## Ant algorithms for discrete optimization (1999)

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Venue: | ARTIFICIAL LIFE |

Citations: | 373 - 43 self |

### BibTeX

@ARTICLE{Dorigo99antalgorithms,

author = {Marco Dorigo and Gianni Di Caro and Luca M. Gambardella},

title = {Ant algorithms for discrete optimization},

journal = {ARTIFICIAL LIFE},

year = {1999},

pages = {137--172}

}

### Years of Citing Articles

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### Abstract

This article presents an overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies’ foraging behavior, and introduces the ant colony optimization (ACO) metaheuristic. In the first part of the article the basic biological findings on real ants are reviewed and their artificial counterparts as well as the ACO metaheuristic are defined. In the second part of the article a number of applications of ACO algorithms to combinatorial optimization and routing in communications networks are described. We conclude with a discussion of related work and of some of the most important aspects of the ACO metaheuristic.

### Citations

8313 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ... Moreover, during all the connection lifetime, the local daemon launches and coordinates exploring ants to re-route the connection paths in case of network congestion or failures. A genetic algorithm =-=[57, 64]-=- is used online to evolve the parameters # and # of the transition rule formula, which determine the relative weight of pheromone and link costs (because of this mechanism the algorithm is called ASGA... |

5369 |
Neural Networks for Pattern Recognition
- Bishop
- 1995
(Show Context)
Citation Context ...eural networks. Ant colonies, being composed of numerous concurrently and locally interacting units, can be seen as "connectionist" systems [42], the most famous examples of which are neural=-= networks [3, 61, 85]-=-. From a structural point of view, the parallel between the ACO meta-heuristic and a generic neural network is obtained by putting each state i visited by ants in correspondence with a neuron i, and t... |

4165 | Reinforcement Learning - An Introduction
- Sutton, Barto
- 1998
(Show Context)
Citation Context ... to note that the ACO-neural network algorithm does not correspond to any existing neural network model. The ACO-neural network is also reminiscent of networks solving reinforcement learning problems =-=[101]-=-. In reinforcement learning the only feedback available to the learner is a numeric signal (the reinforcement) that scores the result of actions. This is also the case in the ACO metaheuristic: The si... |

3933 | Optimization by simulated annealing
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ...go, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimization to note that this is different from what happens, for example, in stochastic hillclimbers [81] or in simulated annealing =-=[68]-=-, where (a) an acceptance criteria is defined and only those randomly generated moves that satisfy the criteria are executed, and (b) the search is usually performed in the space of the solutions. Mon... |

3037 |
H.: Adaption in Natural and Artificial Systems
- Holland
- 1975
(Show Context)
Citation Context ...the more the ants that use the shorter path. If appropriately used, autocatalysis can be a powerful mechanism in population-based optimization algorithms (e.g., in evolutionary computation algorithms =-=[44, 64, 82, 88]-=- autocatalysis is implemented by the selection/reproduction mechanism). In fact, it quickly favors the best individuals, so that they can direct the search process. When using autocatalysis some care ... |

2061 |
Genetic algorithms in search, optimization, and machine learning
- Goldberg
- 1989
(Show Context)
Citation Context ... Moreover, during all the connection lifetime, the local daemon launches and coordinates exploring ants to re-route the connection paths in case of network congestion or failures. A genetic algorithm =-=[59, 66] i-=-s used online to evolve the parameters α and β of the transition rule formula, which determine the relative weight of pheromone and link costs (because of this mechanism the algorithm is called ASGA... |

1930 |
Introduction to the Theory of Neural Computation
- Hertz, Krogh, et al.
- 1991
(Show Context)
Citation Context ...eural networks. Ant colonies, being composed of numerous concurrently and locally interacting units, can be seen as “connectionist” systems [43], the most famous examples of which are neural netwo=-=rks [3, 63, 88]-=-. From a structural point of view, the parallel between the ACO metaheuristic and a generic neural network is obtained by putting each state i visited by ants in correspondence with a neuron i, and th... |

936 | The Ant System: Optimization by a colony of cooperating agents
- Dorigo, Maniezzo, et al.
- 1996
(Show Context)
Citation Context ... i the ant chooses the node j to move to, and the arc (i, j) is added to the tour under construction. This step is repeated until the ant has completed its tour. Three AS algorithms have been defined =-=[19, 33, 40, 41]-=- that differ by the way pheromone trails are updated. These algorithms are called ant-density, ant-quantity, and ant-cycle. In ant-density and ant-quantity ants deposit pheromone while building a solu... |

