What is a Ant colony optimization algorithm? In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. This algorithm is a member of the ant colony algorithms family, in swarm intelligence methods, and it constitutes some metaheuristic optimizations. Initially proposed by Marco Dorigo in 1992 in his PhD thesis, the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food. The original idea has since diversified to solve a wider class of numerical problems, and as a result, several problems have emerged, drawing on various aspects of the behavior of ants. In the natural world, ants (initially) wander randomly, and upon finding food return to their colony while laying down pheromone trails. If other ants find such a path, they are likely not to keep travelling at random, but to instead follow the trail, returning and reinforcing it if they eventually find food. Over time, however, the pheromone trail starts to evaporate, thus reducing its attractive strength. The more time it takes for an ant to travel down the path and back again, the more time the pheromones have to evaporate. A short path, by comparison, gets marched over more frequently, and thus the pheromone density becomes higher on shorter paths than longer ones. Pheromone evaporation also has the advantage of avoiding the convergence to a locally optimal solution. If there were no evaporation at all, the paths chosen by the first ants would tend to be excessively attractive to the following ones. In that case, the exploration of the solution space would be constrained. Thus, when one ant finds a conducive and short path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads to all the ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with simulated ants walking around the graph representing the problem to solve. APPLICATIONS: Ant colony optimization algorithms have been applied to many combinatorial optimization problems, ranging from quadratic assignment to protein folding or routing vehicles and a lot of derived methods have been adapted to dynamic problems in real variables, stochastic problems, multi-targets and parallel implementations. It has also been used to produce near-optimal solutions to the travelling salesman problem. They have an advantage over simulated annealing and genetic algorithm approaches of similar problems when the graph may change dynamically; the ant colony algorithm can be run continuously and adapt to changes in real time. This is of interest in network routing and urban transportation systems. The first ACO algorithm was called the Ant system [8] and it was aimed to solve the travelling salesman problem, in which the goal is to find the shortest round-trip to link a series of cities. The general algorithm is relatively simple and based on a set of ants, each making one of the possible round-trips along the cities. At each stage, the ant chooses to move from one city to another according to some rules: 1. It must visit each city exactly once; 2. A distant city has less chance of being chosen (the visibility); 3. The more intense the pheromone trail laid out on an edge between two cities, the greater the probability that that edge will be chosen; 4. Having completed its journey, the ant deposits more pheromones on all edges it traversed, if the journey is short; 5. After each iteration, trails of pheromones evaporate. With an ACO algorithm, the shortest path in a graph, between two points A and B, is built from a combination of several paths. It is not easy to give a precise definition of what algorithm is or is not an ant colony, because the definition may vary according to the authors and uses. Broadly speaking, ant colony algorithms are regarded as populated metaheuristics with each solution represented by an ant moving in the search space. Ants mark the best solutions and take account of previous markings to optimize their search. They can be seen as probabilistic multi-agent algorithms using a probability distribution to make the transition between each iteration. In their versions for combinatorial problems, they use an iterative construction of solutions. According to some authors, the thing which distinguishes ACO algorithms from other relatives (such as algorithms to estimate the distribution or particle swarm optimization) is precisely their constructive aspect. In combinatorial problems, it is possible that the best solution eventually be found, even though no ant would prove effective. Thus, in the example of the Travelling salesman problem, it is not necessary that an ant actually travels the shortest route: the shortest route can be built from the strongest segments of the best solutions. However, this definition can be problematic in the case of problems in real variables, where no structure of neighbours exists. The collective behaviour of social insects remains a source of inspiration for researchers. The wide variety of algorithms (for optimization or not) seeking self-organization in biological systems has led to the concept of swarm intelligence, which is a very general framework in which ant colony algorithms fit. MATHEMATICS Take a look at picture 4. To adapt the ACO algorithm to scheduling problems, the following parameters have been defined: Number of agents (ants) in the colony; Vapouring factor of pheromone (from the range (0; 1)); The process of choosing these parameters is important and should consider that: For too big number of agents, the individual cycle of algorithm can last quite long, and the values saved in the table (“levels of pheromone”) as a result of addition will determine relatively weak solutions. On the other hand, when the number of agents is too small, most of paths will not be covered and as a result, the best solution can long be uncovered. The situation is similar for the vapouring factor: Too small value will cause that ants will quickly “forget” good solutions and as a result it can quickly come to so called stagnation (the algorithm will stop at one solution, which doesn’t have to be the best one). Too big value of this factor will make ants don’t stop analyze “weak” solutions; furthermore, the new solutions may not be pushed, if time, which has passed since the last solution found will be long enough (it is the values of pheromone saved in the table will be too big). The ACO algorithm defines two more parameters, which let you balance between: α – the amount of pheromone on the path; β – “quality” of the next step; These parameters are chosen for specific task. This way, for parameters: α > β there is bigger influence on the choice of path, which is more often exploited, α < β there is bigger influence on the choice of path, which offers better solution, α = β there is balanced dependency between quality of the path and degree of its exploitation, α = 0 there is a heuristics based only on the quality of passage between consecutive points (ignorance of the level of pheromone on the path), β = 0 there is a heuristics based only on the amount of pheromone (it is the factor of path attendance), α = β = 0 we’ll get the algorithm making division evenly and independently of the amount of pheromone or the quality of solution. Having given the set of neighborhood N of the given point i, amount of pheromone on the path τ and the quality of passage from point i to point j as an element of the table η you can present the probability of passage from point i to j as [6,7]: SOURCES: A. Colorni, M. Dorigo et V. Maniezzo, Distributed Optimization by Ant Colonies, actes de la première conférence européenne sur la vie artificielle, Paris, France, Elsevier Publishing, 134-142, 1991. a b M. Dorigo, Optimization, Learning and Natural Algorithms, PhD thesis, Politecnico di Milano, Italy, 1992.a b T. Stützle et H.H. Hoos, MAX MIN Ant System, Future Generation Computer Systems, volume 16, pages 889-914, 2000 a b M. Dorigo et L.M. Gambardella, Ant Colony System : A Cooperative Learning Approach to the Traveling Salesman Problem, IEEE Transactions on Evolutionary Computation, volume 1, numéro 1, pages 53-66, 1997.X Hu, J Zhang, and Y Li (2008). Orthogonal methods based ant colony search for solving continuous optimization problems. Journal of Computer Science and Technology, 23(1), pp.2-18. intechopen/books/ant-colony-optimization-techniques-and-applications/scheduling-in-manufacturing-systems-ant-colony-approach
Posted on: Tue, 14 Oct 2014 14:37:45 +0000
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