IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 04 Issue: 05 | May-2015, Available @ http://www.ijret.org 317 A NEW HYBRID APPROACH FOR SOLVING TRAVELLING SALESMAN PROBLEM USING ORDERED CROSS OVER 1(OX1) AND GREEDY APPROACH Komal Joshi 1 , Ram Lal Yadav 2 1 M.Tech Scholar, Department of Computer Science and Engineering, Kautilya Institute of Technology and Engineering, Jaipur, Rajasthan 2 Associate Professor, Department of Computer Science and Engineering, Kautilya Institute of Technology and Engineering, Jaipur, Rajasthan Abstract Travelling Salesman Problem is a well known NP problem. It is an optimization problem. Genetic Algorithms are the evolution techniques to solve optimization problems. In this paper a new hybrid technique using ordered cross over 1 (OX1) and greedy approach has been proposed. Experiment results shows that the proposed hybrid cross over is better than the existing cross over operator as the new operator provide a better path when executed for the same number of iterations. Keywords:- Travelling Salesman Problem, ordered cross over 1 (OX1) --------------------------------------------------------------------***------------------------------------------------------------------ 1. INTRODUCTION The travelling salesman problem has been first studied in 1800’s by Sir William Rowan, Hamilton and Thomas Penyngton Kirkman. Hamilton was an Irish mathematician and Kirkman was a British mathematician. In 1857, Hamilton created a game in which a player has to connect 20 specified points by specified connectors. The game was named as Icosian [6] . Later Hamilton has done research on graph theory and contributes to graph theory. In travelling salesman problem a salesman has to visit a number of cities. Salesman has to start its journey from any of the city called the starting city, cover all the cities in the tour and return back on the starting city. Problem is to find the tour such that salesman have to travel minimum distance to cover all the cities. In 1972 the travelling salesman problem has been declared as NP-complete. NP-complete is a class of problems which are non-deterministic polynomial time hard i.e. no polynomial time algorithm is available to solve these problems. TSP is represented by a Hamiltonian cycle which is a NP-complete class problem. So it is very difficult to find optimal tours to solve this problem. Travelling salesman problem has its application in many areas such as Drilling of printed circuit boards, 2. Overhauling gas turbine engines, X-Ray crystallography, Computer wiring, order-picking problem in warehouses etc. Genetic Algorithm (GA) is an optimization techniques which uses special operators such as selection, reproduction and mutation to solve problems which are difficult to solve by using traditional techniques. GA works on some optimization function which may be a minimization function or a maximization function. Genetic Algorithm is also applicable in solving optimization problem such as Travelling Salesman Problem. In literature work has been done on many techniques to solve TSP using Genetic Algorithms. A survey of literature on solving TSP using GA is given in the next section. 2. RELATED WORK Yang Yi and Qian-Sheng Fang [1] proposed an improved Hybrid Genetic algorithm for solving travelling salesman problem on Handel-C. Authors used a greedy approach to improve the performance of genetic algorithm. [5] Poonam Panwar and Sonali Gupta present a survey of soft computing techniques used for optimizing travelling salesman problem. Authors explain that soft computing techniques such as genetic algorithm can be used to solve many problems which belong to NP-complete or NP-hard set of problems. In the paper it has been concluded that soft computing techniques can be applied to solve travelling salesman problem. Author [5] concluded that genetic algorithm perform better in solving travelling salesman problem. The main advantage of GA is that it converges to the solution in very short time. In future work author concluded that a hybrid of existing solutions can be used to solve TSP to enhance the performance of GA. [4] GoharVahdatiet.el.publish a new approach to solve traveling salesman problem using genetic algorithmbased on heuristic crossover and mutation operator. In this paper author proposes a new cross over and mutation technique to solve TSP using GA. Author implemented their work and concluded that the new proposed cross over and mutation operators work better than some existing cross over operators such as OX1, MOC and SWAP operators. [2] Varshika Dwivediet.el. proposed a new strategy to find nearly optimized solution to travelling salesman problem using new cross over technique.