905 |
Adaptation in Natural and Artificial Systems. Ann Arbor
- Holland
- 1975
(Show Context)
Citation Context ...the more the ants that use the shorter path. If appropriately used, autocatalysis can be a powerful mechanism in population-based optimization algorithms (e.g., in evolutionary computation algorithms =-=[45, 66, 85, 91] -=-autocatalysis is implemented by the selection/reproduction mechanism). In fact, it quickly favors the best individuals, 2 Workers are one of the castes in termite colonies. Although Grassé introduced... |

728 | Ant colony system: A cooperative learning approach to the traveling saleman problem
- Dorigo, Gambardella
- 1997
(Show Context)
Citation Context ...ties such as lookahead, local optimization, backtracking, and so on that cannot be found in real ants. In many implementations ants have been hybridized with local optimization procedures (see, e.g., =-=[38, 51, 98]-=-), while, so far, only Michel and Middendorf [78] have used a simple one-step lookahead function and there are no examples of backtracking procedures added to the basic ant capabilities, except for si... |

712 |
Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann--Holzboog
- Rechenberg
- 1973
(Show Context)
Citation Context ...the more the ants that use the shorter path. If appropriately used, autocatalysis can be a powerful mechanism in population-based optimization algorithms (e.g., in evolutionary computation algorithms =-=[45, 66, 85, 91] -=-autocatalysis is implemented by the selection/reproduction mechanism). In fact, it quickly favors the best individuals, 2 Workers are one of the castes in termite colonies. Although Grassé introduced... |

525 |
Tabu Search - part
- GLOVER
- 1990
(Show Context)
Citation Context ... node j only arc (i, j), and not (j, i), is updated. 9 The term tabu list is used here to indicate a simple memory that contains the set of already visited cities and has no relation with tabu search =-=[57, 58]. A-=-rtificial Life Volume 5, Number 2 149 (2) (3)sM. Dorigo, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimization It is clear from Equation 4 that the value �τ k ij (t) depends on... |

506 |
The Connection Machine
- Hillis
- 1985
(Show Context)
Citation Context ...diffusion models adopted in the field of parallel genetic algorithms; see, for example, reviews in [16, 39]). Early experiments with parallel versions of AS for the TSP on the Connection Machine CM-2 =-=[65]-=- adopted the approach of attributing a single processing unit to each ant [4]. Artificial Life Volume 5, Number 2 161sM. Dorigo, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimizat... |

479 |
Simulation and the Monte Carlo Method
- Rubinstein
- 1981
(Show Context)
Citation Context ..., and (b) the search is usually performed in the space of the solutions. Monte Carlo simulation. ACO algorithms can be interpreted as parallel replicated Monte Carlo systems [93]. Monte Carlo systems =-=[87]-=- are general stochastic simulation systems, that is, techniques performing repeated sampling experiments on the model of the system under consideration by making use of a stochastic component in the s... |

433 | Handbook of Evolutionary Computation
- Bäck, Fogel, et al.
- 1997
(Show Context)
Citation Context ...the more the ants that use the shorter path. If appropriately used, autocatalysis can be a powerful mechanism in population-based optimization algorithms (e.g., in evolutionary computation algorithms =-=[45, 66, 85, 91] -=-autocatalysis is implemented by the selection/reproduction mechanism). In fact, it quickly favors the best individuals, 2 Workers are one of the castes in termite colonies. Although Grassé introduced... |

373 |
New methods to color the vertices of a graph
- Brélaz
- 1979
(Show Context)
Citation Context ...graph G so that the number q of colors used is minimum. The algorithm they propose, called ANTCOL, makes use of wellknown graph-coloring heuristics such as recursive large first (RLF) [72] and DSATUR =-=[8]-=-. Costa and Hertz tested ANTCOL on a set of random graphs and compared it with some of the best available heuristics. Results have shown that ANTCOL performance is comparable to that obtained by the o... |

343 | The ant colony optimization metaheuristic
- Dorigo, DiCaro
- 1999
(Show Context)
Citation Context ...tle, if any, difference between using or not using pheromone trails. A more formal definition of the ACO metaheuristic, as well as of the class of problems to which it can be applied, can be found in =-=[35]-=-. Artificial Life Volume 5, Number 2 145sM. Dorigo, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimization 3 Applications of ACO Algorithms There are now available numerous success... |

