Greedy Randomized Adaptive Search Procedure for Traveling Salesman Problem. (May 2005) Seung Ho Lee, B.E., Korea University Chair of Advisory Committee: Dr. Sergiy Butenko In this thesis we use greedy randomize adaptive search procedure (GRASP) to solve the traveling salesman problem (TSP). Starting with nearest neighbor method to construct the initial TSP tour, we apply the 2-opt and the path-...

The traveling salesman problem (TSP) is one of the most important combinational optimization problems that have nowadays received much attention because of its practical applications in industrial and service problems. In this paper, a hybrid two-phase meta-heuristic algorithm called MACSGA used for solving the TSP is presented. At the first stage, the TSP is solved by the modified ant colony s...

We describe a hybrid procedure for solving the traveling salesman problem (TSP) to provable optimality. We first sparsify the instance, and then use a hybrid algorithm that combines a branch-and-cut TSP solver with a Hamiltonian cycle problem solver. We demonstrate that this procedure enables us to solve difficult instances to optimality, including one which had remained unsolved since its cons...

Given a set of nodes and the distances between them, the traveling salesman problem (TSP) consists in finding the shortest route that visits each node exactly once and returns to the first. The Steiner traveling salesman problem (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by a shortest route, eventually visiting some nodes and edges more than on...

We introduce two new combinatorial optimization problems, which are generalizations of the Traveling Salesman Problem (TSP) and the Assignment Problem (AP) and which we call Traveling Salesman Problem of Second Order (TSP2) and Assignment Problem of Second Order (AP2). TSP2 is motivated by an important application in bioinformatics, especially the Permuted Variable Length Markov model. While TS...

We consider the special case of the traveling salesman problem (TSP) in which the distance metric is the shortest-path metric of a planar unweighted graph. We present a polynomial-time approximation scheme (PTAS) for this problem.

The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 100 vertices. In this work, we study the polytope associ...

In this paper, we propose novel adaptation rules for the selforganizing map to solve the prize-collecting traveling salesman problem (PC-TSP). The goal of the PC-TSP is to find a cost-efficient tour to collect prizes by visiting a subset of a given set of locations. In contrast with the classical traveling salesman problem, where all given locations must be visited, locations in the PC-TSP may ...

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...

Traveling Salesman Problem (TSP) is an NP-hard Problem, which has many different real life applications. Genetic Algorithms (GA) are robust and probabilistic search algorithms based on the mechanics of natural selection and survival of the fittest that is used to solve optimization and many real life problems. This paper presents Genetic Algorithm for TSP. Moreover it also shows best suitable p...