doi : 10.25007/ajnu.v7n4a270 Academic Journal of Nawroz University (AJNU) 45 U-Turning Ant Colony Algorithm for Solving Symmetric Traveling Salesman Problem Saman M. Almufti 1 , Awaz A. Shaban 2 College of Computer Science & Information Technology, Duhok, Kurdistan Region - Iraq ABSTRACT This paper provides a new Ant based algorithms called U-Turning Ant colony optimization (U-TACO) for solving a well-known NP-Hard problem, which is widely used in computer science field called Traveling Salesman Problem (TSP). Generally U-Turning Ant colony Optimization Algorithm makes a partial tour as an initial state for the basic conventional Ant Colony algorithm. This paper provides tables and charts for the results obtained by U-Turning Ant colony Optimization for various TSP problems from the TSPLIB95. Keywords: Traveling Salesman Problem (TSP), Ant System (AS), Swarm Intelligence, U-Turning Ant Colony Optimization Algorithm (U-TACO), Symmetric Traveling Salesman Problem (STSP). 1. Introduction In Computer science field, Swarm Intelligence (SI) algorithms are computational intelligence techniques that study the collective behavior in decentralized systems (Almufti, 2017). In the nature real-ants lives in colonies, Ants of a colony are cooperates the process of food searching. Ants are unsystematically travels searching for a food source, ones an ant reaches a food source it returns to the colony by using a chemical substance called pheromone trail that ant deposits it in the way to the food and can be smelled by other ant. U- Turning Ant Colony Optimization algorithm is a new swarm intelligence algorithm based on the Ant colony algorithm in which ants randomly travel searching for the source of Food (Almufti, 2015). In this paper U- Turning Ant Colony Optimization algorithm is used to solve Symmetric Traveling Salesman Problem in which a salesman want to visit all cities in the graph and return to the start city with minimum time and cost (Almufti, 2015; Asaad, R., Abdulnabi, N. 2018). 2. Symmetric Traveling Salesman Problem (STSP) TSP is one of widely used NP-hard problem in combinatorial optimization (Asaad, R., Abdulnabi, N. 2018). In a given graph a number of cities in which every city must be visited once and return to the starting city for completing a tour such that the length of the tour is the shortest among all possible tours (Almufti, 2015; Andrej Kazakov, 2009). Symmetric TSP (STSP) is a type of TSP in which the distance between city A and B is equal to the distance between city B and A. In a graph G(C,A) the distance d(Ci,Cj) = d(Cj, Ci) and the number of tours in the Symmetric TSP (STSP) is (n- 1)!/2 for n cities. Consequently the optimal (minimum length) tour to the STSP can be obtained by finding the summation of the length between cities of a permutation list as shown in equation (1) (Almufti, 2015; Asaad, R., Abdulnabi, N. 2018).  = (∑  () (+1) −1 =1 )+ () (1) (1) Where p is a probability list of cities with minimum distance between cities (pi and pi+1) (Federico Greco 2008; Asaad, R., Abdulnabi, N. 2018). 3. U-Turning Ant Colony Optimization (U-TACO) U-Turning Ant Colony Optimization (U-TACO) is metaheuristic algorithm designed by Saman M. Almufti in his master thesis in (2015), it generally based on the same principles of common Ant System (AS) which was first represented in 1992 by Marco Dorigo in his PhD thesis as a nature-inspired metaheuristics for solving hard combinatorial optimization (CO) problems (Dorigo, 1992; Almufti, 2015; Almufti, 2017). All algorithms that inspired the behavior of real Ant in searching for food source, basically depends on pheromone trail updating and the following of other ants to the pheromone smell: ants deposit pheromones in their way to the food source which takes attention of other swarm ants to the food source and the way that they should take to the food, gradually the way that have more pheromone is the shortest way to the food Academic Journal of Nawroz University (AJNU) Volume 7, No 4 (2018). Regular research paper : Published 21 December 2018 Corresponding author’s e-mail : saman.almofty@gmail.com Copyright ©2017 Saman M. Almufti1, Awaz A. Shaban2. This is an open access article distributed under the Creative Commons Attribution License.