332 |
The traveling salesman problem
- Lawler, Lenstra, et al.
- 1995
(Show Context)
Citation Context ...e problem are given once and for all when the problem is defined and do not change while the problem is being solved. A paradigmatic example of such problems is the classic traveling salesman problem =-=[67, 71, 86]-=-, in which city locations and their relative distances are part of the problem definition and do not change at run time. On the contrary, dynamic problems are defined as a function of some quantities ... |

319 |
Parallel Distributed Processing
- McClelland, Rummelhart
- 1986
(Show Context)
Citation Context ...eural networks. Ant colonies, being composed of numerous concurrently and locally interacting units, can be seen as “connectionist” systems [43], the most famous examples of which are neural netwo=-=rks [3, 63, 88]-=-. From a structural point of view, the parallel between the ACO metaheuristic and a generic neural network is obtained by putting each state i visited by ants in correspondence with a neuron i, and th... |

302 |
Tabu Search - Part II
- Glover
- 1990
(Show Context)
Citation Context ... node j only arc (i, j), and not (j, i), is updated. 9 The term tabu list is used here to indicate a simple memory that contains the set of already visited cities and has no relation with tabu search =-=[57, 58]. A-=-rtificial Life Volume 5, Number 2 149 (2) (3)sM. Dorigo, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimization It is clear from Equation 4 that the value �τ k ij (t) depends on... |

288 |
The traveling salesman problem: A case study
- Johnson, McGeoch
- 1997
(Show Context)
Citation Context ...e problem are given once and for all when the problem is defined and do not change while the problem is being solved. A paradigmatic example of such problems is the classic traveling salesman problem =-=[67, 71, 86]-=-, in which city locations and their relative distances are part of the problem definition and do not change at run time. On the contrary, dynamic problems are defined as a function of some quantities ... |

282 | AntNet: Distributed stigmergetic control for communications networks
- Caro, Dorigo
- 1998
(Show Context)
Citation Context ...ve used a simple one-step lookahead function and there are no examples of backtracking procedures added to the basic ant capabilities, except for simple recovery procedures used by Di Caro and Dorigo =-=[26, 29]-=-. 5 4 In reality, some real ants have a similar behavior: They deposit more pheromone in case of richer food sources. 5 Usually, backtracking strategies are suitable to solve constraint satisfaction p... |

279 |
Computer solutions of the traveling salesman problem
- Lin
- 1965
(Show Context)
Citation Context ... arcs used by the ant that found the best tour from the beginning of the trial. In ACS-3-opt the daemon first activates a local search procedure based on a variant of the 3-opt local search procedure =-=[73] to improve th-=-e solutions generated by the ants and then performs offline pheromone trail update. The offline pheromone trail update rule is τij(t) ← (1 − ρ)τij(t) + ρ�τij(t) (7) where ρ ∈ (0, 1] is a... |

268 |
Connectionist models and their properties
- Feldman, Ballard
- 1982
(Show Context)
Citation Context ...ting resources in unpromising regions of the search space. Neural networks. Ant colonies, being composed of numerous concurrently and locally interacting units, can be seen as “connectionist” syst=-=ems [43]-=-, the most famous examples of which are neural networks [3, 63, 88]. From a structural point of view, the parallel between the ACO metaheuristic and a generic neural network is obtained by putting eac... |

254 |
Artificial Intelligence: A New Synthesis
- Nilsson
- 1998
(Show Context)
Citation Context ...Life Volume 5, Number 2sM. Dorigo, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimization to note that this is different from what happens, for example, in stochastic hillclimbers =-=[81]-=- or in simulated annealing [68], where (a) an acceptance criteria is defined and only those randomly generated moves that satisfy the criteria are executed, and (b) the search is usually performed in ... |

253 |
Learning Automata: An Introduction
- Narendra, Thathachar
- 1989
(Show Context)
Citation Context ...ation, and finally (d) the process is iterated going back to step (b). The similitude with ACS is striking. Stochastic learning automata. This is one of the oldest approaches to machine learning (see =-=[80]-=- for a review). An automaton is defined by a set of possible actions and a vector of associated probabilities, a continuous set of inputs and a learning algorithm to learn input-output associations. A... |

239 |
Distributed optimization by ant colonies
- Colomi, Dorigo, et al.
- 1992
(Show Context)
Citation Context ... i the ant chooses the node j to move to, and the arc (i, j) is added to the tour under construction. This step is repeated until the ant has completed its tour. Three AS algorithms have been defined =-=[19, 33, 40, 41]-=- that differ by the way pheromone trails are updated. These algorithms are called ant-density, ant-quantity, and ant-cycle. In ant-density and ant-quantity ants deposit pheromone while building a solu... |

