词条 | Ant colony optimization algorithms |
释义 |
}} 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. Artificial Ants stand for multi-agent methods inspired by the behavior of real ants. The pheromone-based communication of biological ants is often the predominant paradigm used.[2] Combinations of Artificial Ants and local search algorithms have become a method of choice for numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. The burgeoning activity in this field has led to conferences dedicated solely to Artificial Ants, and to numerous commercial applications by specialized companies such as AntOptima. As an example, Ant colony optimization[3] is a class of optimization algorithms modeled on the actions of an ant colony. Artificial 'ants' (e.g. simulation agents) locate optimal solutions by moving through a parameter space representing all possible solutions. Real ants lay down pheromones directing each other to resources while exploring their environment. The simulated 'ants' similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions.[4] One variation on this approach is the bees algorithm, which is more analogous to the foraging patterns of the honey bee, another social insect. 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,[5][6] 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. From a broader perspective, ACO performs a model-based search[7] and shares some similarities with estimation of distribution algorithms. OverviewIn the natural world, ants of some species (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 instead to follow the trail, returning and reinforcing it if they eventually find food (see Ant communication). 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. The influence of pheromone evaporation in real ant systems is unclear, but it is very important in artificial systems.[8] The overall result is that when one ant finds a good (i.e., short) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads to many 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. Ambient networks of intelligent objectsNew concepts are required since “intelligence” is no longer centralized but can be found throughout all minuscule objects. Anthropocentric concepts have always led us to the production of IT systems in which data processing, control units and calculating forces are centralized. These centralized units have continually increased their performance and can be compared to the human brain. The model of the brain has become the ultimate vision of computers. Ambient networks of intelligent objects and, sooner or later, a new generation of information systems which are even more diffused and based on nanotechnology, will profoundly change this concept. Small devices that can be compared to insects do not dispose of a high intelligence on their own. Indeed, their intelligence can be classed as fairly limited. It is, for example, impossible to integrate a high performance calculator with the power to solve any kind of mathematical problem into a biochip that is implanted into the human body or integrated in an intelligent tag which is designed to trace commercial articles. However, once those objects are interconnected they dispose of a form of intelligence that can be compared to a colony of ants or bees. In the case of certain problems, this type of intelligence can be superior to the reasoning of a centralized system similar to the brain.[9] Nature has given us several examples of how minuscule organisms, if they all follow the same basic rule, can create a form of collective intelligence on the macroscopic level. Colonies of social insects perfectly illustrate this model which greatly differs from human societies. This model is based on the co-operation of independent units with simple and unpredictable behavior.[10] They move through their surrounding area to carry out certain tasks and only possess a very limited amount of information to do so. A colony of ants, for example, represents numerous qualities that can also be applied to a network of ambient objects. Colonies of ants have a very high capacity to adapt themselves to changes in the environment as well as an enormous strength in dealing with situations where one individual fails to carry out a given task. This kind of flexibility would also be very useful for mobile networks of objects which are perpetually developing. Parcels of information that move from a computer to a digital object behave in the same way as ants would do. They move through the network and pass from one knot to the next with the objective of arriving at their final destination as quickly as possible.