Ant colony optimization algorithms

4209:. 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 394:

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 great 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 node to the next with the objective of arriving at their final destination as quickly as possible.

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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 designed to trace commercial articles. However, once those objects are interconnected they develop 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.

3431:{\displaystyle {\begin{aligned}Vc(I_{i,j})=&f\left(\left\vert I_{(i-2,j-1)}-I_{(i+2,j+1)}\right\vert +\left\vert I_{(i-2,j+1)}-I_{(i+2,j-1)}\right\vert \right.\\&+\left\vert I_{(i-1,j-2)}-I_{(i+1,j+2)}\right\vert +\left\vert I_{(i-1,j-1)}-I_{(i+1,j+1)}\right\vert \\&+\left\vert I_{(i-1,j)}-I_{(i+1,j)}\right\vert +\left\vert I_{(i-1,j+1)}-I_{(i-1,j-1)}\right\vert \\&+\left.\left\vert I_{(i-1,j+2)}-I_{(i-1,j-2)}\right\vert +\left\vert I_{(i,j-1)}-I_{(i,j+1)}\right\vert \right)\end{aligned}}} 1896:, it is very difficult to estimate the theoretical speed of convergence. A performance analysis of a continuous ant colony algorithm with respect to its various parameters (edge selection strategy, distance measure metric, and pheromone evaporation rate) showed that its performance and rate of convergence are sensitive to the chosen parameter values, and especially to the value of the pheromone evaporation rate. In 2004, Zlochin and his colleagues showed that ACO-type algorithms are closely related to 7500: 8153: 364:

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.

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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,

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This algorithm controls the maximum and minimum pheromone amounts on each trail. Only the global best tour or the iteration best tour are allowed to add pheromone to its trail. To avoid stagnation of the search algorithm, the range of possible pheromone amounts on each trail is limited to an interval

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Using projected light was presented in a 2007 IEEE paper by Garnier, Simon, et al. as an experimental setup to study pheromone-based communication with micro autonomous robots. Another study presented a system in which pheromones were implemented via a horizontal LCD screen on which the robots moved,

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of intelligent objects and, sooner or later, a new generation of information systems that are even more diffused and based on nanotechnology, will profoundly change this concept. Small devices that can be compared to insects do not possess a high intelligence on their own. Indeed, their intelligence

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Similar to simulated annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest fitness of those generated. To

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All solutions are ranked according to their length. Only a fixed number of the best ants in this iteration are allowed to update their trials. The amount of pheromone deposited is weighted for each solution, such that solutions with shorter paths deposit more pheromone than the solutions with longer

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on a weighted graph. In the first step of each iteration, each ant stochastically constructs a solution, i.e. the order in which the edges in the graph should be followed. In the second step, the paths found by the different ants are compared. The last step consists of updating the pheromone levels

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on the macroscopic level. Colonies of social insects perfectly illustrate this model which greatly differs from human societies. This model is based on the cooperation of independent units with simple and unpredictable behavior. They move through their surrounding area to carry out certain tasks and

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New concepts are required since “intelligence” is no longer centralized but can be found throughout all minuscule objects. Anthropocentric concepts have been known to lead to the production of IT systems in which data processing, control units and calculating power are centralized. These centralized

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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 and shares some similarities

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It is a recursive form of ant system which divides the whole search domain into several sub-domains and solves the objective on these subdomains. 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

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In this algorithm, the global best solution deposits pheromone on its trail after every iteration (even if this trail has not been revisited), along with all the other ants. The elitist strategy has as its objective directing the search of all ants to construct a solution to contain links of the

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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, is marched over more frequently, and thus the

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For 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 convergence for an ant colony algorithm was made in 2000, the graph-based ant system algorithm, and later on for the ACS and MMAS

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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

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When a colony of ants is confronted with the choice of reaching their food via two different routes of which one is much shorter than the other, their choice is entirely random. However, those who use the shorter route reach the food faster and therefore go back and forth more often between the

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Pheromone-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

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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.

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A related global optimization technique which traverses the search space by generating neighboring solutions of the current solution. A superior neighbor is always accepted. An inferior neighbor is accepted probabilistically based on the difference in quality and a temperature parameter. The

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The first ACO algorithm was called the ant system 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

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Each ant needs to construct a solution to move through the graph. To select the next edge in its tour, an ant will consider the length of each edge available from its current position, as well as the corresponding pheromone level. At each step of the algorithm, each ant moves from a state

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adopted in multi-robot and swarm robotic systems. Pheromone-based communication was implemented by different means such as chemical or physical (RFID tags, light, sound) ways. However, those implementations were not able to replicate all the aspects of pheromones as seen in nature.

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prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space.

4230:") 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. 4259:

that substitutes traditional reproduction operators by model-guided operators. Such models are learned from the population by employing machine learning techniques and represented as probabilistic graphical models, from which new solutions can be sampled or generated from

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There 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. In practice, the use of an exchange of information between ants via the environment (a principle called

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In the ant colony optimization algorithms, an artificial ant is a simple computational agent that searches for good solutions to a given optimization problem. To apply an ant colony algorithm, the optimization problem needs to be converted into the problem of finding the

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to direct 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. One variation on this approach is

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An ant colony system (ACS) with communication strategies is developed. The artificial ants are partitioned into several groups. Seven communication methods for updating the pheromone level between groups in ACS are proposed and work on the traveling salesman problem.

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K. Saleem, N. Fisal, M. A. Baharudin, A. A. Ahmed, S. Hafizah and S. Kamilah, "Ant colony inspired self-optimized routing protocol based on cross layer architecture for wireless sensor networks", WSEAS Trans. Commun., vol. 9, no. 10, pp. 669–678, 2010.

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Visualization of the ant colony algorithm applied to the travelling salesman problem. The green lines are the paths chosen by each ant. The blue lines are the paths it may take at each point. When the ant finishes, the pheromone levels are represented in

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L.M. Gambardella and M. Dorigo, "Ant-Q: a reinforcement learning approach to the traveling salesman problem", Proceedings of ML-95, Twelfth International Conference on Machine Learning, A. Prieditis and S. Russell (Eds.), Morgan Kaufmann, pp. 252–260,

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Trails are usually updated 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. An example of a global pheromone updating rule is

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Gupta, D.K.; Arora, Y.; Singh, U.K.; Gupta, J.P., "Recursive Ant Colony Optimization for estimation of parameters of a function", 1st International Conference on Recent Advances in Information Technology (RAIT), vol., no., pp. 448-454, 15–17 March

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2012, Prabhakar and colleagues publish research relating to the operation of individual ants communicating in tandem without pheromones, mirroring the principles of computer network organization. The communication model has been compared to the

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Focuses on combining machine learning with optimization, by adding an internal feedback loop to self-tune the free parameters of an algorithm to the characteristics of the problem, of the instance, and of the local situation around the current

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L.M. Gambardella, E. Taillard, G. Agazzi, "MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows", In D. Corne, M. Dorigo and F. Glover, editors, New Ideas in Optimization, McGraw-Hill, London, UK, pp. 63-76,

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W. N. Chen and J. ZHANG "Ant Colony Optimization Approach to Grid Workflow Scheduling Problem with Various QoS Requirements", IEEE Transactions on Systems, Man, and Cybernetics--Part C: Applications and Reviews, Vol. 31, No. 1,pp.29-43,Jan

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These maintain a pool of solutions rather than just one. The process of finding superior solutions mimics that of evolution, with solutions being combined or mutated to alter the pool of solutions, with solutions of inferior quality being

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A. V. Donati, V. Darley, B. Ramachandran, "An Ant-Bidding Algorithm for Multistage Flowshop Scheduling Problem: Optimization and Phase Transitions", book chapter in Advances in Metaheuristics for Hard Optimization, Springer,

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A. Bauer, B. Bullnheimer, R. F. Hartl and C. Strauss, "Minimizing total tardiness on a single machine using ant colony optimization," Central European Journal for Operations Research and Economics, vol.8, no.2, pp.125-141,

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Marcus Randall, Andrew Lewis, Amir Galehdar, David Thiel. Using Ant Colony Optimisation to Improve the Efficiency of Small Meander Line RFID Antennas.// In 3rd IEEE International e-Science and Grid Computing Conference

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M, den Bseten, T. Stützle and M. Dorigo, "Ant colony optimization for the total weighted tardiness problem," Proceedings of PPSN-VI, Sixth International Conference on Parallel Problem Solving from Nature, vol. 1917 of

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Mohd Murtadha Mohamad,"Articulated Robots Motion Planning Using Foraging Ant Strategy", Journal of Information Technology - Special Issues in Artificial Intelligence, Vol. 20, No. 4 pp. 163–181, December 2008,

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Once the K ants have moved a fixed distance L for N iteration, the decision whether it is an edge or not is based on the threshold T on the pheromone matrix τ. Threshold for the below example is calculated based on

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D. Merkle, M. Middendorf and H. Schmeck, "Ant colony optimization for resource-constrained project scheduling," Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2000), pp.893-900,

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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 be solved.

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K. Saleem and N. Fisal, "Enhanced Ant Colony algorithm for self-optimized data assured routing in wireless sensor networks", Networks (ICON) 2012 18th IEEE International Conference on, pp. 422–427.

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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

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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.

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To 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), loopback and unloopback vibrators 10×10

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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

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An agent-based probabilistic global search and optimization technique best suited to problems where the objective function can be decomposed into multiple independent partial-functions.

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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.

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L.M. Gambardella, M. Dorigo, "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem", INFORMS Journal on Computing, vol.12(3), pp. 237-255, 2000.

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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

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Martins, Jean P.; Fonseca, Carlos M.; Delbem, Alexandre C. B. (25 December 2014). "On the performance of linkage-tree genetic algorithms for the multidimensional knapsack problem".

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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 "

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G. D. Caro and M. Dorigo, "Extending AntNet for best-effort quality-of-service routing," Proceedings of the First International Workshop on Ant Colony Optimization (ANTS’98), 1998.

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trails. If other ants find such a path, they are likely to stop travelling at random and instead follow the trail, returning and reinforcing it if they eventually find food (see

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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

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in his doctoral thesis (which was published in 1992). A technical report extracted from the thesis and co-authored by V. Maniezzo and A. Colorni was published five years later;

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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.

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Jevtić, A.; Quintanilla-Dominguez, J.; Cortina-Januchs, M.G.; Andina, D. (2009). "Edge detection using ant colony search algorithm and multiscale contrast enhancement".

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Ermolaev S.Y., Slyusar V.I. Antenna synthesis based on the ant colony optimization algorithm.// Proc. ICATT’2009, Lviv, Ukraine 6 - 9 Octobre, 2009. - Pages 298 - 300

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J. M. Belenguer, and E. Benavent, "A cutting plane algorithm for capacitated arc routing problem," Computers & Operations Research, vol.30, no.5, pp.705-728, 2003.

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B. Prabhakar, K. N. Dektar, D. M. Gordon, "The regulation of ant colony foraging activity without spatial information ", PLOS Computational Biology, 2012. URL:

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Han, Z., Wang, Y. & Tian, D. Ant colony optimization for assembly sequence planning based on parameters optimization. Front. Mech. Eng. 16, 393–409 (2021).

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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.

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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

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Mladineo, Marko; Veza, Ivica; Gjeldum, Nikola (2017). "Solving partner selection problem in cyber-physical production networks using the HUMANT algorithm".

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Ant colony optimization (ACO) based optimization of 45 nm CMOS-based sense amplifier circuit could converge to optimal solutions in very minimal time.

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The edge selection is biased towards exploitation (i.e. favoring the probability of selecting the shortest edges with a large amount of pheromone);

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WISDOM OF THE MANY : how to create self -organisation and how to use collective... intelligence in companies and in society from mana

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The more intense the pheromone trail laid out on an edge between two cities, the greater the probability that that edge will be chosen;

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While building a solution, ants change the pheromone level of the edges they are selecting by applying a local pheromone updating rule;

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At the end of each iteration, only the best ant is allowed to update the trails by applying a modified global pheromone updating rule.

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Ho, Sin C.; Haugland, Dag (2002). "A Tabu Search Heuristic for the Vehicle Routing Problem with Time Windows and Split Deliveries".

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General purpose optimization software based on ant colony optimization (Matlab, Excel, VBA, C/C++, R, C#, Java, Fortran and Python)

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M. Nardelli; L. Tedesco; A. Bechini (March 2013). "Cross-lattice behavior of general ACO folding for proteins in the HP model".

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Do ants need to estimate the geometrical properties of trail bifurcations to find an efficient route? A swarm robotics test bed.

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Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times

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The ant system is the first ACO algorithm. This algorithm corresponds to the one presented above. It was developed by Dorigo.

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and a lot of derived methods have been adapted to dynamic problems in real variables, stochastic problems, multi-targets and

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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

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are initialized with a random value. The major challenge in the initialization process is determining the heuristic matrix.

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Image edge detected using ACO: The images below are generated using different functions given by the equation (1) to (4).

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X Hu, J Zhang, and Y Li (2008). Orthogonal methods based ant colony search for solving continuous optimization problems.

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Recursive ant colony optimization: a new technique for the estimation of function parameters from geophysical field data

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Nature offers several examples of how minuscule organisms, if they all follow the same basic rule, can create a form of

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round-trips along the cities. At each stage, the ant chooses to move from one city to another according to some rules:

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Having completed its journey, the ant deposits more pheromones on all edges it traversed, if the journey is short;

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of feasible expansions to its current state in each iteration, and moves to one of these in probability. For ant

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2017, successful integration of the multi-criteria decision-making method PROMETHEE into the ACO algorithm (

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Visualization of Traveling Salesman solved by ant system with numerous options and parameters (Java Applet)

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Ant colony optimization (ACO) based reversible circuit synthesis could improve efficiency significantly.

