The Generalized Traveling Salesman Problem (GTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where the node set is partitioned into clusters, and the objective is to find the shortest cycle visiting each cluster exactly once. In this paper, we present a new hybrid Ant Colony System (ACS) algorithm for the symmetric GTSP. The proposed algorithm is a modification of a sim...

The Single Machine Scheduling with Changeover Costs problem is found in many different workshops. In this case, the main criterion is the sequence-dependent changeover-costs or setup times. This Scheduling problem can be modeled as a Traveling Salesman Problem (TSP) and when time constraints are inserted into the model such as due-dates, the resulting problem is known as the Time Dependent Trav...

This is a comment on the article “An O(logn) Approximation Ratio for the Asymmetric Traveling Salesman Path Problem” by C. Chekuri and M. Pál, Theory of Computing 3 (2007), 197–209. We observe that the LP relaxation for the Asymmetric Traveling Salesman Path Problem suggested in Section 5 of that paper is not accurate, and state a corrected linear relaxation for the problem. The inaccuracy occu...

Statistical distributions of quasi-optimal paths in the traveling salesman problem: the role of the initial distribution of cities Revista Mexicana de Física, Solutions to Traveling Salesman Problem have been obtained with several algorithms. However, few of them have discussed about the statistical distribution of lengths for the quasi-optimal path obtained. For a random set of cities such a d...

The Traveling Salesman Problem provides an opportunity to explore whether attempts to optimize an algorithm in fact succeed or fail. Attempted optimizations themselves have time penalties in their execution and those time penalties may be greater than the improvements provided to the algorithm. When approaching the Traveling Salesman Problem not as a graph traversal problem but as a backtrackin...

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation. Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics. Specifica...

We prove that both minimum and maximum traveling salesman problems on complete graphs with edge-distances 1 and 2 (denoted by min TSP12 and max TSP12, respectively) are approximable within 3/4. Based upon this result, we improve the standard approximation ratio known for maximum traveling salesman with distances 1 and 2 from 3/4 to 7/8. Finally, we prove that, for any 2 > 0, it is NP-hard to ap...

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...

An analysis of the dynamic behavior of Evolution Strategies applied to Trav-eling Salesman Problems is presented. For a special class of Traveling Salesman Problems a stochastic model of the optimization process is introduced. Based on this model diierent features determining the optimization process of Evolution Strategies are analyzed. In addition the stochastic model is extended to explain s...