[11] Artificial pheromone systemPheromone-based communication is one of the most effective ways of communication which is widely observed in nature. Pheromone is used by social insects such as bees, ants and termites; both for inter-agent and agent-swarm communications. Due to its feasibility; artificial pheromones have been adopted in multi-robot and swarm robotic systems. Pheromone-based communication was implemented by different means such as chemical [12][13] or physical (RFID tags,[14] light,[15][16][17][18] sound[19]) ways. However, those implementations were not able to replicate all the aspects of pheromones as seen in nature. Using projected light was presented in [20] is an experimental setup to study on pheromone-based communication with micro autonomous robots. Another study that proposed a novel pheromone communication method,COSΦ,[21] for a swarm robotic system based on precise and fast visual localization.[22] The system allows to simulate virtually unlimited number of different pheromones and provides the result of their interaction as a gray-scale image on a horizontal LCD screen that the robots move on. In order to demonstrate the pheromone communication method, Colias[23] autonomous micro robot was deployed as the swarm robotic platform. Common extensionsHere are some of the most popular variations of ACO algorithms. Elitist ant systemThe global best solution deposits pheromone on every iteration along with all the other ants. Max-min ant system (MMAS)Added maximum and minimum pheromone amounts [τmax,τmin]. Only global best or iteration best tour deposited pheromone Ant colony systemIt has been presented above.[25] Rank-based ant system (ASrank)All solutions are ranked according to their length. The amount of pheromone deposited is then weighted for each solution, such that solutions with shorter paths deposit more pheromone than the solutions with longer paths. Continuous orthogonal ant colony (COAC)The pheromone deposit mechanism of COAC is to enable ants to search for solutions collaboratively and effectively. By using an orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and efficiently, with enhanced global search capability and accuracy. The orthogonal design method and the adaptive radius adjustment method can also be extended to other optimization algorithms for delivering wider advantages in solving practical problems.[26] Recursive ant colony optimizationIt is a recursive form of ant system which divides the whole search domain into several sub-domains and solves the objective on these subdomains.[27] The results from all the subdomains are compared and the best few of them are promoted for the next level. The subdomains corresponding to the selected results are further subdivided and the process is repeated until an output of desired precision is obtained. This method has been tested on ill-posed geophysical inversion problems and works well.[28] ConvergenceFor some versions of the algorithm, it is possible to prove that it is convergent (i.e., it is able to find the global optimum in finite time). The first evidence of a convergence ant colony algorithm was made in 2000, the graph-based ant system algorithm, and then algorithms for ACS and MMAS. Like most metaheuristics, it is very difficult to estimate the theoretical speed of convergence. In 2004, Zlochin and his colleagues[29] showed that COA-type algorithms could be assimilated methods of stochastic gradient descent, on the cross-entropy and estimation of distribution algorithm. They proposed these metaheuristics as a "research-based model". A performance analysis of continuous ant colony algorithm based on its various parameter suggest its sensitivity of convergence on parameter tuning.[30] Example pseudo-code and formulaEdge selectionAn ant is a simple computational agent in the ant colony optimization algorithm. It iteratively constructs a solution for the problem at hand. The intermediate solutions are referred to as solution states. At each iteration of the algorithm, each ant moves from a state to state , corresponding to a more complete intermediate solution. Thus, each ant computes a set of feasible expansions to its current state in each iteration, and moves to one of these in probability. For ant , the probability of moving from state to state depends on the combination of two values, viz., the attractiveness of the move, as computed by some heuristic indicating the a priori desirability of that move and the trail level of the move, indicating how proficient it has been in the past to make that particular move. The trail level represents a posteriori indication of the desirability of that move. Trails are updated usually when all ants have completed their solution, increasing or decreasing the level of trails corresponding to moves that were part of "good" or "bad" solutions, respectively. In general, the th ant moves from state to state with probability where is the amount of pheromone deposited for transition from state to , 0 ≤ is a parameter to control the influence of , is