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Hierarchical Bayesian optimization algorithm : toward a new generation of evolutionary algorithms

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An Intelligent Testing System Embedded with an Ant Colony Optimization Based Test Composition Method

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Investigation of cue-based aggregation in static and dynamic environments with a mobile robot swarm

4290: 4202: 3894: 3840: 2347: 147: 6480:"An ant colony optimisation algorithm for the 2D and 3D hydrophobic polar protein folding problem" 5946:

2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)

5801:," Applications of Evolutionary Computing: Proceedings of Evo Workshops, vol.2037, pp.60-69, 2001. 5490: 5324: 4951: 4679:

Birattari, M.; Pellegrini, P.; Dorigo, M. (2007). "On the Invariance of Ant Colony Optimization".

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of the move, indicating how proficient it has been in the past to make that particular move. The

390: 274: 269:

algorithms have become a preferred method for numerous optimization tasks involving some sort of

98: 7123: 6768:, Actes de AAAI Spring Symposium on Parallel Models of Intelligence, Stanford, Californie, 1988. 6386:

Protein Folding in Hydrophobic-Polar Lattice Model: A Flexible Ant- Colony Optimization Approach

6262: 6105:"A Rule-Based Model for Bankruptcy Prediction Based on an Improved Genetic Ant Colony Algorithm" 4270:

temperature parameter is modified as the algorithm progresses to alter the nature of the search.

3930:) is updated where as in step 5 the evaporation rate of the trail is updated which is given by: 1435: 1290: 1260: 1230: 1095: 1065: 975: 687: 650: 572: 8460: 8120: 7993: 7935: 7920: 7810: 7688: 7337: 7314: 7281: 7042: 6213: 6161: 5839:," Proceedings of the 2001 Argentinian Congress on Computer Science, vol.2, pp.1027-1040, 2001. 5678: 5552:

A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows

5518: 5485: 4649: 4565: 4420:

1994, Appleby and Steward of British Telecommunications Plc published the first application to

4256: 3443: 253:

technique for solving computational problems that can be reduced to finding good paths through

164: 7199: 7095: 6766:

The collective behaviour of Ants : an Example of Self-Organization in Massive Parallelism

5167: 3816: 1927:: The ants prefer the smaller drop of honey over the more abundant, but less nutritious, sugar 1152: 516: 8269: 8174: 7824: 7790: 7693: 7635: 7516: 7322: 7302: 7102: 6933: 5785: 4964: 4884: 4856: 4824: 4585: 4139: 4136: 4109: 3856: 1045: 417: 5850:

Ordinary Kriging Metamodel-Assisted Ant Colony Algorithm for Fast Analog Design Optimization

5314:," Proceedings of ANTS 2002, vol. 2463 of Lecture Notes in Computer Science, pp.14-27, 2002. 5055: 4371: 2045:

Multistage flowshop scheduling problem (MFSP) with sequence dependent setup/changeover times

1210: 407:

with the robots having downward facing light sensors to register the patterns beneath them.

8480: 8445: 8283: 8230: 8137: 7871: 7698: 7610: 6918: 6227:

Optimizing Discounted Cash Flows in Project Scheduling--An Ant Colony Optimization Approach

6142:", IEEE Transactions on Evolutionary Computation, volume 11, number 5, pages 651—665, 2007. 4596: 4537: 4484: 4023: 2389: 2021: 1901: 1810:

In the ant colony system algorithm, the original ant system was modified in three aspects:

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T. Stützle, "An ant approach to the flow shop problem," Technical report AIDA-97-07, 1997.

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Ant Colony System : A Cooperative Learning Approach to the Traveling Salesman Problem

4749: 4747: 295:. Artificial 'ants' (e.g. simulation agents) locate optimal solutions by moving through a 8: 8490: 8465: 8455: 8045: 7940: 7805: 7758: 7748: 7600: 7588: 7401: 7384: 7289: 6359: 6248: 6139: 5737: 5312:

ACO applied to group shop scheduling: a case study on intensification and diversification

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2000, special issue of the Future Generation Computer Systems journal on ant algorithms

4470:

1999, Bonabeau, Dorigo and Theraulaz publish a book dealing mainly with artificial ants

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represent the trail level and attractiveness for the other possible state transitions.

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Portfolio Optimization Using Ant Colony Method a Case Study on Tehran Stock Exchange.

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1997, Dorigo and Gambardella proposed ant colony system hybridized with local search;

4239: 2129: 2123: 2042:

Single-machine total tardiness problem with sequence dependent setup times (SMTTPDST)

1956: 368: 7047:

Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem

6695: 6328: 6311: 6089: 6027: 5539:

Solving the pickup and delivery problem with time windows using reactive tabu search

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An ant colony optimization approach to the probabilistic traveling salesman problem

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A swarm-based optimization algorithm based on natural water drops flowing in rivers

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Ant Colony Optimization: Artificial Ants as a Computational Intelligence Technique

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An ant algorithm with a new pheromone evaluation rule for total tardiness problems

4410:

1989, implementation of a model of behavior for food by Ebling and his colleagues;

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2004, Dorigo and Stützle publish the Ant Colony Optimization book with MIT Press

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An ant colony optimization algorithm for the redundancy allocation problem (RAP)

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Stützle, Thomas (1997). "MAX-MIN Ant System for Quadratic Assignment Problems".

3891:

The pheromone matrix is updated twice. in step 3 the trail of the ant (given by

3853:. The probability with which the ant moves is given by the probability equation 2082:

Vehicle routing problem with time windows and multiple service workers (VRPTWMS)

1947:

implementations. It has also been used to produce near-optimal solutions to the

1908:. They proposed an umbrella term "Model-based search" to describe this class of 8475: 8409: 8386: 8220: 8215: 8198: 8191: 8084: 7767: 7652: 7539: 7473: 7444: 6976:

http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002670

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Jevtić, A.; Melgar, I.; Andina, D. (2009). "Ant based edge linking algorithm".

6009: 5919:

Ant colony system with extremal dynamics for point matching and pose estimation

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A. V. Donati, R. Montemanni, N. Casagrande, A. E. Rizzoli, L. M. Gambardella, "

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Alice in pheromone land: An experimental setup for the study of ant-like robots

4619: 4210: 4191: 4114: 2191: 305: 8152: 7226:

University of Kaiserslautern, Germany, AG Wehn: Ant Colony Optimization Applet

6466:

Estimating unsaturated soil hydraulic parameters using ant colony optimization

6375:", IEEE Transactions on Power Electronic. Vol. 24, No.1, pp.147-162, Jan 2009. 6373:

Extended Ant Colony Optimization Algorithm for Power Electronic Circuit Design

5823: 5799:

Colored Ant System and local search to design local telecommunication networks

1843:

to force a higher exploration of solutions. The trails are reinitialized to τ

8510: 8349: 8091: 8062: 8040: 7925: 7909: 6579:

Ant Routing, Searching and Topology Estimation Algorithms for Ad Hoc Networks

6337: 6251:", IEEE Transactions on Multimedia, vol. 10, no. 7, pp. 1356--1365 - nov 2008 5953: 5449:(2002). "The periodic vehicle routing problem with intermediate facilities". 4721:

Ant Colony Optimization by Marco Dorigo and Thomas Stützle, MIT Press, 2004.

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1997, Schoonderwoerd and his colleagues published an improved application to

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Ant behavior was the inspiration for the metaheuristic optimization technique

7038:", IEEE Transactions on Systems, Man, and Cybernetics–Part B, 26 (1): 29–41. 6615: 6420: 6138:

D. Martens, M. De Backer, R. Haesen, J. Vanthienen, M. Snoeck, B. Baesens, "

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Get in touch: cooperative decision making based on robot-to-robot collisions

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Reversible Circuit Synthesis Using ACO and SA based Quinne-McCluskey Method

5208:

D. Martens, M. De Backer, R. Haesen, J. Vanthienen, M. Snoeck, B. Baesens,

5017:

Cue-based aggregation with a mobile robot swarm: a novel fuzzy-based method

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Thierens, Dirk (11 September 2010). "The Linkage Tree Genetic Algorithm".

6413:

SAC '13: Proceedings of the 28th Annual ACM Symposium on Applied Computing

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An ant colony optimization algorithm for the 2D HP protein folding problem

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Imitation of honeybee aggregation with collective behavior of swarm robots

4952:

Artificial pheromone system using rfid for navigation of autonomous robots

438:

generateSolutions() daemonActions() pheromoneUpdate()

8450: 8399: 8240: 8096: 7950: 7332: 7149:

Advances in Bio-inspired Computing for Combinatorial Optimization Problem

7046: 5327:," Journal of the Operational Research Society, vol.53, pp.895-906, 2002. 5103: 4532:

2004, Zlochin and Dorigo show that some algorithms are equivalent to the

4280: 4217:", which is a very general framework in which ant colony algorithms fit. 4198: 4128: 4009:{\displaystyle \tau _{new}\leftarrow (1-\psi )\tau _{old}+\psi \tau _{0}} 3847: 493:, corresponding to a more complete intermediate solution. Thus, each ant 258: 250: 7209: 6796:, Proceedings of the SCS Multiconference on Distributed Simulation, 1989 6249:

Image Retrieval over Networks : Active Learning using Ant Algorithm

5824:

S. Fidanova, "ACO algorithm for MKP using various heuristic information"

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1998, Dorigo launches first conference dedicated to the ACO algorithms;

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Ant colony optimization algorithms for solving transportation problems

6175:

Two ant colony algorithms for best-effort routing in datagram networks

5987:"Edge Detection of an Image based on Ant ColonyOptimization Technique" 5579:"The simulated trading heuristic for solving vehicle routing problems" 4519:

2002, first applications in the design of schedule, Bayesian networks;

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Time Dependent Vehicle Routing Problem with a Multi Ant Colony System

4913:

A cellular automata ant memory model of foraging in a swarm of robots

4811:

Marco Dorigo and Thomas Stützle, Ant Colony Optimization, p.12. 2004.

4375: 4227: 4206: 3833:

in each of above functions adjusts the functions’ respective shapes.

718:

represents a posteriori indication of the desirability of that move.

353: 309: 300: 288: 242: 6264:

Optimization of energy supply networks using ant colony optimization

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Model-based search for combinatorial optimization: A critical survey

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An Ant Foraging Model Implemented on the Time Warp Operating System

6614:

Pelikan, Martin; Goldberg, David E.; Cantú-Paz, Erick (July 1999).

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2002, Bianchi and her colleagues suggested the first algorithm for

4379: 315:

This algorithm is a member of the ant colony algorithms family, in

7242:

Ant Colony Optimization Algorithm Implementation (Python Notebook)

6563:

ACO algorithms with guaranteed convergence to the optimal solution

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2009 IEEE International Conference on Systems, Man and Cybernetics

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The following are the steps involved in edge detection using ACO:

2079:

Time dependent vehicle routing problem with time windows (TDVRPTW)

352:, and upon finding food return to their colony while laying down 8035: 7672: 6792:

M. Ebling, M. Di Loreto, M. Presley, F. Wieland, et D. Jefferson,

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An ejection chain approach for the generalized assignment problem

5708:

Adaptive search heuristics for the generalized assignment problem

5141: 4407:, which will give the idea of ant colony optimization algorithms; 4334:

A method that make use of clustering approach, extending the ACO.

3567:{\displaystyle f(x)=\lambda x^{2},\quad {\text{for x ≥ 0; (2)}}} 2178:

Unloopback vibrators 10×10, synthesized by means of ACO algorithm

1936: 278: 7219: 5188:

ACO for Continuous Function Optimization: A Performance Analysis

5097: 5095: 4179: 2174: 2166: 1983:

A distant city has less chance of being chosen (the visibility);

1920: 1794:

Here are some of the most popular variations of ACO algorithms.

8069: 7049:". IEEE Transactions on Evolutionary Computation, 1 (1): 53–66. 6907:, Future Generation Computer Systems, volume 16, numéro 8, 2000 6410: 6046: 5812:

Metaheuristics for the edge-weighted k-cardinality tree problem

4652:(1997). "Learning Approach to the Traveling Salesman Problem". 4188: 2680:{\displaystyle Z=\sum _{i=1:M_{1}}\sum _{j=1:M_{2}}Vc(I_{i,j})} 2170:

Loopback vibrators 10×10, synthesized by means of ACO algorithm

1002:

is the amount of pheromone deposited for transition from state

349: 4355: 348:

In the natural world, ants of some species (initially) wander

213: 8311: 6852:, Adaptive Behaviour, volume 5, numéro 2, pages 169-207, 1997 5786:

An ant-based framework for very strongly constrained problems

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COSΦ: artificial pheromone system for robotic swarms research

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1989, the work of Goss, Aron, Deneubourg and Pasteels on the

3850: 3843: 3512:{\displaystyle f(x)=\lambda x,\quad {\text{for x ≥ 0; (1)}}} 1931:

Ant colony optimization algorithms have been applied to many

6752:

Probabilistic Behaviour in Ants : a Strategy of Errors?

4767: 4765: 4763: 4620:

Monmarché Nicolas; Guinand Frédéric; Siarry Patrick (2010).

4506: 1462:

is the amount of pheromone deposited for a state transition

8057: 7978: 6846:

R. Schoonderwoerd, O. Holland, J. Bruten et L. Rothkrantz,

4502: 4390: 3796: 3675: 3263: 2911: 2505:{\displaystyle \eta _{(i,j)}={\tfrac {1}{Z}}*Vc*I_{(i,j)},} 1702: 1591:

problem (with moves corresponding to arcs of the graph) by

328: 7036:

Ant System: Optimization by a Colony of Cooperating Agents

6934:

Bi-Criterion Optimization with Multi Colony Ant Algorithms

6134: 6132: 6064:

2009 35th Annual Conference of IEEE Industrial Electronics

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Ant system: optimization by a colony of cooperating agents

4787:

Fladerer, Johannes-Paul; Kurzmann, Ernst (November 2019).

