In this paper, the main known exact and heuristic solution approaches and algorithms for the symmetric Traveling Salesman Problem (TSP), published after 1992, are surveyed. The paper categorize the most important existing algorithm to 6 main groups: i) Genetic algorithms, ii) Ant colony methods, iii) Neural Methods, iv) Local search algorithms and Tabu search, v) Lagrangian methods and vi) Bran...

In this paper, we propose a solution method for the Generalized Traveling Salesman Problem (GTSP) based on a Memetic Algorithm (Genetic Algorithm plus Local Search, see, e.g., [7]). The GTSP is a generalization of the well-known Traveling Salesman Problem (TSP). The main contribution of the paper stands in the crossover operator based on the exploration of a large neighborhood around the father...

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...

This paper is a survey of genetic algorithms for t h e traveling salesman problem. Genetic algorithms are randomized search techniques that simulate some of the processes observed i n natural evolution. In this paper, a simple genetic algorithm is introduced, and various extensions are presented to solve t h e traveling salesman problem. Computational results are also repor ted for both random ...

This paper presents the application of the PSO (Particle Swarm Optimization) as a tool to solve the Traveling Salesman Problem. The proposed application consists of using a technique based on Artificial Intelligent – AI. It is based in the simulation of social interaction between individuals of a population. Here, each element of population moves in the hyper-space and they are attracted by pos...

Imperial competitive algorithm (ICA) simulates a multi-agent algorithm. Each agent is like a kingdom has its country, and the strongest country in each agent is called imperialist, others are colony. Countries are competitive with imperialist which in the same kingdom by evolving. So this country will move in the search space to find better solutions with higher fitness to be a new imperialist....

Let G = (V, E) be a graph and w: E -» R+ be a length function. Given S C V, a Steiner tour is a cycle passing at least once through each vertex of S . In this paper we investigate naturally submodular graphs: graphs for which the length function of the Steiner tours is submodular. We provide two characterizations of naturally submodular graphs, an 0(n) time algorithm for identifying such graphs...

In the recently published book on the Traveling Salesman Problem, half of Chapter 6 [18] is devoted to domination analysis (DA) of heuristics for the Traveling Salesman Problem. Another chapter [16] is a detailed overview of the whole area of DA. Both chapters are of considerable length. The purpose of this paper is to give a short introduction to results and applications of DA. While we do not...

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutatio...

Traveling salesman problem is of the known and classical problems at Research in Operations. Many scientific activities can be solved as traveling salesman problem. Existing methods for solving hard problems (such as the traveling salesman problem) consists of a large number of variables and constraints which reduces their practical efficiency in solving problems with the original size. In rece...