the desirability of state transition (a priori knowledge, typically , where is the distance) and ≥ 1 is a parameter to control the influence of . and represent the attractiveness and trail level for the other possible state transitions. Pheromone updateWhen all the ants have completed a solution, the trails are updated by where is the amount of pheromone deposited for a state transition , is the pheromone evaporation coefficient and is the amount of pheromone deposited by th ant, typically given for a TSP problem (with moves corresponding to arcs of the graph) by where is the cost of the th ant's tour (typically length) and is a constant. ApplicationsAnt 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[31] 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:
Scheduling problem
Vehicle routing problem
Assignment problem
Set problem
Device sizing problem in nanoelectronics physical design
Antennas optimization and synthesisTo optimize the form of antennas, ant colony algorithms can be used. As example can be considered antennas RFID-tags based on ant colony algorithms (ACO).,[72] loopback and unloopback vibrators 10×10[71] Image processingThe ACO algorithm is used in image processing for image edge detection and edge linking.[73][74]
The graph here is the 2-D image and the ants traverse from one pixel depositing pheromone.The movement of ants from one pixel to another is directed by the local variation of the image's intensity values. This movement causes the highest density of the pheromone to be deposited at the edges. The following are the steps involved in edge detection using ACO:[75][76][77] Step1: Initialization: There are various methods to determine the heuristic matrix. For the below example the heuristic matrix was calculated based on the local statistics: the local statistics at the pixel position (i,j). Where is the image of size ,which is a normalization factor can be calculated using the following functions:The parameter in each of above functions adjusts the functions’ respective shapes. Step 2 Construction process: The ant's movement is based on 4-connected pixels or 8-connected pixels. The probability with which the ant moves is given by the probability equation Step 3 and Step 5 Update process: The pheromone matrix is updated twice. in step 3 the trail of the ant (given by ) is updated where as in step 5 the evaporation rate of the trail is updated which is given by the below equation. , where is the pheromone decay coefficient Step 7 Decision Process: Image Edge detected using ACO:
Other applications
Definition difficultyWith an ACO algorithm, the shortest path in a graph, between two points A and B, is built from a combination of several paths.[101] 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.[102] 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.[103] In their versions for combinatorial problems, they use an iterative construction of solutions.[104] 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",[9] which is a very general framework in which ant colony algorithms fit. Stigmergy algorithmsThere is in practice a large number of algorithms claiming to be "ant colonies", without always sharing the general framework of optimization by canonical ant colonies (COA).[105] In practice, the use of an exchange of information between ants via the environment (a principle called "stigmergy") is deemed enough for an algorithm to belong to the class of ant colony algorithms. This principle has led some authors to create the term "value" to organize methods and behavior based on search of food, sorting larvae, division of labour and cooperative transportation.[106] Related methods
HistoryThe inventors are Frans Moyson and Bernard Manderick. Pioneers of the field include Marco Dorigo, Luca Maria Gambardella.[111] {{image frame|content=ImageSize = width:210 height:300 PlotArea = width:170 height:280 left:40 bottom:10 DateFormat = yyyy Period = from:1985 till:2005 TimeAxis = orientation:vertical ScaleMajor = unit:year increment:5 start:1985 Colors= id:fond value:white #rgb(0.95,0.95,0.98) id:marque value:rgb(1,0,0) id:marque_fond value:rgb(1,0.9,0.9) BackgroundColors = canvas:fond Define $dx = 7 # décalage du texte à droite de la barre Define $dy = -3 # décalage vertical Define $dy2 = 6 # décalage vertical pour double texte PlotData= from:1989 till:1989 shift:($dx,$dy) text:studies of collective behavior from:1991 till:1992 shift:($dx,$dy) text:ant system (AS) from:1995 till:1995 shift:($dx,$dy) text:continuous problem (CACO) from:1996 till:1996 shift:($dx,$dy) text:ant colony system (ACS) from:1996 till:1996 shift:($dx,$dy2) text:max-min ant system (MMAS) from:2000 till:2000 shift:($dx,$dy) text:proof to convergence (GBAS) from:2001 till:2001 shift:($dx,$dy) text:multi-objective algorithm }} Chronology of ant colony optimization algorithms.
