Original article | doi: 10.25007/ajnu.v6n3a78 46 Academic Journal of Nawroz University (AJNU) Using Swarm Intelligence for solving NP- Hard Problems Saman M. Almufti Department of Computer Science and Information Technology, College of Computer Science & Information Technology, Nawroz University, Duhok, Iraq ABSTRACT Swarm Intelligence algorithms are computational intelligence algorithms inspired from the collective behavior of real swarms such as ant colony, fish school, bee colony, bat swarm, and other swarms in the nature. Swarm Intelligence algorithms are used to obtain the optimal solution for NP-Hard problems that are strongly believed that their optimal solution cannot be found in an optimal bounded time. Travels Salesman Problem (TSP) is an NP-Hard problem in which a salesman wants to visit all cities and return to the start city in an optimal time. This article applies most efficient heuristic based Swarm Intelligence algorithms which are Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Bat algorithm (BA), and Ant Colony Optimization (ACO) algorithm to find a best solution for TSP which is one of the most well-known NP-Hard problems in computational optimization. Results are given for different TSP problems comparing the best tours founds by BA, ABC, PSO and ACO. KEY WORDS: Swarm Intelligence, NP-Hard problem, Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Bat algorithm (BA), and Ant Colony Algorithm (ACO) 1. INTRODUCTION Swarm Intelligence algorithms are computational intelligence techniques studies the collective behavior in decentralized systems (Almufti, 2015). Such systems are made up of a population of simple individual’s agents interacting locally with each other and with the environment around themselves (Almufti, 2015). This paper focuses on the comparative analysis of most successful methods of optimization techniques inspired by Swarm Intelligence (SI): Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO), Bat Colony Optimization (BA), and Artificial Bee Colony (ABC) for solving one of the most well-known NP- Hard problems which is called Travels Salesman Problem (TSP) (Almufti, 2015) , (Andrej Kazakov, 2009). 2. OVERVIEW OF SWARM INTELLIGENCE ALGORITHMS Swarm intelligence(SI),which is an artificial intelligence (AI) field, is concerned with the designing of intelligent interactive multi-agent systems that cooperate to gather to achieve a specific goal. Swarm intelligence is defined by Dorigo M as “The emergent collective intelligence of groups of simple agents”( Li, Y.: 2010). Swarm-based algorithms are inspired from behaviors of some social living beings (insects, animal, and bacteria’s) in the nature, such as ants, birds, bats, bees, termites, and fishes. The most remarkable features of swarm systems are Self-organization and decentralized control that naturally leads to an emergent behavior in the colony. Emergent behavior is an interactive property that emerges a local interaction among all system components (agents) and it is not possible to be achieved alone by any agent in the system (Almufti, 2015). In computer science there are many algorithms that are designed as an inspiration of real collective behavior systems in the nature, swarm intelligence algorithms includes Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Artificial Immune System, Bat algorithm, Bacterial Foraging, Stochastic diffusion search, Glowworm Swarm Optimization, Gravitational search algorithm, Cat Swarm Optimization, and other optimization algorithms (Almufti, 2015). Swarm intelligence works on two basic principles: self- Academic Journal of Nawroz University (AJNU) Volume 6, No 3(2017), 10 pages Received 1 May 2017; Accepted 1 August 2017 Regular research paper: Published 8 August 2017 Corresponding author’s e-mail: Saman.almofty@gmail.com Copyright ©2017 Saman M. Abdulrahman. This is an open access article distributed under the Creative Commons Attribution License.