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of the move, as computed by some heuristic indicating the

375: 308:, which is more analogous to the foraging patterns of the 6201:

An ant colony algorithm for classification rule discovery

4760: 4678: 4099:

ACO has also proven effective in edge linking algorithms.

2073:

Vehicle routing problem with pick-up and delivery (VRPPD)

262: 6758: 6613: 6190:," Machine Learning, volume 82, number 1, pp. 1-42, 2011 5576: 2190:

The ACO algorithm is used in image processing for image

2149:

Device sizing problem in nanoelectronics physical design

2135:

Weight constrained graph tree partition problem (WCGTPP)

2033:

Single machine total weighted tardiness problem (SMTWTP)

299:

representing all possible solutions. Real ants lay down

7103:

Ant colony optimization: Introduction and recent trends

6203:," Data Mining: A heuristic Approach, pp.191-209, 2002. 6129: 5110: 2036:

Resource-constrained project scheduling problem (RCPSP)

7068:

Swarm Intelligence: From Natural to Artificial Systems

7052:

M. Dorigo, G. Di Caro & L. M. Gambardella, 1999. "

6876:

Parallelization Strategies for Ant Colony Optimization

6849:

Ant-based load balancing in telecommunication networks

6777:

S. Goss, S. Aron, J.-L. Deneubourg et J.-M. Pasteels,

5710:," Mathware & soft computing, vol.9, no.2-3, 2002. 5177:," Near Surface Geophysics, vol. 11, no. 3, pp.325-339 5032:." 2007 IEEE Swarm Intelligence Symposium. IEEE, 2007. 2454: 2322: 2161: 1693: 1677: 1664: 1654: 6783:, Naturwissenschaften, volume 76, pages 579-581, 1989 6254: 6214:

Data mining with an ant colony optimization algorithm

5837:

An ant system for the maximum independent set problem

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After each iteration, trails of pheromones evaporate.

1772: 1752: 1725: 1600: 1573: 1535: 1515: 1491: 1468: 1438: 1335: 1293: 1263: 1233: 1213: 1193: 1155: 1128: 1098: 1068: 1048: 1028: 1008: 978: 790: 767: 747: 727: 690: 653: 630: 610: 575: 555: 519: 499: 479: 459: 284:

As an example, ant colony optimization is a class of

7789: 6708: 6188:

Editorial Survey: Swarm Intelligence for Data Mining

6162:

AntNet: a mobile agents approach to adaptive routing

5934:", Soft Computing, vol. 10, no.7, pp. 623-628, 2006. 5814:," Technical Report TR/IRIDIA/2003-02, IRIDIA, 2003. 5694:

MAX-MIN Ant System for Quadratic Assignment Problems

4915:." Applied Mathematical Modelling 47, 2017: 551-572. 4771:

M. Zlochin, M. Birattari, N. Meuleau, et M. Dorigo,

4501:

2001, the first use of COA algorithms by companies (

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Gupta, D.K.; Gupta, J.P.; Arora, Y.; Shankar, U., "

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2016, first application to peptide sequence design.

