An Improved GA-Based algorithm for Travelling Salesman Problem Chieng Hock Hung, Noorhaniza Wahid
An Improved GA-Based algorithm for Travelling Salesman Problem 1
Chieng Hock Hung, 2Noorhaniza Wahid Faculty of Computer Science and Information Technology Universiti Tun Hussein Onn Malaysia 86400 Parit Raja, Johor, Malaysia,
[email protected] 2 Faculty of Computer Science and Information Technology Universiti Tun Hussein Onn Malaysia 86400 Parit Raja, Johor, Malaysia,
[email protected]
*1,Corresponding Author
Abstract Travelling Salesman Problem (TSP) is a NP-hard problem that has been widely studied in the field of combinatorial. The problem in TSP can be described as, a salesman who desires to visit n cities, and supposed to find out the shortest tour through visiting all the cities exactly once and finally returning to the city where he started. In the past, Genetic Algorithm (GA) was highlighted to have good performance in solving TSP. However, GA often suffers from premature convergence due to the difficulty in preventing the loss of genetic diversity in the population. To overcome this drawback, GA that using Simplified Swarm Optimization (SSO) algorithm’s characteristic is proposed. This proposed algorithm is called Genetic Simplified Swarm Algorithm (GSSA). The used characteristic was named as Solution Update Mechanism (SUM). SUM was modified beforehand by embedding the three different GA’s mutation operators in it. These mutation operators are the inversion, displacement, and pairwise swap mutation operators. The proposed algorithm was tested with other GAs that contains different mutation operators on 8 benchmark instances that selected from TSPLIB. Generally, the application of the GSSA gives much more effective results regarding the best and average results in most of the instances. The GSSA outperformed the other GAs with 6 out of 8 TSP instances on both best and average results. Obtained results in this study showed that the proposed algorithm is much more efficient and outperformed in most of the TSP instances compared to the other GAs.
Keywords: Travelling Salesman Problem, Genetic Algorithm, mutation operator, Solution Update Mechanism, Simplified Swarm Optimization
1. Introduction TSP is an NP-hard problem that has been widely studied in the field of combinatorial optimization [1]. It was first formulated by Karl Menger in 1930 [2][3]. The name “Travelling Salesman Problem” was introduced by Hassler Whitney in Princeton University at 1934 [4]. In 1954, TSP was derived as an integer program and solved by using cutting plane method by Dantzig [5]. Later, TSP was revealed as an NP-hard problem in 1972 by Karp due to its computational complexity in the manner of finding the optimal tour [6]. Due to its computational complexity, a large number of heuristic and exact methods have been proposed to provide the optimal solutions [7]. TSP can be described as follow, a salesman who desires to visit n cities, and supposed to find out the shortest Hamilton tour through visiting all the cities exactly once and finally returning to the city where he started. According to Matai et al. [8] feasible solutions of TSP is given as (n-1)!/2 where n represents the number of cities. TSP can be presented on a complete undirected graph G = (V, E), where V = {1,…,n} is denote to the vertex node or city, E = {(i, j) : i, j∈V, i
