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Swarm Intelligence Technique ACO and Traveling Salesman Problem
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1002 Swarm Intelligence Technique ACO and Traveling Salesman Problem Harsh Bhalani1, Dr. Seema Mahajan2, Prof. Zalak Vyas3 1Student, Dept. of Computer Engineering, Indus University, Gujarat, India. 2Head of the Dept. , Dept. of Computer Engineering, Indus University, Gujarat, India. 3Assistant Professor , Dept. of Computer Engineering, Indus University, Gujarat, India. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract – A swarm is a large number of homogenous, simple agents interacting locally among themselves, andtheir environment. Swarm Intelligence (SI) can be defined as a relatively new branch of Artificial Intelligence that is used to model the collective behavior of social swarms in nature. The inspiration often comes from nature, especially biological systems. The social interactions among swarmindividuals can be either direct or indirect. Examples of direct interaction are through visual or audio contact, such as the waggle dance of honey bees. Indirect interaction occurs when one individual changes the environment and the other individualsrespond to the new environment, such as the pheromone trails of ants that they deposit on their way to search for food sources. Examples in natural system SI include bacterial growth, ant colonies, bird flocking, and microbiological intelligence. This paper comprises a snapshot of ant colony optimization algorithm with its application in Traveling Salesman problem (TSP). Key Words: Swarm Intelligence (SI), Artificial Intelligence (AI), Ant Colony Optimization (ACO), and Traveling Salesman Problem (TSP). 1. INTRODUCTION The various techniques of swarm intelligence used by researchers are as follows: 1. Particle Swarm Optimization 2. Ant Colony Optimization 3. Bees Algorithm 4. Artificial Bee Colony Algorithm 5. Differential evolution 6. Artificial Immune System 7. Bat Algorithm 8. Glowworm Swarm Optimization 9. Gravitational Search Algorithm We mainly discuss the Ant Colony Optimization (A.C.O) algorithm in this paper. 1.1 Ant Colony Optimization In 1991, Ant Colony Optimization (ACO) was introduced by M. Dorigo and colleagues for the solution of hard combinatorial optimization (CO) problems.ACOdraws inspiration from the social behavior of ant colonies. It is a shown in Fig-1. A. Ants in a pheromone trail between nest and food B. An obstacle interrupts the trail C. Ants find two paths to go around the obstacle D. A new pheromone trail is formed along the shorter path Fig -1: Pattern of path following by Ants 1.1.1 Ant Colony Optimization Metaheuristic As shown in the basic flow of ACO in Fig-2, the objective of ACO’s third step is toconstructantsolutions(i.e., find the quality paths on the problem’s construction graph) by stochastically moving through neighbor nodes of the graph.
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1003 Fig -2: Basic Flow chart of ACO Ants are driven by a probability rule to sequentially choose the solution components that make use of pheromone trail intensities and heuristic information. Where: is the probability of the kth ant to move from node i to node j at the tth iteration/time step. is the set of nodes in the neighborhood of the kth ant in the tth node. is the pheromone amount on the arc connecting node i and node j, weighted by α. is the heuristic value of the arc connecting node i and node j, weighted by β. The heuristic value is usually a non-increasing function in the moving cost from node i to node j. α and β are weight parameters that control the relative importance of the pheromone versus heuristic information, and application depend constant. The pheromone trail updated by all ants in the iteration. Ants select nextvertex bya stochasticfunction which depends on both pheromone and problem- specific heuristic . 1.1.2. ACO Example: Traveling Salesman Problem In TSP, the goal is to find the shortest possible tour from the salesman’s home city to a finite number of customer cities with only one constraint that each city must be visited just once before finally returning to the starting home city. There are many different ways to translate the above principles into a computational system apt to solve the TSP. In our ant colony system (ACS) an artificial ant k in city r chooses the city s to move to among those whichdonot belong to its working memory by applying the following probabilistic formula: where τ(r,u) is the amount of pheromone trail on edge (r,u), ɲ(r,u) is a heuristic function, which was chosen to be the inverse of the distance between cities r and u, β is a parameter which weighs the relative importance of pheromone trail and of closeness, q is a value chosen randomly with uniform probability in [0,1], q0 (0≤q0≤1)isa parameter, and S is a random variable selected according to the following probability distribution, which favors edges which are shorter and have a higher level of pheromone trail: where (r,s) is the probability with which ant k chooses to move from city r to city s. Local updating is intended to avoid a very strong edge being chosen by all the ants: Every time an edge is chosen by an ant its amount of pheromone is changed by applying the local trail updating formula:
3.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1004 where is a parameter. Local trail updating is also motivated by trail evaporation in real ants. Typical parameter settings for TSP are: m = n (i.e., number of ants = number of cities), α = 1, β=2 to 5, ρ=0.5, and = . 1.2. ACS: Ant Colony System Ant Colony System has been introduced to improve Ant System’s performance. ACSdiffersin3mainfactorsfrom Ant System. ACS uses a more aggressive action choice rule than AS. Second is that, the pheromone is added only to arcs that belong to global best solution. Third, wheneverantuses an arc (i, j) to move from city i to city j, it removes some pheromone from the arc. In ACS, ants choose the next city by using the pseudo-random-proportional action choice rule: When located at city I, ant k moves, with probability q0, to city l. It is the best possible move as decided by learned pheromone trails and heuristic information. In ACS, only global best ant is allowed to add pheromone after every iteration. Thus, the update is modified to Here, it is important to note that the trail updateonlyapplies to the arcs of the global-best tour. Aditionally to the global updatingrule,theantsusea local update rule that they apply after having crossed an arc during the tour construction: where is parameter.The effect of this is to make an already chosen arc less desirable. So that exploration of not yet visited arcs is increased. 2. CONCLUSIONS This paper presents an approach for solving Traveling Salesman Problem based on ant colony algorithm. The improved version of ACO algorithmbasedonAntColony System is also presented, which gives a better solution of traveling salesman problem compared to ACO algorithm. REFERENCES [1] Ant colonies for Traveling Salesman Problem. TR/IRIDIA/1996-3 - Marco Dorigo & Luca Gambardella [2] M. Dorigo and T. Stützle. Ant Colony Optimization. MIT press, Cambridge, MA, 2004 [3] M. Dorigo, M. Birattari, T. Stuzle, Ant Colony Optimization, Artificial Ants as a Computational Intelligence Technique, IEEE Computational Intelligence Magazine, November 2006. [4] Y. Zhang, Z-l.Pei, J-h.Yang, Y-c. Liang, An Improved Ant Colony Optimization Algorithm Based onRoute Optimization and Its Applications in Traveling Salesman Problem, IEEE 2007. 1-42441509-8. [5] Swarm Intelligence: Concepts, Models and Application -Hazem Ahmed & Janice I. Glasgow
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