The Traveling Salesman Problem (TSP) is one of the most widely studied problems in combinatorial optimization. It has long been known to be NP-hard and hence research on developing algorithms for the TSP has focused on approximate methods in addition to exact methods. Tabu search is one of the most widely applied metaheuristic for solving the TSP. In this paper, we review the tabu search litera...

The traveling salesman problem (TSP), can be used as a typical combinatorial optimization problem, to describe wide variety of practical engineering problems in various fields. In this study, the personnel and equipment utilization transportation industry was abstracted, more general class TSPs with replenishment arcs proposed, an model minimize total travel time established, ant colony algorit...

We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces inflexible traversal operation in LKH, lets prog...

In this paper, we propose a new approach to solving the Traveling Salesman Problem (TSP), for which no exact algorithm is known that allows find solution in polynomial time. The proposed based on optimization by ants. It puts several colonies competition improved solutions (in execution time and quality) large TSP instances, efficiently explore range of possible solutions. results our experimen...

We study the Multi-Depot Multiple Traveling Salesman Problem (MDMTSP), which is a variant of the very well-known Traveling Salesman Problem (TSP). In the MDMTSP an unlimited number of salesmen have to visit a set of customers using routes that can be based on a subset of available depots. The MDMTSP is an NPhard problem because it includes the TSP as a particular case when there is only one dep...

In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the TSP. On the other hand, experimental data also supports the hypothesis of convex hull i.e. human relies on convex hull to search for the optimal tour for the T...

The Resource-Constrained Traveling Salesman Problem (RCTSP) is formulated as follows. A set of n cities is given (denoted by V ); travelling from city i to city j incurs cost cij as well as resource consumption rij . The objective is to find a minimum cost Hamilton cycle (or tour) that consumes not more than Rmax units of the resource, where Rmax is some constant. The cost (resource consumption...

Inspired by the cooperation mechanisms of Th cells, we propose a new algorithm named cooperation artificial immune system and apply it to traveling salesman problem (TSP). Simulation results show that the cooperation immune model has better performance than the model without cooperation.

We design a new LP-based algorithm for the graphic s-t path Traveling Salesman Problem (TSP), which achieves the best approximation factor of 1.5. The algorithm is based on the idea of narrow cuts due to An, Kleinberg, and Shmoys. It partly answers an open question of Sebő.

Ant Colony Optimization (ACO) is a promising new approach to combinatorial optimization. Here ACO is applied to the traveling salesman problem (TSP). Using a genetic algorithm (GA) to nd the best set of parameters, we demonstrate the good performance of ACO in nding good solutions