The Traveling Salesman Problem

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Abstract- This paper is a survey of genetic algorithms for the traveling salesman problem and its optimization. Traveling salesman problem is most commonly optimization problem based on Genetic Algorithm(GAs).Genetic algorithms are randomized search techniques that imitate some of the processes observed in natural selection.Through this research describe how the traveling salesman problem is solved by the heuristic method of genetic algorithms(GAs).The main purpose of this study is to propose a new fittest criteria to be used as method for finding the optimal solution for TSP. 1. Introduction - The Traveling Salesman Problem (TSP) is a classical combinatorial optimization problem, which is simple to state but very difficult to solve. This…show more content…
He mentions the TSP, although not by that name, by suggesting that to cover as many locations as possible without visiting any location twice is the most important aspect of the scheduling of a tour. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved completely and even problems with millions of cities can be approximated with in a small fraction.This research work proposes a new crossover operator for solving the traveling salesman problem. On the basis of the structure of the cost matrix, the TSPs are classified into two groups – symmetric and asymmetric.The TSP is symmetric if cij = cji, for all i, j and asymmetric otherwise. For an n-city asymmetric TSP, there are (n − )!1 possible solutions, one or more of which gives the minimum cost. For an n-city symmetric TSP, there are (n − 1)!/2 possible solutions along with their reverse cyclic permutations having the same total cost. In either case the number of solutions becomes very large for even reasonably large n so that an exhaustive search is…show more content…
It is better than conventional AI in that it is more robust. Unlike older AI systems, they do not break easily even if the inputs changed slightly, or in the presence of reasonable noise. Also, in searching a large state-space, multi-modal state-space, or n-dimensional surface, a genetic algorithm may offer significant benefits over more typical search of optimization techniques. (linear programming, heuristic, depth-first, breath-first, and praxis.) The idea with GA is to use this power of evolution to solve optimization problems. The father of the original Genetic Algorithm was John Holland who invented it in the early 1970's. Genetic Algorithms (GAs) are adaptive heuristic search algorithm based on the evolutionary ideas of natural selection and genetics. As such they represent an intelligent exploitation of a random search used to solve optimization problems. Although randomised, GAs are by no means random, instead they exploit historical information to direct the search into the region of better performance within the search space. The genetic algorithm process consists of the
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