4512:2001, Iredi and his colleagues published the first 8496:Task allocation and partitioning of social insects 6061: 5930:H. Nezamabadi-pour, S. Saryazdi, and E. Rashedi, " 5835:G. Leguizamon, Z. Michalewicz and Martin Schutz, " 4366:Chronology of ant colony optimization algorithms. 4064: 4032: 4008: 3922: 3878: 3825: 3802: 3681: 3566: 3511: 3461: 3430: 2679: 2567: 2527: 2504: 2410: 2375: 2336: 2270: 2226: 1778: 1758: 1738: 1708: 1579: 1559: 1521: 1497: 1477: 1454: 1421: 1309: 1279: 1249: 1219: 1199: 1179: 1137: 1114: 1084: 1054: 1034: 1014: 994: 961: 773: 753: 733: 706: 669: 636: 616: 596: 561: 541: 505: 485: 465: 6749:J.L. Denebourg, J.M. Pasteels et J.C. Verhaeghe, 6212:R. S. Parpinelli, H. S. Lopes and A. A Freitas, " 6199:R. S. Parpinelli, H. S. Lopes and A. A Freitas, " 5577:Bachem, A.; Hochstättler, W.; Malich, M. (1996). 5444: 4757:, PhD thesis, Politecnico di Milano, Italy, 1992. 3469:can be calculated using the following functions: 2076:Vehicle routing problem with time windows (VRPTW) 1850: 8508: 7034:M. Dorigo, V. Maniezzo & A. Colorni, 1996. " 6397:A. Shmygelska, R. A. Hernández and H. H. Hoos, " 6310:Zaidman, Daniel; Wolfson, Haim J. (2016-08-01). 4814: 4786: 4463:1999, Gambardella, Taillard and Agazzi proposed 4385:1983, Deneubourg and his colleagues studied the 2138:Arc-weighted l-cardinality tree problem (AWlCTP) 7108:M. Dorigo, M. Birattari & T. Stützle, 2006 6042:"File Exchange – Ant Colony Optimization (ACO)" 5764:A new version of ant system for subset problems 4950:Sakakibara, Toshiki, and Daisuke Kurabayashi. " 4440:1996, publication of the article on ant system; 2337:{\displaystyle K=(M_{1}*M_{2})^{\tfrac {1}{2}}} 1935:problems, ranging from quadratic assignment to 1227:≥ 1 is a parameter to control the influence of 1062:≥ 0 is a parameter to control the influence of 7066:E. Bonabeau, M. Dorigo et G. Theraulaz, 1999. 6477: 6309: 5889: 5887: 5885: 5848:O. Okobiah, S. P. Mohanty, and E. Kougianos, " 4396:1988, and Moyson Manderick have an article on 2067:Split delivery vehicle routing problem (SDVRP) 2030:Single machine total tardiness problem (SMTTP) 644:depends on the combination of two values, the 397: 7994: 7262: 7029:Optimization, Learning and Natural Algorithms 6780:Self-organized shortcuts in the Argentine ant 6740:, Insectes Sociaux, numéro 6, p. 41-80, 1959. 6670:Parallel Problem Solving from Nature, PPSN XI 6371:J. ZHANG, H. Chung, W. L. Lo, and T. Huang, " 5788:," Proceedings of ANTS2000, pp.222-227, 2002. 5636: 5612:International Journal of Production Economics 5079: 5077: 5075: 5073: 5071: 4755:Optimization, Learning and Natural Algorithms 4681:IEEE Transactions on Evolutionary Computation 4654:IEEE Transactions on Evolutionary Computation 4494:2000, Gutjahr provides the first evidence of 7823: 7215:AntSim - Simulation of Ant Colony Algorithms 6989:International Journal of Production Research 6919:A graph-based Ant System and its convergence 6593:A. Ajith; G. Crina; R. Vitorino (éditeurs), 5236:," Technical report TR/IRIDIA/2003-17, 2003. 4863:. London: Hermes Science. pp. 259–265. 4378:to explain the behavior of nest building in 1833: 7301: 7031:, PhD thesis, Politecnico di Milano, Italy. 6478:Shmygelska, Alena; Hoos, Holger H. (2005). 6260: 6140:Classification with Ant Colony Optimization 5882: 5211:Classification with Ant Colony Optimization 4926:Ant trails-an example for robots to follow? 4133:Discounted cash flows in project scheduling 2061:Multi-depot vehicle routing problem (MDVRP) 64:Learn how and when to remove these messages 8001: 7987: 7269: 7255: 7018: 6946:L. Bianchi, L.M. Gambardella et M.Dorigo, 6616:"BOA: The Bayesian Optimization Algorithm" 5868:M. Sarkar, P. Ghosal, and S. P. Mohanty, " 5475: 5144:Journal of Computer Science and Technology 5068: 5056:A practical multirobot localization system 5019:." Adaptive Behavior 22.3 (2014): 189-206. 4941:." Swarm Intelligence 8.3 (2014): 227-246. 4911:Lima, Danielli A., and Gina MB Oliveira. " 2058:Capacitated vehicle routing problem (CVRP) 2052: 1805: 7515: 7200:Scholarpedia Ant Colony Optimization page 6505: 6495: 6327: 6120: 5943: 5682: 5594: 5522: 5489: 5417: 5384: 5356:https://doi.org/10.1007/s11465-020-0613-3 2070:Stochastic vehicle routing problem (SVRP) 2048:Assembly sequence planning (ASP) problems 261:methods inspired by the behavior of real 201:Learn how and when to remove this message 183:Learn how and when to remove this message 121:Learn how and when to remove this message 7503:Optimization computes maxima and minima. 7054:Ant Algorithms for Discrete Optimization 6887:É. Bonabeau, M. Dorigo et G. Theraulaz, 6771: 6667: 5639:European Journal of Operational Research 5609: 5451:European Journal of Operational Research 5420:European Journal of Operational Research 5366: 5006:" PLoS Comput Biol 9.3 (2013): e1002903. 4739:Distributed Optimization by Ant Colonies 4178: 4174: 4087: 2173: 2165: 1995: 1969: 1919: 1567:is the amount of pheromone deposited by 1122:is the desirability of state transition 410: 220: 212: 146:This article includes a list of general 7587: 6642: 6384:X. M. Hu, J. ZHANG，J. Xiao and Y. Li, " 5691: 5676: 5083:M. Dorigo, V. Maniezzo, et A. Colorni, 4883: 4855: 4823: 4584: 4220: 1869:Continuous orthogonal ant colony (COAC) 1860:Parallel ant colony optimization (PACO) 376:Ambient networks of intelligent objects 14: 8509: 7232:Ant algorithm simulation (Java Applet) 7105:". Physics of Life Reviews, 2: 353-373 6931:S. Iredi, D. Merkle et M. Middendorf, 6807:Positive feedback as a search strategy 6805:Dorigo M., V. Maniezzo et A. Colorni, 6528:Fred W. Glover, Gary A. Kochenberger, 5984: 5323:C. Gagné, W. L. Price and M. Gravel, " 4861:Inventer l'Ordinateur du XXIème Siècle 4737:A. Colorni, M. Dorigo et V. Maniezzo, 4434:1996, Gambardella and Dorigo proposed 4427:1995, Gambardella and Dorigo proposed 4187:ant colony algorithms are regarded as 8104:Patterns of self-organization in ants 7982: 7907: 7723: 7699:Principal pivoting algorithm of Lemke 7586: 7514: 7300: 7250: 7189:Journal of Accounting. 2018 Mar;8(1). 6900:M. Dorigo, G. Di Caro et T. Stützle, 6358:Xiao. M.Hu, J. ZHANG, and H. Chung, " 6305: 6303: 6102: 5512: 4405:collective behavior of Argentine ants 4296:Modeled on vertebrate immune systems. 4144:Energy and electricity network design 4103: 2144:Maximum independent set problem (MIS) 2086: 2064:Period vehicle routing problem (PVRP) 2003: 1980:It must visit each city exactly once; 1824: 1766:th ant's tour (typically length) and 1560:{\displaystyle \Delta \tau _{xy}^{k}} 338:estimation of distribution algorithms 323:optimizations. Initially proposed by 6865:, Bruxelles, Belgique, octobre 1998. 6225:W. N. Chen, J. ZHANG and H. Chung, " 6186:D. Martens, B. Baesens, T. Fawcett " 6109:Mathematical Problems in Engineering 5186:V.K.Ojha, A. Abraham and V. Snasel, 4889:Nanocomputers and Swarm Intelligence 4835:John Wiley & Sons. p. 214. 4829:Nanocomputers and Swarm Intelligence 4590:Nanocomputers and Swarm Intelligence 4321:Gravitational search algorithm (GSA) 4250:Estimation of distribution algorithm 4205:to make the transition between each 2027:Permutation flow shop problem (PFSP) 1906:estimation of distribution algorithm 1789: 132: 70: 29: 8522:Optimization algorithms and methods 7063:". Artificial Life, 5 (2): 137–172. 5932:Edge detection using ant algorithms 5762:G. Leguizamon and Z. Michalewicz, " 5515:Computers & Operations Research 5367:Toth, Paolo; Vigo, Daniele (2002). 4542:algorithms to estimate distribution 4331:Ant colony clustering method (ACCM) 4040:is the pheromone decay coefficient 2185: 2162:Antennas optimization and synthesis 2039:Group-shop scheduling problem (GSP) 1320: 24: 8114:symmetry breaking of escaping ants 7908: 7498: 7343:Successive parabolic interpolation 7140:A. Kazharov, V. Kureichik, 2010. " 7080:M. Dorigo & T. Stützle, 2004. 6647:(1st ed.). Berlin: Springer. 6300: 4967:." Adaptive Behavior (2016): 1-17. 4476:2000, Hoos and Stützle invent the 4233: 3889:Step 3 and step 5: Update process. 1963:and urban transportation systems. 1797: 1601: 1536: 1398: 896: 893: 890: 887: 884: 881: 878: 681:desirability of that move and the 152:it lacks sufficient corresponding 25: 8533: 7724: 7663:Projective algorithm of Karmarkar 7205:Ant Colony Optimization Home Page 7193: 6261:Warner, Lars; Vogel, Ute (2008). 5478:Computers and Operations Research 5276:Lecture Notes in Computer Science 1878:Recursive ant colony optimization 1507:pheromone evaporation coefficient 447: 319:methods, and it constitutes some 45:This article has multiple issues. 8151: 7658:Ellipsoid algorithm of Khachiyan 7561:Sequential quadratic programming 7398:Broyden–Fletcher–Goldfarb–Shanno 7237:Java Ant Colony System Framework 6980: 6968: 6955: 6940: 6925: 6910: 6903:Special issue on "Ant Algorithms 6894: 6891:, Oxford University Press, 1999. 6881: 6868: 6855: 6840: 6831: 6821: 6812: 6799: 6786: 6743: 6729: 6702: 6661: 6636: 6607: 6587: 6571: 6555: 6538: 6522: 6471: 6454: 6445: 6404: 6391: 6378: 6365: 4498:for an algorithm of ant colonies 4483:2000, first applications to the 4147:Grid workflow scheduling problem 1839:. All edges are initialized to τ 137: 75: 34: 6352: 6290: 6247:D. Picard, M. Cord, A. Revel, " 6241: 6232: 6219: 6206: 6193: 6180: 6167: 6154: 6145: 6096: 6055: 6034: 5993: 5978: 5937: 5924: 5911: 5898: 5862: 5842: 5829: 5817: 5804: 5791: 5778: 5769: 5756: 5743: 5730: 5713: 5700: 5670: 5657: 5630: 5603: 5570: 5544: 5537:W. P. Nanry and J. W. Barnes, " 5531: 5506: 5469: 5438: 5411: 5402: 5393: 5360: 5348: 5330: 5317: 5304: 5294: 5281: 5267: 5258: 5248: 5239: 5226: 5217: 5202: 5193: 5180: 5160: 5150: 5135: 5126: 5101:M. Dorigo et L.M. Gambardella, 5048: 5035: 5022: 5009: 4996: 4983: 4970: 4957: 4944: 4931: 4918: 4905: 4877: 4849: 4805: 4456:1998, Stützle proposes initial 4065:{\displaystyle 0<\tau <1} 3839:The ant's movement is based on 3558: 3503: 2690:is a normalization factor, and 2141:Multiple knapsack problem (MKP) 1915: 53:or discuss these issues on the 8517:Nature-inspired metaheuristics 7616:Reduced gradient (Frank–Wolfe) 5985:Gupta, Charu; Gupta, Sunanda. 5749:Y. C. Liang and A. E. Smith, " 5550:R. Bent and P.V. Hentenryck, " 5287:D. Merkle and M. Middendorf, " 4780: 4731: 4715: 4638: 4613: 4578: 4487:, scheduling sequence and the 4150:Inhibitory peptide design for 4125:Connectionless network routing 3971: 3959: 3956: 3915: 3903: 3755: 3732: 3706: 3700: 3634: 3611: 3591: 3585: 3536: 3530: 3488: 3482: 3456: 3450: 3409: 3391: 3378: 3360: 3337: 3313: 3300: 3276: 3242: 3218: 3205: 3181: 3158: 3140: 3127: 3109: 3079: 3055: 3042: 3018: 2995: 2971: 2958: 2934: 2900: 2876: 2863: 2839: 2816: 2792: 2779: 2755: 2729: 2710: 2674: 2655: 2494: 2482: 2445: 2433: 2405: 2393: 2368: 2356: 2318: 2291: 2271:{\displaystyle I_{M_{1}M_{2}}} 2117: 2099:Generalized assignment problem 1951:. They have an advantage over 1886: 1851:Rank-based ant system (ASrank) 1587:th ant, typically given for a 1364: 1352: 1349: 953: 932: 929: 908: 860: 839: 836: 815: 536: 530: 13: 1: 7946:Spiral optimization algorithm 7566:Successive linear programming 7001:10.1080/00207543.2016.1234084 6329:10.1093/bioinformatics/btw133 5692:Stützle, Thomas (July 1997). 