220 |
Assignment problems and the location of economic activities
- Koopmans, Beckmann
- 1957
(Show Context)
Citation Context ...nment problem (QAP) is the problem of assigning n facilities to n locations so that the cost of the assignment, which is a function of the way facilities have been assigned to locations, is minimized =-=[67]-=-. The QAP was, after the TSP, the first problem to be attacked by an AS-like algorithm. This was a reasonable choice, since the QAP is a generalization of the TSP. 10 Maniezzo, Colorni and Dorigo (199... |

210 |
Scheduling of vehicles from a central depot to a number of delivery points
- Clarke, Wright
- 1964
(Show Context)
Citation Context ...ned by Bullnheimer, Hartl, and Strauss for the above problem, is a direct extension of AS based on their ASrank algorithm discussed in Section 3.1.1. They used various standard heuristics for the VRP =-=[18, 82]-=- and added a simple local optimizer based on the 2-opt heuristic [24]. They also adapted the way the tabu list is built by taking into consideration the constraints on the maximum total tour length L ... |

199 |
Numerische Optimierung von Computer--Modellen mittels der Evolutionsstrategie
- Schwefel
- 1977
(Show Context)
Citation Context |

192 | Ant colonies for the traveling salesman problem, BioSystems
- Dorigo, Gambardella
- 1997
(Show Context)
Citation Context ...ly ordered. Problem Authors Year Main Algorithm name references name Traveling Dorigo, Maniezzo, & Colorni 1991 [33, 40, 41] AS salesman Gambardella & Dorigo 1995 [49] Ant-Q Dorigo & Gambardella 1996 =-=[37, 38, 50] -=-ACS & ACS-3-opt Stützle & Hoos 1997 [98, 97] MMAS Bullnheimer, Hartl, & Strauss 1997 [12] ASrank Quadratic Maniezzo, Colorni, & Dorigo 1994 [77] AS-QAP assignment Gambardella, Taillard, & Dorigo 1997... |

190 |
La reconstruction du nid et les coordinations interindividuelles chez bellicositermes natalensis et cubitermes sp. La théorie de la stigmergie: essai d’interprétation du comportement des termites constructeurs
- Grassé
- 1959
(Show Context)
Citation Context ... property of the ant colony. It is also interesting to note that ants can perform this specific behavior using a simple form of indirect communication mediated by pheromone laying, known as stigmergy =-=[62]-=-. 1 The above-described experiments have been run in strongly constrained conditions. A formal proof of the pheromone-driven shortest path-finding behavior in the general case is missing. Bruckstein e... |

186 | Removing the genetics from the standard genetic algorithm
- Baluja, Caruana
- 1995
(Show Context)
Citation Context ...age of ants that selected the shorter path. After Goss et al. 1989 [60]. equation: Um+1 = Um + 1, if ψ ≤ PU , Um+1 = Um otherwise, where ψ is a random variable uniformly distributed over the inter=-=val [0,1]-=-. Monte Carlo simulations were run to test the correspondence between this model and the real data: Results of simulations were in agreement with the experiments with real ants when parameters were se... |

178 |
Learning with Delayed Rewards
- Watkins
- 1989
(Show Context)
Citation Context ...y better on symmetric problems and ACS-3-opt on asymmetric ones. To conclude, we mention that ACS was the direct successor of Ant-Q (1995) [35, 48], an algorithm that tried to merge AS and Q-learning =-=[99]-=- properties. In fact, Ant-Q di#ers from ACS only in the value # 0 used by ants to perform online step-by-step pheromone updates. The idea was to update pheromone trails with a value which was a predic... |

177 | Antbased load balancing in telecommunications networks
- Schoonderwoerd, Holland, et al.
- 1997
(Show Context)
Citation Context ...owing. Role of the local heuristic. Most of the ACO algorithms presented combine pheromone trails with local heuristic values to obtain ant-decision tables. An exception are the Schoonderwoerd et al. =-=[89, 90]-=- ABC algorithm and all the derived algorithms (ABCsmart ants, ABC-backward, regular ants, and CAF) in which ant-decision tables are obtained using only pheromone trail values. Current wisdom indicates... |