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M. Hu, J. ZHANG,J. Xiao and Y. Li, "Protein Folding in Hydrophobic-Polar Lattice Model: A Flexible Ant- Colony Optimization Approach ", Protein and Peptide Letters, Volume 15, Number 5, 2008, Pp. 469-477. 97. ^A. Shmygelska, R. A. Hernández and H. H. Hoos, "An ant colony optimization algorithm for the 2D HP protein folding problem," Proceedings of the 3rd International Workshop on Ant Algorithms/ANTS 2002, Lecture Notes in Computer Science, vol.2463, pp.40-52, 2002. 98. ^{{cite book |author1=M. Nardelli |author2=L. Tedesco |author3=A. Bechini |title= Cross-lattice behavior of general ACO folding for proteins in the HP model |journal= Proc. Of ACM SAC 2013|year=2013|pages=1320–1327 |doi= 10.1145/2480362.2480611|isbn=9781450316569 }} 99. ^L. Wang and Q. D. Wu, "Linear system parameters identification based on ant system algorithm," Proceedings of the IEEE Conference on Control Applications, pp. 401-406, 2001. 100. ^K. C. Abbaspour, R. Schulin, M. T. 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B.|title=On the performance of linkage-tree genetic algorithms for the multidimensional knapsack problem|journal=Neurocomputing|date=25 December 2014|volume=146|pages=17–29|doi=10.1016/j.neucom.2014.04.069}} 111. ^{{cite journal|last = Manderick, Moyson |first = Bernard, Frans |authorlink = Manderick, Bernard, and Moyson, Frans |title = The collective behavior of ants: An example of self-organization in massive parallelism. |publisher = Proceedings of the AAAI Spring Symposium on Parallel Models of Intelligence |place = Stanford |year = 1988}} 112. ^P.-P. Grassé, La reconstruction du nid et les coordinations inter-individuelles chez Belicositermes natalensis et Cubitermes sp. La théorie de la Stigmergie : Essai d’interprétation du comportement des termites constructeurs, Insectes Sociaux, numéro 6, p. 41-80, 1959. 113. ^J.L. Denebourg, J.M. Pasteels et J.C. 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Stützle, Parallelization Strategies for Ant Colony Optimization, Proceedings of PPSN-V, Fifth International Conference on Parallel Problem Solving from Nature, Springer-Verlag, volume 1498, pages 722-731, 1998. 122. ^É. Bonabeau, M. Dorigo et G. Theraulaz, Swarm intelligence, Oxford University Press, 1999. 123. ^M. Dorigo , G. Di Caro et T. Stützle, [https://www.academia.edu/download/30765111/FGCS-Editorial-final.pdf Special issue on "Ant Algorithms]", Future Generation Computer Systems, volume 16, numéro 8, 2000 124. ^W.J. Gutjahr, A graph-based Ant System and its convergence, Future Generation Computer Systems, volume 16, pages 873-888, 2000. 125. ^S. Iredi, D. Merkle et M. Middendorf, [https://link.springer.com/chapter/10.1007/3-540-44719-9_25 Bi-Criterion Optimization with Multi Colony Ant Algorithms], Evolutionary Multi-Criterion Optimization, First International Conference (EMO’01), Zurich, Springer Verlag, pages 359-372, 2001. 126. ^L. Bianchi, L.M. Gambardella et M.Dorigo, An ant colony optimization approach to the probabilistic traveling salesman problem, PPSN-VII, Seventh International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, Springer Verlag, Berlin, Allemagne, 2002. 127. ^M. Dorigo and T. Stützle, Ant Colony Optimization, MIT Press, 2004. 128. ^B. Prabhakar, K. N. Dektar, D. M. Gordon, "The regulation of ant colony foraging activity without spatial information ", PLOS Computational Biology, 2012. URL: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002670 129. ^{{cite journal|last1=Mladineo|first1=Marko|last2=Veza|first2=Ivica|last3=Gjeldum|first3=Nikola|title=Solving partner selection problem in cyber-physical production networks using the HUMANT algorithm|journal=International Journal of Production Research|date=2017|volume=55|issue=9|pages=2506–2521|doi=10.1080/00207543.2016.1234084}} Publications (selected)
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3 : Articles which contain graphical timelines|Nature-inspired metaheuristics|Algorithms |
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