5624:10.1016/S0925-5273(98)00250-3 5500:10.1016/S0305-0548(03)00155-2 5463:10.1016/S0377-2217(01)00206-5 5432:10.1016/S0377-2217(96)00253-6 5386:10.1016/S0166-218X(01)00351-1 4572: 4556:Transmission Control Protocol 4413:1991, M. Dorigo proposed the 3923:{\displaystyle \tau _{(x,y)}} 3837:Step 2: Construction process. 2376:{\displaystyle \tau _{(i,j)}} 2111:Redundancy allocation problem 331:seeking a path between their 291:modeled on the actions of an 8075:Mixed-species foraging flock 8026:Agent-based model in biology 8008: 7684:Simplex algorithm of Dantzig 7556:Augmented Lagrangian methods 7183:Abolmaali S, Roodposhti FR. 6723:10.1016/j.neucom.2014.04.069 6678:10.1007/978-3-642-15844-5_27 5917:S. Meshoul and M Batouche, " 5797:R. Cordone and F. Maffioli," 5784:V Maniezzo and M Milandri, " 5596:10.1016/0166-218X(95)00027-O 5583:Discrete Applied Mathematics 5373:Discrete Applied Mathematics 4546:2005, first applications to 4361:Chronology of ACO algorithms 4273:Reactive search optimization 4152:protein protein interactions 2105:Frequency assignment problem 2093:Quadratic assignment problem 257:. Artificial ants represent 7: 8322:Particle swarm optimization 7070:, Oxford University Press. 6173:G. D. Caro and M. Dorigo, " 4937:Fujisawa, Ryusuke, et al. " 4534:stochastic gradient descent 4489:satisfaction of constraints 4338:Stochastic diffusion search 4300:Particle swarm optimization 2568:{\displaystyle M_{1}*M_{2}} 2010:Sequential ordering problem 1949:travelling salesman problem 1898:stochastic gradient descent 398:Artificial pheromone system 343: 101:the claims made and adding 10: 8538: 8031:Collective animal behavior 6961:M. Dorigo and T. Stützle, 6530:Handbook of Metaheuristics 6072:10.1109/IECON.2009.5415195 6010:10.1109/ICSMC.2009.5345922 5706:R. Lourenço and D. Serra " 5651:10.1016/j.ejor.2004.08.018 4989:Schmickl, Thomas, et al. " 4347: 4156:Intelligent testing system 1933:combinatorial optimization 1529:is the number of ants and 1455:{\displaystyle \tau _{xy}} 1310:{\displaystyle \eta _{xz}} 1280:{\displaystyle \tau _{xz}} 1250:{\displaystyle \eta _{xy}} 1115:{\displaystyle \eta _{xy}} 1085:{\displaystyle \tau _{xy}} 995:{\displaystyle \tau _{xy}} 707:{\displaystyle \tau _{xy}} 670:{\displaystyle \eta _{xy}} 597:{\displaystyle p_{xy}^{k}} 8423: 8385: 8340: 8292: 8160: 8149: 8016: 7963: 7916: 7903: 7887:Push–relabel maximum flow 7862: 7778: 7736: 7732: 7719: 7689:Revised simplex algorithm 7671: 7643: 7629: 7599: 7595: 7582: 7548: 7527: 7523: 7510: 7496: 7472: 7420: 7383: 7360: 7351: 7313: 7309: 7296: 7096:"Ant Colony Optimization" 6764:F. Moyson, B. Manderick, 6160:G.D. Caro and M. Dorigo " 5810:C. Blum and M.J. Blesa, " 5119:T. Stützle et H.H. Hoos, 4161:electronic circuit design 4075:Step 7: Decision process. 3765:for 0 ≤ x ≤ 3644:for 0 ≤ x ≤ 3462:{\displaystyle f(\cdot )} 1847:when nearing stagnation. 1834:Max-min ant system (MMAS) 312:, another social insect. 8360:Self-propelled particles 7412:Symmetric rank-one (SR1) 7393:Berndt–Hall–Hall–Hausman 6643:Pelikan, Martin (2005). 6464:, M. T. Van Genuchten, " 5954:10.1109/CEC.2008.4630880 5054:Krajník, Tomáš, et al. " 5028:Garnier, Simon, et al. " 5015:Arvin, Farshad, et al. " 5002:Garnier, Simon, et al. " 4963:Arvin, Farshad, et al. " 4693:10.1109/tevc.2007.892762 4458:parallel implementations 4291:Artificial immune system 4203:probability distribution 3826:{\displaystyle \lambda } 1180:{\displaystyle 1/d_{xy}} 741:th ant moves from state 542:{\displaystyle A_{k}(x)} 8441:Collective intelligence 8307:Ant colony optimization 7936:Parallel metaheuristics 7744:Approximation algorithm 7455:Powell's dog leg method 7407:Davidon–Fletcher–Powell 7303:Unconstrained nonlinear 7082:Ant Colony Optimization 7019:Publications (selected) 6963:Ant Colony Optimization 6595:Stigmergic Optimization 6577:Santpal Singh Dhillon, 6421:10.1145/2480362.2480611 4976:Farshad Arvin, et al. " 4374:invented the theory of 4313:Intelligent water drops 3879:{\displaystyle P_{x,y}} 2212:Step 1: Initialization. 2053:Vehicle routing problem 1806:Ant colony system (ACS) 1055:{\displaystyle \alpha } 391:collective intelligence 240:ant colony optimization 167:more precise citations. 8461:Microbial intelligence 8121:Shoaling and schooling 7921:Evolutionary algorithm 7504: 6497:10.1186/1471-2105-6-30 6415:. pp. 1320–1327. 6004:. pp. 2193–2198. 5875:July 29, 2014, at the 5855:March 4, 2016, at the 5447:Speranza, Maria Grazia 5041:Farshad Arvin et al. " 4885:Waldner, Jean-Baptiste 4857:Waldner, Jean-Baptiste 4825:Waldner, Jean-Baptiste 4586:Waldner, Jean-Baptiste 4257:evolutionary algorithm 4183: 4092: 4066: 4034: 4010: 3924: 3880: 3827: 3804: 3683: 3568: 3561:for x ≥ 0; (2) 3513: 3506:for x ≥ 0; (1) 3463: 3432: 2681: 2569: 2529: 2506: 2412: 2377: 2338: 2272: 2228: 2179: 2171: 2000: 1976: 1928: 1892:algorithms. Like most 1780: 1760: 1740: 1710: 1666: uses curve 1581: 1561: 1523: 1499: 1479: 1456: 1423: 1397: 1311: 1281: 1251: 1221: 1220:{\displaystyle \beta } 1201: 1181: 1139: 1116: 1086: 1056: 1036: 1016: 996: 963: 775: 755: 735: 708: 671: 638: 618: 598: 563: 543: 507: 487: 467: 227: 218: 27:Optimization algorithm 7694:Criss-cross algorithm 7517:Constrained nonlinear 7502: 7323:Golden-section search 4924:Russell, R. Andrew. " 4597:John Wiley & Sons 4182: 4175:Definition difficulty 4170:System identification 4140:information retrieval 4110:Bankruptcy prediction 4091: 4067: 4035: 4033:{\displaystyle \psi } 4011: 3925: 3881: 3828: 3805: 3684: 3569: 3514: 3464: 3433: 2682: 2570: 2535:is the image of size 2530: 2507: 2413: 2411:{\displaystyle (i,j)} 2378: 2339: 2273: 2229: 2177: 2169: 1999: 1973: 1923: 1781: 1761: 1741: 1739:{\displaystyle L_{k}} 1711: 1582: 1562: 1524: 1500: 1498:{\displaystyle \rho } 1480: 1457: 1424: 1383: 1312: 1282: 1252: 1222: 1207:is the distance) and 1202: 1182: 1149:knowledge, typically 1140: 1117: 1087: 1057: 1037: 1017: 997: 964: 776: 756: 736: 709: 672: 639: 619: 604:of moving from state 599: 564: 544: 508: 488: 468: 411:Algorithm and formula 226:anthill and the food. 224: 216: 8481:Spatial organization 8446:Decentralised system 8284:Sea turtle migration 8138:Swarming (honey bee) 7611:Cutting-plane method 7114:. TR/IRIDIA/2006-023 6672:. pp. 264–273. 6622:. pp. 525–532. 5948:. pp. 751–756. 4538:cross-entropy method 4221:Stigmergy algorithms 4119:Connection-oriented 4044: 4024: 3937: 3895: 3857: 3817: 3694: 3579: 3524: 3476: 3444: 2697: 2582: 2539: 2519: 2425: 2390: 2348: 2282: 2238: 2218: 2022:Open-shop scheduling 1902:Cross-entropy method 1830:current best route. 1770: 1750: 1723: 1598: 1571: 1533: 1513: 1489: 1466: 1436: 1333: 1291: 1261: 1231: 1211: 1191: 1153: 1126: 1096: 1066: 1046: 1026: 1006: 976: 788: 765: 745: 725: 688: 651: 628: 608: 573: 553: 517: 497: 477: 457: 8456:Group size measures 8018:Biological swarming 7941:Simulated annealing 7759:Integer programming 7749:Dynamic programming 7589:Convex optimization 7450:Levenberg–Marquardt 7147:C-M. Pintea, 2014, 6584:, IOS Press, (2008) 6122:10.1155/2013/753251 5738:S. P. M. van Hoesel 5445:Angelelli, Enrico; 5345:, pp.111-138, 2008. 5278:, pp.611-620, 2000. 4791:. BOOKS ON DEMAND. 4666:10.1109/4235.585892 4387:collective behavior 4264:Simulated annealing 4201:algorithms using a 2344:. Pheromone matrix 2016:Job-shop scheduling 1953:simulated annealing 1746:is the cost of the 1621: 1556: 1418: 952: 928: 859: 835: 808: 593: 236:operations research 8471:Predator satiation 8332:Swarm (simulation) 8327:Swarm intelligence 8302:Agent-based models 8133:Swarming behaviour 7621:Subgradient method 7505: 7430:Conjugate gradient 7338:Nelder–Mead method 7059:2018-10-06 at the 6965:, MIT Press, 2004. 6889:Swarm intelligence 6484:BMC Bioinformatics 6103:Zhang, Y. (2013). 5690: • 5173:2019-12-21 at the 5121:MAX MIN Ant System 5061:2019-10-16 at the 4478:max-min ant system 4422:telecommunications 4372:Pierre-Paul Grassé 4326:swarm intelligence 4307:swarm intelligence 4240:Genetic algorithms 4215:swarm intelligence 4184: 4104:Other applications 4093: 4062: 4030: 4006: 3920: 3876: 3823: 3800: 3795: 3679: 3674: 3564: 3509: 3459: 3428: 3426: 2677: 2648: 2619: 2565: 2525: 2502: 2463: 2408: 2373: 2334: 2331: 2268: 2234:ants on the image 2224: 2194:and edge linking. 2180: 2172: 2087:Assignment problem 2004:Scheduling problem 2001: 1977: 1929: 1825:Elitist ant system 1776: 1756: 1736: 1706: 1701: 1697: 1681: 1668: 1658: 1604: 1577: 1557: 1539: 1519: 1495: 1478:{\displaystyle xy} 1475: 1452: 1419: 1401: 1307: 1277: 1247: 1217: 1197: 1177: 1138:{\displaystyle xy} 1135: 1112: 1082: 1052: 1032: 1012: 992: 959: 935: 911: 907: 842: 818: 791: 771: 751: 731: 704: 667: 634: 614: 594: 576: 569:, the probability 559: 539: 503: 483: 463: 427:ACO_MetaHeuristic 317:swarm intelligence 306:the bees algorithm 228: 219: 86:possibly contains 8504: 8503: 8491:Military swarming 8436:Animal navigation 8355:Collective motion 8342:Collective motion 8209:reverse migration 8143:Swarming motility 7976: 7975: 7959: 7958: 7899: 7898: 7895: 7894: 7858: 7857: 7819: 7818: 7715: 7714: 7711: 7710: 7707: 7706: 7578: 7577: 7574: 7573: 7494: 7493: 7490: 7489: 7468: 7467: 7179:978-1-4673-4523-1 7168:978-960-474-200-4 7157:978-3-642-40178-7 7135:978-1-84821-194-0 7094:M. Dorigo, 2007. 7043:L. M. Gambardella 6687:978-3-642-15843-8 6654:978-3-540-23774-7 6603:978-3-540-34689-0 6546:"Ciad-Lab |" 6535:, Springer (2003) 6460:K. C. Abbaspour, 6322:(15): 2289–2296. 6277:978-3-8322-7313-2 6081:978-1-4244-4648-3 6019:978-1-4244-2793-2 5963:978-1-4244-1822-0 5484:(12): 1947–1964. 5343:978-3-540-72959-4 5146:, 23(1), pp.2-18. 4898:978-1-84704-002-2 4870:978-2-7462-1516-0 4842:978-1-84704-002-2 4650:L. M. Gambardella 4631:978-1-84821-194-0 4606:978-1-84704-002-2 4448:telecommunication 4436:ant colony system 4398:self-organization 4260:guided-crossover. 3791: 3774: 3766: 3753: 3670: 3653: 3645: 3632: 3562: 3507: 2620: 2591: 2528:{\displaystyle I} 2462: 2330: 2227:{\displaystyle K} 2130:Partition problem 2124:Set cover problem 1957:genetic algorithm 1790:Common extensions 1779:{\displaystyle Q} 1759:{\displaystyle k} 1696: 1680: 1679: in its tour 1667: 1657: 1580:{\displaystyle k} 1522:{\displaystyle m} 1200:{\displaystyle d} 1035:{\displaystyle y} 1015:{\displaystyle x} 957: 865: 781:with probability 774:{\displaystyle y} 754:{\displaystyle x} 734:{\displaystyle k} 637:{\displaystyle y} 617:{\displaystyle x} 562:{\displaystyle k} 506:{\displaystyle k} 486:{\displaystyle y} 466:{\displaystyle x} 369:positive feedback 358:Ant communication 211: 210: 203: 193: 192: 185: 131: 130: 123: 88:original research 68: 16:(Redirected from 8529: 8317:Crowd simulation 8294:Swarm algorithms 8265:Insect migration 8170:Animal migration 8162:Animal migration 8155: 8080:Mobbing behavior 8003: 7996: 7989: 7980: 7979: 7905: 7904: 7821: 7820: 7787: 7786: 7764:Branch and bound 7754:Greedy algorithm 7734: 7733: 7721: 7720: 7641: 7640: 7597: 7596: 7584: 7583: 7525: 7524: 7512: 7511: 7460:Truncated Newton 7375:Wolfe conditions 7358: 7357: 7311: 7310: 7298: 7297: 7271: 7264: 7257: 7248: 7247: 7041:M. Dorigo & 7013: 7012: 6995:(9): 2506–2521. 