141 | The ant system applied to the quadratic assignment problem
- Maniezzo, Colorni
- 1999
(Show Context)
Citation Context ...uss 1997 [12] ASrank Quadratic Maniezzo, Colorni, & Dorigo 1994 [77] AS-QAP assignment Gambardella, Taillard, & Dorigo 1997 [53, 54] HAS-QAPa Stützle & Hoos 1998 [99] MMAS-QAP Maniezzo & Colorni 1998=-= [76]-=- AS-QAPb Maniezzo 1998 [75] ANTS-QAP Job-shop scheduling Colorni, Dorigo, & Maniezzo 1994 [20] AS-JSP Vehicle Bullnheimer, Hartl, & Strauss 1996 [15, 11, 13] AS-VRP routing Gambardella, Taillard, & Ag... |

140 | Macs-vrptw: A multiple ant colony system for vehicle routing problems with time windows
- Gambardella, Taillard, et al.
- 1999
(Show Context)
Citation Context ...aniezzo 1998 [75] ANTS-QAP Job-shop scheduling Colorni, Dorigo, & Maniezzo 1994 [20] AS-JSP Vehicle Bullnheimer, Hartl, & Strauss 1996 [15, 11, 13] AS-VRP routing Gambardella, Taillard, & Agazzi 1999 =-=[52]-=- HAS-VRP Sequential ordering Gambardella & Dorigo 1997 [51] HAS-SOP Graph coloring Costa & Hertz 1997 [22] ANTCOL Shortest common Michel & Middendorf supersequence 1998 [78, 79] AS-SCS a HAS-QAP is an... |

132 |
The complexity of flowshop and jobshop scheduling
- Garey, Johnson, et al.
- 1976
(Show Context)
Citation Context ... that of assigning operations to machines so that the maximum of the completion times of all operations is minimized and no two jobs are processed at the same time on the same machine. JSP is NP-hard =-=[55]-=-. 10 In fact, the TSP can be seen as the problem of assigning to each of n cities a different number chosen between 1 and n. QAP, as the TSP, is NP-hard [92]. 11 HAS-QAP is an ant algorithm that, alth... |

127 | Positive feedback as a search strategy
- Dorigo, Maniezzo, et al.
- 1991
(Show Context)
Citation Context ...escribed. We conclude with a discussion of related work and of some of the most important aspects of the ACO meta-heuristic. 1 Introduction Ant algorithms were first proposed by Dorigo and colleagues =-=[33, 39]-=- as a multi-agent approach to di#cult combinatorial optimization problems like the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). There is currently a lot of ongoing acti... |

124 |
Ant can colour graphs
- Costa, Hertz
- 1997
(Show Context)
Citation Context ...eimer, Hartl, & Strauss 1996 [15, 11, 13] AS-VRP routing Gambardella, Taillard, & Agazzi 1999 [52] HAS-VRP Sequential ordering Gambardella & Dorigo 1997 [51] HAS-SOP Graph coloring Costa & Hertz 1997 =-=[22]-=- ANTCOL Shortest common Michel & Middendorf supersequence 1998 [78, 79] AS-SCS a HAS-QAP is an ant algorithm that does not follow all the aspects of the ACO metaheuristic. b This is a variant of the o... |

122 | The self-organizing exploratory pattern of the argentine ant
- Deneubourg, Aron, et al.
- 1990
(Show Context)
Citation Context ...passages on each of the two branches per unit of time as a function of time. Eventually, after an initial short transitory phase, the upper branch becomes the most used. After Deneubourg et al., 1990 =-=[25]. -=-To study in controlled conditions the ants’ foraging behavior, the binary bridge experiment has been set up by Deneubourg et al. [25] (see Figure 1a). The nest of a colony of ants of the species Lin... |

119 | Antnet: A mobile agents approach to adaptive routing
- Caro, Dorigo
- 1997
(Show Context)
Citation Context ...ve used a simple one-step lookahead function and there are no examples of backtracking procedures added to the basic ant capabilities, except for simple recovery procedures used by Di Caro and Dorigo =-=[26, 29]-=-. 5 4 In reality, some real ants have a similar behavior: They deposit more pheromone in case of richer food sources. 5 Usually, backtracking strategies are suitable to solve constraint satisfaction p... |

118 |
Scheduling problems and travelling salesman : the genetic edge recombination operator
- Whitley, Starkweather, et al.
- 1989
(Show Context)
Citation Context ...nging from 30 to 75 cities). The results [40, 41] were very interesting and disappointing at the same time. AS was able to find and improve the best solution found by a genetic algorithm for Oliver30 =-=[106]-=-, a 30-city problem, and it had a performance similar or better than that of some general-purpose heuristics with which it was compared. Unfortunately, for problems of growing dimensions AS never reac... |

