International Journal of Computer Applications (0975 – 8887) Volume 157 – No 7, January 2017 47 Parallel Computing Approach to Solve Travelling Salesman Problem Harshala C. Ingole Department of Computer Engineering St. Vincent Pallotti College of Engineering and Technology Nagpur, India Vivek B. Kute Department of Computer Engineering St. Vincent Pallotti College of Engineering and Technology Nagpur,India ABSTRACT Travelling Salesman Problem (TSP) is eminent in combinatorial optimization problem. A typical problem in computational mathematics, scientific and business application such as VLSI chip design, social network analysis. TSP, combinatorial optimization problem belongs to the class of NP-Hard, and becomes significant method of verifying the correctness and feasibility of new algorithm. With the accuracy results and efficient cutting branch strategy of branch and bound algorithm, it used to solve TSP. However, branch and bound algorithm not suitable for large scale TSP with sequential execution. In this paper parallel branch and bound algorithm has been improved and proposed to solve the symmetric TSP. This paper uses parallel program code based on multithreading concept to verify TSP. The experimental result shows our algorithm is efficient, and solves the large scale TSP problem which cannot be solved by sequential branch and bound. General Terms Parallel Computing, Combinatorial Optimization, Travelling Salesman Problem Keywords Travelling Salesman Problem, Branch and Bound Algorithm, Parallel Computing 1. INTRODUCTION Travelling Salesman Problem (TSP), first expressed as computational mathematics problem in 1930.TSP, extensively studied problem in combinatorial optimization [1].Solution to this problem cannot be find in polynomial time. On solving optimization problem, requires to get the best possible solution from all available solution spaces. The “best” solution inferred that more than one solution available. The travelling salesman problem results in more than one solution, but the aim is to find the best possible solution for large scale TSP amongst all available solution spaces in a polynomial time and the performance also increased [2].TSP widely used in VLSI chip design, network routing, robot control, gene sequencing, vehicle routing [3]. And also finds its application in the areas like logistics, transportation, and semiconductor industries. Methods of solving TSP can be categorized in two directions such as exact algorithm and approximate algorithm. These two methods give the solution but with certain issues, as Exact algorithms search for the whole solution space tree and obtain the global optimal solution. The global optimal solution guarantees the exact solution to the problem but not with the higher performance. E.g. branch-and-bound method, linear programming method, and dynamic programming method. As approximate algorithm finds as nearer as to the optimal solution in a reasonable amount of time but the solution does not guarantees the exact optimal solution to the TSP problem. E.g. greedy algorithm, genetic algorithms, simulated annealing algorithm, neural network algorithm and ant colony algorithm [2].With the comparison of this two methods of solving the TSP problem, the former one has requires the exponential time to solve and difficult to acquire the large scale problem. As Exponential algorithms have some advantages as simple method, small amount of calculation requires and so on. So feasible for small scale problem but as size of nodes get increased it doesn’t give the nearer optimal solution in polynomial time. To solve TSP in an acceptable time the parallel computing mechanism taken into account .The parallel computing in which the computations carried out simultaneously ,the principle behind that the computational task divides into subtask and solves independently and after completion results get combined. This paper is organized as follows: Section II describes the background of TSP and branch and bound algorithm and related work. Section III describes the design and implementation of parallel branch and bound algorithm. In Section IV the branch and bound performance evaluation results in parallel execution is presented. The last section is our conclusion and future work. 2. BACKGROUND AND LITERATURE SURVEY This section starts with introduction to TSP, Branch and Bound algorithm and then discusses literature survey. 2.1 TSP Introduction Operation research and theoretical computer science addresses the TSP as NP-Hard problem [4]. TSP used to find the shortest path to travel through the given number of cities. Travelling Salesman Problem states that given a number of cities and the distances between them, salesman has to visit all the given cities exactly once and return back to the city from where he started with the minimized cost. In TSP [5], given a complete undirected graph G = (V, E) that has nonnegative integer cost c(u.v) associated with each edge (u ,v) ϵ E ,and to find a Hamiltonian cycle (a tour) of G with minimum cost path. As an extension of notation, let c(A) denote the total coat of in the subset A ⊆ E :