6984: 6978: 6972: 6966: 6959: 6953: 6944: 6938: 6929: 6923: 6914: 6908: 6898: 6892: 6885: 6879: 6872: 6866: 6859: 6853: 6844: 6838: 6835: 6829: 6825: 6819: 6816: 6810: 6803: 6797: 6790: 6784: 6775: 6769: 6762: 6756: 6747: 6741: 6733: 6727: 6726: 6706: 6700: 6699: 6665: 6659: 6658: 6640: 6634: 6633: 6611: 6605: 6591: 6585: 6575: 6569: 6559: 6553: 6552: 6550: 6542: 6536: 6526: 6520: 6519: 6509: 6499: 6475: 6469: 6458: 6452: 6449: 6443: 6442: 6408: 6402: 6395: 6389: 6382: 6376: 6369: 6363: 6356: 6350: 6349: 6331: 6307: 6298: 6294: 6288: 6287: 6285: 6284: 6269: 6258: 6252: 6245: 6239: 6236: 6230: 6223: 6217: 6210: 6204: 6197: 6191: 6184: 6178: 6171: 6165: 6158: 6152: 6149: 6143: 6136: 6127: 6126: 6124: 6100: 6094: 6093: 6059: 6053: 6052: 6038: 6032: 6031: 5997: 5991: 5990: 5982: 5976: 5975: 5941: 5935: 5928: 5922: 5915: 5909: 5902: 5896: 5891: 5880: 5866: 5860: 5846: 5840: 5833: 5827: 5821: 5815: 5808: 5802: 5795: 5789: 5782: 5776: 5773: 5767: 5760: 5754: 5747: 5741: 5734: 5728: 5723:and F. Glover, " 5717: 5711: 5704: 5698: 5697: 5688: 5686: 5674: 5668: 5661: 5655: 5654: 5634: 5628: 5627: 5607: 5601: 5600: 5598: 5574: 5568: 5564: 5555: 5548: 5542: 5535: 5529: 5528: 5526: 5510: 5504: 5503: 5493: 5473: 5467: 5466: 5442: 5436: 5435: 5415: 5409: 5406: 5400: 5397: 5391: 5390: 5388: 5379:(1–3): 487–512. 5364: 5358: 5352: 5346: 5334: 5328: 5321: 5315: 5308: 5302: 5298: 5292: 5285: 5279: 5271: 5265: 5262: 5256: 5252: 5246: 5243: 5237: 5230: 5224: 5221: 5215: 5206: 5200: 5197: 5191: 5184: 5178: 5164: 5158: 5154: 5148: 5139: 5133: 5130: 5124: 5117: 5108: 5099: 5090: 5081: 5066: 5052: 5046: 5039: 5033: 5026: 5020: 5013: 5007: 5000: 4994: 4987: 4981: 4974: 4968: 4961: 4955: 4948: 4942: 4935: 4929: 4922: 4916: 4909: 4903: 4902: 4881: 4875: 4874: 4853: 4847: 4846: 4821: 4812: 4809: 4803: 4802: 4784: 4778: 4769: 4758: 4751: 4742: 4735: 4729: 4719: 4713: 4712: 4676: 4670: 4669: 4642: 4636: 4635: 4617: 4611: 4610: 4582: 4566:HUMANT algorithm 4071: 4069: 4068: 4063: 4039: 4037: 4036: 4031: 4015: 4013: 4012: 4007: 4005: 4004: 3989: 3988: 3955: 3954: 3929: 3927: 3926: 3921: 3919: 3918: 3885: 3883: 3882: 3877: 3875: 3874: 3832: 3830: 3829: 3824: 3809: 3807: 3806: 3801: 3799: 3798: 3792: 3789: 3775: 3772: 3767: 3764: 3754: 3752: 3744: 3736: 3688: 3686: 3685: 3680: 3678: 3677: 3671: 3668: 3654: 3651: 3646: 3643: 3633: 3631: 3623: 3615: 3573: 3571: 3570: 3565: 3563: 3560: 3554: 3553: 3518: 3516: 3515: 3510: 3508: 3505: 3468: 3466: 3465: 3460: 3437: 3435: 3434: 3429: 3427: 3423: 3419: 3418: 3414: 3413: 3412: 3382: 3381: 3346: 3342: 3341: 3340: 3304: 3303: 3255: 3251: 3247: 3246: 3245: 3209: 3208: 3167: 3163: 3162: 3161: 3131: 3130: 3092: 3088: 3084: 3083: 3082: 3046: 3045: 3004: 3000: 2999: 2998: 2962: 2961: 2917: 2913: 2910: 2909: 2905: 2904: 2903: 2867: 2866: 2825: 2821: 2820: 2819: 2783: 2782: 2728: 2727: 2686: 2684: 2683: 2678: 2673: 2672: 2647: 2646: 2645: 2618: 2617: 2616: 2574: 2572: 2571: 2566: 2564: 2563: 2551: 2550: 2534: 2532: 2531: 2526: 2511: 2509: 2508: 2503: 2498: 2497: 2464: 2455: 2449: 2448: 2417: 2415: 2414: 2409: 2382: 2380: 2379: 2374: 2372: 2371: 2343: 2341: 2340: 2335: 2333: 2332: 2323: 2316: 2315: 2303: 2302: 2277: 2275: 2274: 2269: 2267: 2266: 2265: 2264: 2255: 2254: 2233: 2231: 2230: 2225: 2186:Image processing 1941:routing vehicles 1925:Knapsack problem 1785: 1783: 1782: 1777: 1765: 1763: 1762: 1757: 1745: 1743: 1742: 1737: 1735: 1734: 1715: 1713: 1712: 1707: 1705: 1704: 1698: 1694: 1682: 1678: 1669: 1665: 1659: 1655: 1650: 1649: 1640: 1620: 1615: 1586: 1584: 1583: 1578: 1566: 1564: 1563: 1558: 1555: 1550: 1528: 1526: 1525: 1520: 1504: 1502: 1501: 1496: 1484: 1482: 1481: 1476: 1461: 1459: 1458: 1453: 1451: 1450: 1428: 1426: 1425: 1420: 1417: 1412: 1396: 1391: 1379: 1378: 1348: 1347: 1321:Pheromone update 1316: 1314: 1313: 1308: 1306: 1305: 1286: 1284: 1283: 1278: 1276: 1275: 1256: 1254: 1253: 1248: 1246: 1245: 1226: 1224: 1223: 1218: 1206: 1204: 1203: 1198: 1186: 1184: 1183: 1178: 1176: 1175: 1163: 1144: 1142: 1141: 1136: 1121: 1119: 1118: 1113: 1111: 1110: 1091: 1089: 1088: 1083: 1081: 1080: 1061: 1059: 1058: 1053: 1041: 1039: 1038: 1033: 1021: 1019: 1018: 1013: 1001: 999: 998: 993: 991: 990: 968: 966: 965: 960: 958: 956: 951: 946: 927: 922: 906: 905: 904: 899: 863: 858: 853: 834: 829: 813: 807: 802: 780: 778: 777: 772: 760: 758: 757: 752: 740: 738: 737: 732: 721:In general, the 713: 711: 710: 705: 703: 702: 676: 674: 673: 668: 666: 665: 643: 641: 640: 635: 623: 621: 620: 615: 603: 601: 600: 595: 592: 587: 568: 566: 565: 560: 548: 546: 545: 540: 529: 528: 512: 510: 509: 504: 492: 490: 489: 484: 472: 470: 469: 464: 383:Ambient networks 232:computer science 206: 199: 188: 181: 177: 174: 168: 163:this article by 154:inline citations 141: 140: 133: 126: 119: 115: 112: 106: 103:inline citations 79: 78: 71: 60: 38: 37: 30: 21: 8537: 8536: 8532: 8531: 8530: 8528: 8527: 8526: 8507: 8506: 8505: 8500: 8419: 8381: 8336: 8288: 8156: 8147: 8012: 8007: 7977: 7972: 7955: 7912: 7891: 7854: 7815: 7792: 7781: 7774: 7728: 7703: 7667: 7634: 7625: 7602: 7591: 7570: 7544: 7540:Penalty methods 7535:Barrier methods 7519: 7506: 7486: 7482:Newton's method 7464: 7416: 7379: 7347: 7328:Powell's method 7305: 7292: 7275: 7196: 7101:C. Blum, 2005 " 7098:. Scholarpedia. 7061:Wayback Machine 7021: 7016: 6985: 6981: 6973: 6969: 6960: 6956: 6945: 6941: 6930: 6926: 6915: 6911: 6899: 6895: 6886: 6882: 6873: 6869: 6860: 6856: 6845: 6841: 6836: 6832: 6826: 6822: 6817: 6813: 6804: 6800: 6791: 6787: 6776: 6772: 6763: 6759: 6748: 6744: 6734: 6730: 6707: 6703: 6688: 6666: 6662: 6655: 6641: 6637: 6630: 6612: 6608: 6592: 6588: 6576: 6572: 6560: 6556: 6548: 6544: 6543: 6539: 6527: 6523: 6476: 6472: 6459: 6455: 6450: 6446: 6431: 6409: 6405: 6396: 6392: 6383: 6379: 6370: 6366: 6357: 6353: 6308: 6301: 6295: 6291: 6282: 6280: 6278: 6267: 6259: 6255: 6246: 6242: 6237: 6233: 6224: 6220: 6211: 6207: 6198: 6194: 6185: 6181: 6172: 6168: 6159: 6155: 6150: 6146: 6137: 6130: 6101: 6097: 6082: 6060: 6056: 6051:. 21 July 2023. 6040: 6039: 6035: 6020: 5998: 5994: 5983: 5979: 5964: 5942: 5938: 5929: 5925: 5916: 5912: 5903: 5899: 5892: 5883: 5877:Wayback Machine 5867: 5863: 5857:Wayback Machine 5847: 5843: 5834: 5830: 5822: 5818: 5809: 5805: 5796: 5792: 5783: 5779: 5774: 5770: 5761: 5757: 5748: 5744: 5735: 5731: 5718: 5714: 5705: 5701: 5689: 5675: 5671: 5662: 5658: 5635: 5631: 5608: 5604: 5575: 5571: 5565: 5558: 5549: 5545: 5536: 5532: 5524:10.1.1.392.4034 5511: 5507: 5474: 5470: 5443: 5439: 5416: 5412: 5407: 5403: 5398: 5394: 5365: 5361: 5353: 5349: 5335: 5331: 5322: 5318: 5309: 5305: 5299: 5295: 5286: 5282: 5272: 5268: 5263: 5259: 5253: 5249: 5244: 5240: 5231: 5227: 5222: 5218: 5207: 5203: 5198: 5194: 5185: 5181: 5175:Wayback Machine 5165: 5161: 5155: 5151: 5140: 5136: 5131: 5127: 5118: 5111: 5100: 5093: 5082: 5069: 5063:Wayback Machine 5053: 5049: 5040: 5036: 5027: 5023: 5014: 5010: 5001: 4997: 4988: 4984: 4975: 4971: 4962: 4958: 4949: 4945: 4936: 4932: 4923: 4919: 4910: 4906: 4899: 4882: 4878: 4871: 4854: 4850: 4843: 4822: 4815: 4810: 4806: 4799: 4785: 4781: 4770: 4761: 4752: 4745: 4736: 4732: 4720: 4716: 4677: 4673: 4643: 4639: 4632: 4622:Artificial Ants 4618: 4614: 4607: 4599:. p. 225. 4583: 4579: 4575: 4548:protein folding 4514:multi-objective 4364: 4363: 4362: 4359: 4358: 4356: 4350: 4236: 4234:Related methods 4223: 4177: 4166:Protein folding 4121:network routing 4106: 4045: 4042: 4041: 4025: 4022: 4021: 4000: 3996: 3978: 3974: 3944: 3940: 3938: 3935: 3934: 3902: 3898: 3896: 3893: 3892: 3864: 3860: 3858: 3855: 3854: 3818: 3815: 3814: 3794: 3793: 3788: 3786: 3777: 3776: 3771: 3763: 3761: 3745: 3737: 3735: 3713: 3712: 3695: 3692: 3691: 3673: 3672: 3667: 3665: 3656: 3655: 3650: 3642: 3640: 3624: 3616: 3614: 3598: 3597: 3580: 3577: 3576: 3559: 3549: 3545: 3525: 3522: 3521: 3504: 3477: 3474: 3473: 3445: 3442: 3441: 3425: 3424: 3390: 3386: 3359: 3355: 3354: 3350: 3312: 3308: 3275: 3271: 3270: 3266: 3265: 3262: 3253: 3252: 3217: 3213: 3180: 3176: 3175: 3171: 3139: 3135: 3108: 3104: 3103: 3099: 3090: 3089: 3054: 3050: 3017: 3013: 3012: 3008: 2970: 2966: 2933: 2929: 2928: 2924: 2915: 2914: 2875: 2871: 2838: 2834: 2833: 2829: 2791: 2787: 2754: 2750: 2749: 2745: 2744: 2740: 2735: 2717: 2713: 2700: 2698: 2695: 2694: 2662: 2658: 2641: 2637: 2624: 2612: 2608: 2595: 2583: 2580: 2579: 2559: 2555: 2546: 2542: 2540: 2537: 2536: 2520: 2517: 2516: 2481: 2477: 2453: 2432: 2428: 2426: 2423: 2422: 2391: 2388: 2387: 2355: 2351: 2349: 2346: 2345: 2321: 2317: 2311: 2307: 2298: 2294: 2283: 2280: 2279: 2260: 2256: 2250: 2246: 2245: 2241: 2239: 2236: 2235: 2219: 2216: 2215: 2214:Randomly place 2199:Edge detection: 2188: 2164: 2151: 2120: 2089: 2055: 2006: 1961:network routing 1918: 1889: 1880: 1871: 1862: 1853: 1846: 1842: 1836: 1827: 1808: 1800: 1798:Ant system (AS) 1792: 1786:is a constant. 1771: 1768: 1767: 1751: 1748: 1747: 1730: 1726: 1724: 1721: 1720: 1700: 1699: 1692: 1690: 1684: 1683: 1676: 1663: 1653: 1651: 1645: 1641: 1636: 1626: 1625: 1616: 1608: 1599: 1596: 1595: 1572: 1569: 1568: 1551: 1543: 1534: 1531: 1530: 1514: 1511: 1510: 1490: 1487: 1486: 1467: 1464: 1463: 1443: 1439: 1437: 1434: 1433: 1413: 1405: 1392: 1387: 1371: 1367: 1340: 1336: 1334: 1331: 1330: 1323: 1298: 1294: 1292: 1289: 1288: 1268: 1264: 1262: 1259: 1258: 1238: 1234: 1232: 1229: 1228: 1212: 1209: 1208: 1192: 1189: 1188: 1168: 1164: 1159: 1154: 1151: 1150: 1127: 1124: 1123: 1103: 1099: 1097: 1094: 1093: 1073: 1069: 1067: 1064: 1063: 1047: 1044: 1043: 1027: 1024: 1023: 1007: 1004: 1003: 983: 979: 977: 974: 973: 947: 939: 923: 915: 900: 877: 876: 869: 864: 854: 846: 830: 822: 814: 812: 803: 795: 789: 786: 785: 766: 763: 762: 746: 743: 742: 726: 723: 722: 695: 691: 689: 686: 685: 658: 654: 652: 649: 648: 629: 626: 625: 609: 606: 605: 588: 580: 574: 571: 570: 554: 551: 550: 524: 520: 518: 515: 514: 513:computes a set 498: 495: 494: 478: 475: 474: 458: 455: 454: 450: 445: 413: 400: 378: 346: 297:parameter space 275:vehicle routing 207: 196: 195: 194: 189: 178: 172: 169: 159:Please help to 158: 142: 138: 127: 116: 110: 107: 92: 80: 76: 39: 35: 28: 23: 22: 18:Artificial ants 15: 12: 11: 5: 8535: 8525: 8524: 8519: 8502: 8501: 8499: 8498: 8493: 8488: 8483: 8478: 8476:Quorum sensing 8473: 8468: 8463: 8458: 8453: 8448: 8443: 8438: 8433: 8427: 8425: 8424:Related topics 8421: 8420: 8418: 8417: 8412: 8410:Swarm robotics 8407: 8402: 8397: 8391: 8389: 8387:Swarm robotics 8383: 8382: 8380: 8379: 8374: 8369: 8368: 8367: 8357: 8352: 8346: 8344: 8338: 8337: 8335: 8334: 8329: 8324: 8319: 8314: 8309: 8304: 8298: 8296: 8290: 8289: 8287: 8286: 8281: 8280: 8279: 8278: 8277: 8262: 8261: 8260: 8255: 8245: 8244: 8243: 8238: 8233: 