108 |
Adaptation in Natural and Arti Systems. The
- Holland
- 1975
(Show Context)
Citation Context ...the more the ants that use the shorter path. If appropriately used, autocatalysis can be a powerful mechanism in population-based optimization algorithms (e.g., in evolutionary computation algorithms =-=[44, 64, 82, 88]-=- autocatalysis is implemented by the selection/reproduction mechanism). In fact, it quickly favors the best individuals, so that they can direct the search process. When using autocatalysis some care ... |

105 | Ant-Q: A reinforcement learning approach to the traveling salesman problem
- Gambardella, Dorigo
- 1995
(Show Context)
Citation Context ...tion by application and chronologically ordered. Problem Authors Year Main Algorithm name references name Traveling Dorigo, Maniezzo, & Colorni 1991 [33, 40, 41] AS salesman Gambardella & Dorigo 1995 =-=[49] -=-Ant-Q Dorigo & Gambardella 1996 [37, 38, 50] ACS & ACS-3-opt Stützle & Hoos 1997 [98, 97] MMAS Bullnheimer, Hartl, & Strauss 1997 [12] ASrank Quadratic Maniezzo, Colorni, & Dorigo 1994 [77] AS-QAP as... |

104 | The MAX –MIN ant system and local search for the traveling salesman problem
- Stützle, Hoos
- 1997
(Show Context)
Citation Context ...ties such as lookahead, local optimization, backtracking, and so on that cannot be found in real ants. In many implementations ants have been hybridized with local optimization procedures (see, e.g., =-=[38, 51, 98]-=-), while, so far, only Michel and Middendorf [78] have used a simple one-step lookahead function and there are no examples of backtracking procedures added to the basic ant capabilities, except for si... |

103 | An improved ant system algorithm for the vehicle routing problem
- Bullnheimer, Hartl, et al.
- 1997
(Show Context)
Citation Context ... & Hoos 1998 [99] MMAS-QAP Maniezzo & Colorni 1998 [76] AS-QAPb Maniezzo 1998 [75] ANTS-QAP Job-shop scheduling Colorni, Dorigo, & Maniezzo 1994 [20] AS-JSP Vehicle Bullnheimer, Hartl, & Strauss 1996 =-=[15, 11, 13]-=- AS-VRP routing Gambardella, Taillard, & Agazzi 1999 [52] HAS-VRP Sequential ordering Gambardella & Dorigo 1997 [51] HAS-SOP Graph coloring Costa & Hertz 1997 [22] ANTCOL Shortest common Michel & Midd... |

100 |
Ant-like agents for load balancing in telecommunication networks
- Schoonderwoerd, Holland, et al.
- 1997
(Show Context)
Citation Context ...binatorial optimization problems. Classification by application and chronologically ordered. Problem name Authors Year Main Algorithm references name Connection-oriented Schoonderwoerd, Holland, 1996 =-=[90, 89] -=-ABC network routing Bruten, & Rothkrantz White, Pagurek, & Oppacher 1998 [105] ASGA Di Caro & Dorigo 1998 [30] AntNet-FS Bonabeau, Henaux, Guérin, 1998 [6] ABC-smart Snyers, Kuntz, & Theraulaz ants C... |

98 |
Ant system for job-shop scheduling
- Colorni, Dorigo, et al.
- 1994
(Show Context)
Citation Context ...ella, Taillard, & Dorigo 1997 [53, 54] HAS-QAPa Stützle & Hoos 1998 [99] MMAS-QAP Maniezzo & Colorni 1998 [76] AS-QAPb Maniezzo 1998 [75] ANTS-QAP Job-shop scheduling Colorni, Dorigo, & Maniezzo 1994=-= [20]-=- AS-JSP Vehicle Bullnheimer, Hartl, & Strauss 1996 [15, 11, 13] AS-VRP routing Gambardella, Taillard, & Agazzi 1999 [52] HAS-VRP Sequential ordering Gambardella & Dorigo 1997 [51] HAS-SOP Graph colori... |

95 |
Genetic and hybrid algorithms for graph coloring
- Fleurent, Fefland
- 1996
(Show Context)
Citation Context ...e other heuristics: On 20 randomly generated graphs of 100 nodes with any two nodes connected with probability 0.5 the average number of colors used by ANTCOL was 15.05, whereas the best known result =-=[23, 44]-=- is 14.95. More research will be necessary to establish whether the proposed use of two pheromone trails can be a useful addition to ACO algorithms. 13 Consider for example the set L ={bcab, bccb, baa... |