the proposed model, which is more applicable than the traditional versions, each city has diffe...

this paper presented a mixed integer programming for integrated scheduling and process planning. the presented process plan included some orders with precedence relations similar to multiple traveling salesman problem (mtsp), which was categorized as an np-hard problem. these types of problems are also called advanced planning because of simultaneously determining the appropriate sequence and m...

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...