8228: 8221:Fish migration 8218: 8216:Cell migration 8213: 8212: 8211: 8206: 8199:Bird migration 8196: 8195: 8194: 8192:coded wire tag 8189: 8188: 8187: 8177: 8166: 8164: 8158: 8157: 8150: 8148: 8146: 8145: 8140: 8135: 8130: 8129: 8128: 8118: 8117: 8116: 8111: 8101: 8100: 8099: 8089: 8088: 8087: 8085:feeding frenzy 8077: 8072: 8067: 8066: 8065: 8055: 8054: 8053: 8048: 8038: 8033: 8028: 8022: 8020: 8014: 8013: 8006: 8005: 7998: 7991: 7983: 7974: 7973: 7971: 7970: 7964: 7961: 7960: 7957: 7956: 7954: 7953: 7948: 7943: 7938: 7933: 7928: 7923: 7917: 7914: 7913: 7910:Metaheuristics 7901: 7900: 7897: 7896: 7893: 7892: 7890: 7889: 7884: 7882:Ford–Fulkerson 7879: 7874: 7868: 7866: 7860: 7859: 7856: 7855: 7853: 7852: 7850:Floyd–Warshall 7847: 7842: 7841: 7840: 7829: 7827: 7817: 7816: 7814: 7813: 7808: 7803: 7797: 7795: 7784: 7776: 7775: 7773: 7772: 7771: 7770: 7756: 7751: 7746: 7740: 7738: 7730: 7729: 7717: 7716: 7713: 7712: 7709: 7708: 7705: 7704: 7702: 7701: 7696: 7691: 7686: 7680: 7678: 7669: 7668: 7666: 7665: 7660: 7655: 7653:Affine scaling 7649: 7647: 7645:Interior point 7638: 7627: 7626: 7624: 7623: 7618: 7613: 7607: 7605: 7593: 7592: 7580: 7579: 7576: 7575: 7572: 7571: 7569: 7568: 7563: 7558: 7552: 7550: 7549:Differentiable 7546: 7545: 7543: 7542: 7537: 7531: 7529: 7521: 7520: 7508: 7507: 7497: 7495: 7492: 7491: 7488: 7487: 7485: 7484: 7478: 7476: 7470: 7469: 7466: 7465: 7463: 7462: 7457: 7452: 7447: 7442: 7437: 7432: 7426: 7424: 7418: 7417: 7415: 7414: 7409: 7404: 7395: 7389: 7387: 7381: 7380: 7378: 7377: 7372: 7366: 7364: 7355: 7349: 7348: 7346: 7345: 7340: 7335: 7330: 7325: 7319: 7317: 7307: 7306: 7294: 7293: 7274: 7273: 7266: 7259: 7251: 7245: 7244: 7239: 7234: 7229: 7223: 7217: 7212: 7207: 7202: 7195: 7194:External links 7192: 7191: 7190: 7181: 7170: 7159: 7145: 7138: 7127: 7115: 7106: 7099: 7092: 7078: 7064: 7050: 7039: 7032: 7020: 7017: 7015: 7014: 6979: 6967: 6954: 6939: 6924: 6916:W.J. Gutjahr, 6909: 6893: 6880: 6867: 6854: 6839: 6830: 6820: 6811: 6798: 6785: 6770: 6757: 6742: 6735:P.-P. Grassé, 6728: 6711:Neurocomputing 6701: 6686: 6660: 6653: 6635: 6628: 6606: 6586: 6570: 6554: 6537: 6521: 6470: 6453: 6444: 6429: 6403: 6390: 6377: 6364: 6351: 6316:Bioinformatics 6299: 6289: 6276: 6253: 6240: 6231: 6218: 6205: 6192: 6179: 6166: 6153: 6144: 6128: 6095: 6080: 6054: 6033: 6018: 5992: 5977: 5962: 5936: 5923: 5910: 5897: 5881: 5861: 5841: 5828: 5816: 5803: 5790: 5777: 5768: 5755: 5742: 5736:K. I. Aardal, 5729: 5712: 5699: 5684:10.1.1.47.5167 5669: 5656: 5645:(2): 606–622. 5629: 5618:(3): 249–258. 5602: 5589:(1–3): 47–72. 5569: 5556: 5543: 5530: 5505: 5468: 5457:(2): 233–247. 5437: 5410: 5401: 5392: 5359: 5347: 5329: 5316: 5303: 5293: 5280: 5266: 5257: 5247: 5238: 5225: 5216: 5201: 5192: 5179: 5159: 5149: 5134: 5125: 5109: 5091: 5067: 5047: 5034: 5021: 5008: 4995: 4982: 4969: 4956: 4943: 4930: 4917: 4904: 4897: 4876: 4869: 4848: 4841: 4813: 4804: 4797: 4779: 4759: 4743: 4730: 4714: 4671: 4637: 4630: 4624:. Wiley-ISTE. 4612: 4605: 4576: 4574: 4571: 4570: 4569: 4562: 4559: 4551: 4544: 4530: 4527: 4520: 4517: 4510: 4499: 4492: 4481: 4474: 4471: 4468: 4461: 4454: 4451: 4444: 4441: 4438: 4432: 4425: 4418: 4411: 4408: 4401: 4394: 4383: 4360: 4354: 4353: 4352: 4351: 4349: 4346: 4345: 4344: 4341: 4335: 4332: 4329: 4322: 4319: 4316: 4310: 4303: 4297: 4294: 4288: 4284: 4278: 4274: 4271: 4267: 4261: 4253: 4247: 4243: 4235: 4232: 4222: 4219: 4211:social insects 4192:metaheuristics 4176: 4173: 4172: 4171: 4168: 4163: 4157: 4154: 4148: 4145: 4142: 4134: 4131: 4126: 4123: 4117: 4115:Classification 4112: 4105: 4102: 4101: 4100: 4061: 4058: 4055: 4052: 4049: 4029: 4018: 4017: 4003: 3999: 3995: 3992: 3987: 3984: 3981: 3977: 3973: 3970: 3967: 3964: 3961: 3958: 3953: 3950: 3947: 3943: 3917: 3914: 3911: 3908: 3905: 3901: 3873: 3870: 3867: 3863: 3822: 3813:The parameter 3811: 3810: 3797: 3787: 3785: 3782: 3779: 3778: 3770: 3762: 3760: 3757: 3751: 3748: 3743: 3740: 3734: 3731: 3728: 3725: 3722: 3719: 3718: 3716: 3711: 3708: 3705: 3702: 3699: 3689: 3676: 3666: 3664: 3661: 3658: 3657: 3649: 3641: 3639: 3636: 3630: 3627: 3622: 3619: 3613: 3610: 3607: 3604: 3603: 3601: 3596: 3593: 3590: 3587: 3584: 3574: 3557: 3552: 3548: 3544: 3541: 3538: 3535: 3532: 3529: 3519: 3502: 3499: 3496: 3493: 3490: 3487: 3484: 3481: 3458: 3455: 3452: 3449: 3439: 3438: 3422: 3417: 3411: 3408: 3405: 3402: 3399: 3396: 3393: 3389: 3385: 3380: 3377: 3374: 3371: 3368: 3365: 3362: 3358: 3353: 3349: 3345: 3339: 3336: 3333: 3330: 3327: 3324: 3321: 3318: 3315: 3311: 3307: 3302: 3299: 3296: 3293: 3290: 3287: 3284: 3281: 3278: 3274: 3269: 3264: 3261: 3258: 3256: 3254: 3250: 3244: 3241: 3238: 3235: 3232: 3229: 3226: 3223: 3220: 3216: 3212: 3207: 3204: 3201: 3198: 3195: 3192: 3189: 3186: 3183: 3179: 3174: 3170: 3166: 3160: 3157: 3154: 3151: 3148: 3145: 3142: 3138: 3134: 3129: 3126: 3123: 3120: 3117: 3114: 3111: 3107: 3102: 3098: 3095: 3093: 3091: 3087: 3081: 3078: 3075: 3072: 3069: 3066: 3063: 3060: 3057: 3053: 3049: 3044: 3041: 3038: 3035: 3032: 3029: 3026: 3023: 3020: 3016: 3011: 3007: 3003: 2997: 2994: 2991: 2988: 2985: 2982: 2979: 2976: 2973: 2969: 2965: 2960: 2957: 2954: 2951: 2948: 2945: 2942: 2939: 2936: 2932: 2927: 2923: 2920: 2918: 2916: 2912: 2908: 2902: 2899: 2896: 2893: 2890: 2887: 2884: 2881: 2878: 2874: 2870: 2865: 2862: 2859: 2856: 2853: 2850: 2847: 2844: 2841: 2837: 2832: 2828: 2824: 2818: 2815: 2812: 2809: 2806: 2803: 2800: 2797: 2794: 2790: 2786: 2781: 2778: 2775: 2772: 2769: 2766: 2763: 2760: 2757: 2753: 2748: 2743: 2739: 2736: 2734: 2731: 2726: 2723: 2720: 2716: 2712: 2709: 2706: 2703: 2702: 2688: 2687: 2676: 2671: 2668: 2665: 2661: 2657: 2654: 2651: 2644: 2640: 2636: 2633: 2630: 2627: 2623: 2615: 2611: 2607: 2604: 2601: 2598: 2594: 2590: 2587: 2562: 2558: 2554: 2549: 2545: 2524: 2513: 2512: 2501: 2496: 2493: 2490: 2487: 2484: 2480: 2476: 2473: 2470: 2467: 2461: 2458: 2452: 2447: 2444: 2441: 2438: 2435: 2431: 2407: 2404: 2401: 2398: 2395: 2370: 2367: 2364: 2361: 2358: 2354: 2329: 2326: 2320: 2314: 2310: 2306: 2301: 2297: 2293: 2290: 2287: 2263: 2259: 2253: 2249: 2244: 2223: 2202: 2201: 2192:edge detection 2187: 2184: 2163: 2160: 2159: 2158: 2155: 2150: 2147: 2146: 2145: 2142: 2139: 2136: 2133: 2127: 2119: 2116: 2115: 2114: 2108: 2102: 2096: 2088: 2085: 2084: 2083: 2080: 2077: 2074: 2071: 2068: 2065: 2062: 2059: 2054: 2051: 2050: 2049: 2046: 2043: 2040: 2037: 2034: 2031: 2028: 2025: 2019: 2013: 2005: 2002: 1994: 1993: 1990: 1987: 1984: 1981: 1917: 1914: 1910:metaheuristics 1894:metaheuristics 1888: 1885: 1879: 1876: 1870: 1867: 1861: 1858: 1852: 1849: 1844: 1840: 1835: 1832: 1826: 1823: 1822: 1821: 1818: 1815: 1807: 1804: 1799: 1796: 1791: 1788: 1775: 1755: 1733: 1729: 1717: 1716: 1703: 1691: 1689: 1686: 1685: 1675: 1672: 1662: 1652: 1648: 1644: 1639: 1635: 1632: 1631: 1629: 1624: 1619: 1614: 1611: 1607: 1603: 1576: 1554: 1549: 1546: 1542: 1538: 1518: 1494: 1474: 1471: 1449: 1446: 1442: 1430: 1429: 1416: 1411: 1408: 1404: 1400: 1395: 1390: 1386: 1382: 1377: 1374: 1370: 1366: 1363: 1360: 1357: 1354: 1351: 1346: 1343: 1339: 1322: 1319: 1304: 1301: 1297: 1274: 1271: 1267: 1244: 1241: 1237: 1216: 1196: 1174: 1171: 1167: 1162: 1158: 1134: 1131: 1109: 1106: 1102: 1079: 1076: 1072: 1051: 1031: 1011: 989: 986: 982: 970: 969: 955: 950: 945: 942: 938: 934: 931: 926: 921: 918: 914: 910: 903: 898: 895: 892: 889: 886: 883: 880: 875: 872: 868: 862: 857: 852: 849: 845: 841: 838: 833: 828: 825: 821: 817: 811: 806: 801: 798: 794: 770: 750: 730: 701: 698: 694: 664: 661: 657: 646:attractiveness 633: 613: 591: 586: 583: 579: 558: 538: 535: 532: 527: 523: 502: 482: 462: 449: 448:Edge selection 446: 423: 421:on each edge. 412: 409: 399: 396: 377: 374: 345: 342: 209: 208: 191: 190: 145: 143: 136: 129: 128: 83: 81: 74: 69: 43: 42: 40: 33: 26: 9: 6: 4: 3: 2: 8534: 8523: 8520: 8518: 8515: 8514: 8512: 8497: 8494: 8492: 8489: 8487: 8484: 8482: 8479: 8477: 8474: 8472: 8469: 8467: 8464: 8462: 8459: 8457: 8454: 8452: 8449: 8447: 8444: 8442: 8439: 8437: 8434: 8432: 8429: 8428: 8426: 8422: 8416: 8413: 8411: 8408: 8406: 8403: 8401: 8398: 8396: 8393: 8392: 8390: 8388: 8384: 8378: 8375: 8373: 8370: 8366: 8363: 8362: 8361: 8358: 8356: 8353: 8351: 8350:Active matter 8348: 8347: 8345: 8343: 8339: 8333: 8330: 8328: 8325: 8323: 8320: 8318: 8315: 8313: 8310: 8308: 8305: 8303: 8300: 8299: 8297: 8295: 8291: 8285: 8282: 8276: 8273: 8272: 8271: 8268: 8267: 8266: 8263: 8259: 8256: 8254: 8251: 8250: 8249: 8246: 8242: 8239: 8237: 8234: 8232: 8229: 8227: 8226:diel vertical 8224: 8223: 8222: 8219: 8217: 8214: 8210: 8207: 8205: 8202: 8201: 8200: 8197: 8193: 8190: 8186: 8183: 8182: 8181: 8178: 8176: 8173: 8172: 8171: 8168: 8167: 8165: 8163: 8159: 8154: 8144: 8141: 8139: 8136: 8134: 8131: 8127: 8124: 8123: 8122: 8119: 8115: 8112: 8110: 8107: 8106: 8105: 8102: 8098: 8095: 8094: 8093: 8090: 8086: 8083: 8082: 8081: 8078: 8076: 8073: 8071: 8068: 8064: 8063:herd behavior 8061: 8060: 8059: 8056: 8052: 8049: 8047: 8044: 8043: 8042: 8039: 8037: 8034: 8032: 8029: 8027: 8024: 8023: 8021: 8019: 8015: 8011: 8004: 7999: 7997: 7992: 7990: 7985: 7984: 7981: 7969: 7966: 7965: 7962: 7952: 7949: 7947: 7944: 7942: 7939: 7937: 7934: 7932: 7929: 7927: 7926:Hill climbing 7924: 7922: 7919: 7918: 7915: 7911: 7906: 7902: 7888: 7885: 7883: 7880: 7878: 7875: 7873: 7870: 7869: 7867: 7865: 7864:Network flows 7861: 7851: 7848: 7846: 7843: 7839: 7836: 7835: 7834: 7831: 7830: 7828: 7826: 7825:Shortest path 7822: 7812: 7809: 7807: 7804: 7802: 7799: 7798: 7796: 7794: 7793:spanning tree 7788: 7785: 7783: 7777: 7769: 7765: 7762: 7761: 7760: 7757: 7755: 7752: 7750: 7747: 7745: 7742: 7741: 7739: 7735: 7731: 7727: 7726:Combinatorial 7722: 7718: 7700: 7697: 7695: 7692: 7690: 7687: 7685: 7682: 7681: 7679: 7677: 7674: 7670: 7664: 7661: 7659: 7656: 7654: 7651: 7650: 7648: 7646: 7642: 7639: 7637: 7632: 7628: 7622: 7619: 7617: 7614: 7612: 7609: 7608: 7606: 7604: 7598: 7594: 7590: 7585: 7581: 7567: 7564: 7562: 7559: 7557: 7554: 7553: 7551: 7547: 7541: 7538: 7536: 7533: 7532: 7530: 7526: 7522: 7518: 7513: 7509: 7501: 7483: 7480: 7479: 7477: 7475: 7471: 7461: 7458: 7456: 7453: 7451: 7448: 7446: 7443: 7441: 7438: 7436: 7433: 7431: 7428: 7427: 7425: 7423: 7422:Other methods 7419: 7413: 7410: 7408: 7405: 7403: 7399: 7396: 7394: 7391: 7390: 7388: 7386: 7382: 7376: 7373: 7371: 7368: 7367: 7365: 7363: 7359: 7356: 7354: 7350: 7344: 7341: 7339: 7336: 7334: 7331: 7329: 7326: 7324: 7321: 7320: 7318: 7316: 7312: 7308: 7304: 7299: 7295: 7291: 7287: 7283: 7279: 7272: 7267: 7265: 7260: 7258: 7253: 7252: 7249: 7243: 7240: 7238: 7235: 7233: 7230: 7227: 7224: 7221: 7220:MIDACO-Solver 7218: 7216: 7213: 7211: 7208: 7206: 7203: 7201: 7198: 7197: 7188: 7187: 7182: 7180: 7176: 7171: 7169: 7165: 7160: 7158: 7154: 7150: 7146: 7143: 7139: 7136: 7132: 7128: 7125: 7121: 7116: 7113: 7112: 7107: 7104: 7100: 7097: 7093: 7091: 7090:0-262-04219-3 7087: 7084:, MIT Press. 7083: 7079: 7077: 7076:0-19-513159-2 7073: 7069: 7065: 7062: 7058: 7055: 7051: 7048: 7044: 7040: 7037: 7033: 7030: 7026: 7023: 7022: 7010: 7006: 7002: 6998: 6994: 6990: 6983: 6977: 6971: 6964: 6958: 6951: 6950: 6943: 6936: 6935: 6928: 6921: 6920: 6913: 6906: 6904: 6897: 6890: 6884: 6877: 6871: 6864: 6858: 6851: 6850: 6843: 6834: 6824: 6815: 6808: 6802: 6795: 6789: 6782: 6781: 6774: 6767: 6761: 6754: 6753: 6746: 6739: 6738:constructeurs 6732: 6724: 6720: 6716: 6712: 6705: 6697: 6693: 6689: 6683: 6679: 6675: 6671: 6664: 6656: 6650: 6646: 6639: 6631: 6629:9781558606111 6625: 6621: 6617: 6610: 6604: 6600: 6596: 6590: 6583: 6580: 6574: 6567: 6564: 6558: 6547: 6541: 6534: 6531: 6525: 6517: 6513: 6508: 6503: 6498: 6493: 6489: 6485: 6481: 6474: 6467: 6463: 6457: 6448: 6440: 6436: 6432: 6430:9781450316569 6426: 6422: 6418: 6414: 6407: 6400: 6394: 6387: 6381: 6374: 6368: 6361: 6355: 6347: 6343: 6339: 6335: 6330: 6325: 6321: 6317: 6313: 6306: 6304: 6293: 6279: 6273: 6266: 6265: 6257: 6250: 6244: 6235: 6228: 6222: 6215: 6209: 6202: 6196: 6189: 6183: 6176: 6170: 6163: 6157: 6148: 6141: 6135: 6133: 6123: 6118: 6114: 6110: 6106: 6099: 6091: 6087: 6083: 6077: 6073: 6069: 6065: 6058: 6050: 6048: 6043: 6037: 6029: 6025: 6021: 6015: 6011: 6007: 6003: 5996: 5988: 5981: 5973: 5969: 5965: 5959: 5955: 5951: 5947: 5940: 5933: 5927: 5920: 5914: 5907: 5901: 5895: 5890: 5888: 5886: 5878: 5874: 5871: 5865: 5858: 5854: 5851: 5845: 5838: 5832: 5825: 5820: 5813: 5807: 5800: 5794: 5787: 5781: 5772: 5765: 5759: 5752: 5746: 5739: 5733: 5726: 5722: 5716: 5709: 5703: 5695: 5685: 5680: 5673: 5666: 5660: 5652: 5648: 5644: 5640: 5633: 5625: 5621: 5617: 5613: 5606: 5597: 5592: 5588: 5584: 5580: 5573: 5563: 5561: 5553: 5547: 5540: 5534: 5525: 5520: 5516: 5509: 5501: 5497: 5492: 5491:10.1.1.8.7096 5487: 5483: 5479: 5472: 5464: 5460: 5456: 5452: 5448: 5441: 5433: 5429: 5425: 5421: 5414: 5405: 5396: 5387: 5382: 5378: 5374: 5370: 5363: 5357: 5351: 5344: 5340: 5333: 5326: 5320: 5313: 5307: 5297: 5290: 5284: 5277: 5270: 5261: 5251: 5242: 5235: 5229: 5220: 5213: 5212: 5205: 5196: 5189: 5183: 5176: 5172: 5169: 5163: 5153: 5147: 5145: 5138: 5129: 5122: 5116: 5114: 5106: 5105: 5098: 5096: 5088: 5087: 5080: 5078: 5076: 5074: 5072: 5064: 5060: 5057: 5051: 5044: 5038: 5031: 5025: 5018: 5012: 5005: 4999: 4992: 4986: 4979: 4973: 4966: 4960: 4953: 4947: 4940: 4934: 4927: 4921: 4914: 4908: 4900: 4894: 4890: 4886: 4880: 4872: 4866: 4862: 4858: 4852: 4844: 4838: 4834: 4830: 4826: 4820: 4818: 4808: 4800: 4798:9783750422421 4794: 4790: 4783: 4776: 4775: 4768: 4766: 4764: 4756: 4750: 4748: 4740: 4734: 4728: 4727:0-262-04219-3 4724: 4718: 4710: 4706: 4702: 4698: 4694: 4690: 4686: 4682: 4675: 4667: 4663: 4659: 4655: 4651: 4647: 4641: 4633: 4627: 4623: 4616: 4608: 4602: 4598: 4595: 4591: 4587: 4581: 4577: 4567: 4563: 4560: 4557: 4552: 4549: 4545: 4543: 4539: 4535: 4531: 4528: 4525: 4521: 4518: 4515: 4511: 4508: 4504: 4500: 4497: 4493: 4490: 4486: 4482: 4479: 4475: 4472: 4469: 4466: 4462: 4459: 4455: 4452: 4449: 4445: 4442: 4439: 4437: 4433: 4430: 4426: 4423: 4419: 4416: 4412: 4409: 4406: 4402: 4399: 4395: 4392: 4388: 4384: 4381: 4377: 4373: 4369: 4368: 4367: 4342: 4339: 4336: 4333: 4330: 4327: 4323: 4320: 4317: 4314: 4311: 4308: 4304: 4301: 4298: 4295: 4292: 4289: 4285: 4282: 4279: 4275: 4272: 4268: 4265: 4262: 4258: 4254: 4251: 4248: 4244: 4241: 4238: 4237: 4231: 4229: 4218: 4216: 4212: 4208: 4204: 4200: 4197: 4196:probabilistic 4193: 4190: 4181: 4169: 4167: 4164: 4162: 4158: 4155: 4153: 4149: 4146: 4143: 4141: 4138: 4135: 4132: 4130: 4127: 4124: 4122: 4118: 4116: 4113: 4111: 4108: 4107: 4098: 4097:Edge linking: 4095: 4094: 4090: 4086: 4083: 4081: 4080:Otsu's method 4076: 4072: 4059: 4056: 4053: 4050: 4047: 4027: 4001: 3997: 3993: 3990: 3985: 3982: 3979: 3975: 3968: 3965: 3962: 3951: 3948: 3945: 3941: 3933: 3932: 3931: 3912: 3909: 3906: 3899: 3890: 3886: 3871: 3868: 3865: 3861: 3852: 3849: 3845: 3842: 3838: 3834: 3820: 3783: 3780: 3768: 3758: 3749: 3746: 3741: 3738: 3729: 3726: 3723: 3720: 3714: 3709: 3703: 3697: 3690: 3662: 3659: 3647: 3637: 3628: 3625: 3620: 3617: 3608: 3605: 3599: 3594: 3588: 3582: 3575: 3555: 3550: 3546: 3542: 3539: 3533: 3527: 3520: 3500: 3497: 3494: 3491: 3485: 3479: 3472: 3471: 3470: 3453: 3447: 3420: 3415: 3406: 3403: 3400: 3397: 3394: 3387: 3383: 3375: 3372: 3369: 3366: 3363: 3356: 3351: 3347: 3343: 3334: 3331: 3328: 3325: 3322: 3319: 3316: 3309: 3305: 3297: 3294: 3291: 3288: 3285: 3282: 3279: 3272: 3267: 3259: 3257: 3248: 3239: 3236: 3233: 3230: 3227: 3224: 3221: 3214: 3210: 3202: 3199: 3196: 3193: 3190: 3187: 3184: 3177: 3172: 3168: 3164: 3155: 3152: 3149: 3146: 3143: 3136: 3132: 3124: 3121: 3118: 3115: 3112: 3105: 3100: 3096: 3094: 3085: 3076: 3073: 3070: 3067: 3064: 3061: 3058: 3051: 3047: 3039: 3036: 3033: 3030: 3027: 3024: 3021: 3014: 3009: 3005: 3001: 2992: 2989: 2986: 2983: 2980: 2977: 2974: 2967: 2963: 2955: 2952: 2949: 2946: 2943: 2940: 2937: 2930: 2925: 2921: 2919: 2906: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2872: 2868: 2860: 2857: 2854: 2851: 2848: 2845: 2842: 2835: 2830: 2826: 2822: 2813: 2810: 2807: 2804: 2801: 2798: 2795: 2788: 2784: 2776: 2773: 2770: 2767: 2764: 2761: 2758: 2751: 2746: 2741: 2737: 2732: 2724: 2721: 2718: 2714: 2707: 2704: 2693: 2692: 2691: 2669: 2666: 2663: 2659: 2652: 2649: 2642: 2638: 2634: 2631: 2628: 2625: 2621: 2613: 2609: 2605: 2602: 2599: 2596: 2592: 2588: 2585: 2578: 2577: 2576: 2560: 2556: 2552: 2547: 2543: 2522: 2499: 2491: 2488: 2485: 2478: 2474: 2471: 2468: 2465: 2459: 2456: 2450: 2442: 2439: 2436: 2429: 2421: 2420: 2419: 2402: 2399: 2396: 2384: 2365: 2362: 2359: 2352: 2327: 2324: 2312: 2308: 2304: 2299: 2295: 2288: 2285: 2261: 2257: 2251: 2247: 2242: 2221: 2213: 2209: 2206: 2200: 2197: 2196: 2195: 2193: 2183: 2176: 2168: 2156: 2153: 2152: 2143: 2140: 2137: 2134: 2131: 2128: 2125: 2122: 2121: 2112: 2109: 2106: 2103: 2100: 2097: 2094: 2091: 2090: 2081: 2078: 2075: 2072: 2069: 2066: 2063: 2060: 2057: 2056: 2047: 2044: 2041: 2038: 2035: 2032: 2029: 2026: 2024:problem (OSP) 2023: 2020: 2018:problem (JSP) 2017: 2014: 2011: 2008: 2007: 1998: 1991: 1988: 1985: 1982: 1979: 1978: 1972: 1968: 1964: 1962: 1958: 1954: 1950: 1946: 1942: 1938: 1934: 1926: 1922: 1913: 1911: 1907: 1903: 1899: 1895: 1884: 1875: 1866: 1857: 1848: 1831: 1819: 1816: 1813: 1812: 1811: 1803: 1795: 1787: 1773: 1753: 1731: 1727: 1687: 1673: 1670: 1660: 1646: 1642: 1637: 1633: 1627: 1622: 1617: 1612: 1609: 1605: 1594: 1593: 1592: 1590: 1574: 1552: 1547: 1544: 1540: 1516: 1508: 1492: 1472: 1469: 1447: 1444: 1440: 1414: 1409: 1406: 1402: 1393: 1388: 1384: 1380: 1375: 1372: 1368: 1361: 1358: 1355: 1344: 1341: 1337: 1329: 1328: 1327: 1318: 1302: 1299: 1295: 1272: 1269: 1265: 1242: 1239: 1235: 1214: 1194: 1172: 1169: 1165: 1160: 1156: 1148: 1132: 1129: 1107: 1104: 1100: 1077: 1074: 1070: 1049: 1029: 1009: 987: 984: 980: 948: 943: 940: 936: 924: 919: 916: 912: 901: 873: 870: 866: 855: 850: 847: 843: 831: 826: 823: 819: 809: 804: 799: 796: 792: 784: 783: 782: 768: 748: 728: 719: 717: 699: 696: 692: 684: 680: 662: 659: 655: 647: 631: 611: 589: 584: 581: 577: 556: 533: 525: 521: 500: 480: 460: 444: 443:end procedure 441: 437: 433: 430: 426: 422: 419: 418:shortest path 408: 404: 395: 392: 387: 384: 373: 370: 365: 361: 359: 355: 351: 341: 339: 334: 330: 326: 322: 321:metaheuristic 318: 313: 311: 307: 302: 298: 294: 290: 287: 282: 280: 277:and internet 276: 272: 268: 264: 260: 256: 252: 251:probabilistic 248: 244: 241: 237: 233: 223: 215: 205: 202: 187: 184: 176: 166: 162: 156: 155: 149: 144: 135: 134: 125: 122: 114: 104: 100: 96: 90: 89: 84:This article 82: 73: 72: 67: 65: 58: 57: 52: 51: 46: 41: 32: 31: 19: 8431:Allee effect 8405:Nanorobotics 8395:Ant robotics 8372:Vicsek model 7931:Local search 7877:Edmonds–Karp 7833:Bellman–Ford 7603:minimization 7435:Gauss–Newton 7385:Quasi–Newton 7370:Trust region 7278:Optimization 7184: 7109: 7081: 7067: 7028: 6992: 6988: 6982: 6970: 6962: 6957: 6947: 6942: 6932: 6927: 6917: 6912: 6901: 6896: 6888: 6883: 6875: 6874:T. Stützle, 6870: 6862: 6857: 6847: 6842: 6833: 6823: 6814: 6806: 6801: 6793: 6788: 6778: 6773: 6765: 6760: 6750: 6745: 6736: 6731: 6714: 6710: 6704: 6669: 6663: 6644: 6638: 6619: 6609: 6594: 6589: 6578: 6573: 6562: 6561:WJ Gutjahr, 6557: 6540: 6529: 6524: 6487: 6483: 6473: 6456: 6447: 6412: 6406: 6393: 6380: 6367: 6354: 6319: 6315: 6292: 6281:. Retrieved 6263: 6256: 6243: 6234: 6221: 6208: 6195: 6182: 6169: 6156: 6147: 6112: 6108: 6098: 6063: 6057: 6045: 6036: 6001: 5995: 5980: 5945: 5939: 5926: 5913: 5900: 5864: 5844: 5831: 5819: 5806: 5793: 5780: 5771: 5758: 5745: 5732: 5719:M. 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Dorigo, 4753:M. Dorigo, 4496:convergence 4400:among ants; 4281:Tabu search 4199:multi-agent 4137:Distributed 4129:Data mining 3848:8-connected 3841:4-connected 2118:Set problem 1939:folding or 1887:Convergence 716:trail level 683:trail level 434:terminated 259:multi-agent 173:August 2018 165:introducing 111:August 2018 8511:Categories 8365:clustering 8258:philopatry 8236:salmon run 8231:Lessepsian 7782:algorithms 7290:heuristics 7282:Algorithms 6462:R. Schulin 6283:2018-10-09 6115:: 753251. 5721:T. Ibaraki 5426:: 95–112. 5310:C. Blum, " 5232:C. Blem, " 4831:. London: 4660:(1): 214. 4592:. London: 4573:References 4524:stochastic 4485:scheduling 4465:macs-vrptw 4415:ant system 4246:discarded. 301:pheromones 293:ant colony 289:algorithms 148:references 95:improve it 50:improve it 8486:Stigmergy 8466:Mutualism 8126:bait ball 7737:Paradigms 7636:quadratic 7353:Gradients 7315:Functions 7124:0128-3790 7045:, 1997. " 7025:M. 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Dorigo 4550:problems. 4516:algorithm 4507:AntOptima 4450:networks; 4376:stigmergy 4277:solution. 4228:stigmergy 4207:iteration 4189:populated 4054:τ 4028:ψ 3998:τ 3994:ψ 3976:τ 3969:ψ 3966:− 3957:← 3942:τ 3900:τ 3821:λ 3769:λ 3750:λ 3739:π 3730:⁡ 3721:π 3648:λ 3629:λ 3618:π 3609:⁡ 3543:λ 3495:λ 3454:⋅ 3384:− 3373:− 3332:− 3320:− 3306:− 3283:− 3237:− 3225:− 3211:− 3188:− 3133:− 3116:− 3048:− 3037:− 3025:− 2964:− 2953:− 2941:− 2895:− 2869:− 2846:− 2785:− 2774:− 2762:− 2622:∑ 2593:∑ 2553:∗ 2475:∗ 2466:∗ 2430:η 2353:τ 2305:∗ 1695:otherwise 1606:τ 1602:Δ 1541:τ 1537:Δ 1493:ρ 1441:τ 1403:τ 1399:Δ 1385:∑ 1369:τ 1362:ρ 1359:− 1350:← 1338:τ 1296:η 1266:τ 1236:η 1215:β 1101:η 1071:τ 1050:α 981:τ 949:β 937:η 925:α 913:τ 874:∈ 867:∑ 856:β 844:η 832:α 820:τ 761:to state 693:τ 656:η 624:to state 473:to state 432:while not 425:procedure 354:pheromone 310:honey bee 243:algorithm 99:verifying 56:talk page 8415:Symbrion 8377:BIO-LGCA 8180:tracking 8109:ant mill 8051:sort sol 8046:flocking 8010:Swarming 7968:Software 7845:Dijkstra 7676:exchange 7474:Hessians 7440:Gradient 7057:Archived 7027:, 1992. 6696:28648829 6568:, (2002) 6516:15710037 6346:27153578 6090:34664559 6028:11654036 5873:Archived 5853:Archived 5517:: 2000. 5171:Archived 5059:Archived 4887:(2008). 4859:(2007). 4827:(2008). 4588:(2008). 4526:problem; 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Ant colony optimization algorithms

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