## Ant algorithms for discrete optimization (1999)

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Venue: | ARTIFICIAL LIFE |

Citations: | 372 - 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

### OpenURL

### 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

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(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... |

727 | Gambardella : Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem
- Dorigo, M
- 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... |

437 | Evolutionary Computation
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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... |

374 |
New methods to color the vertices of a graph
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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... |

342 | The ant colony optimization meta-heuristic
- Dorigo, Caro
- 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... |

282 | AntNet: Distributed Stigmergetic Control for Communication 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... |

268 |
Connectionist models and their properties
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(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... |

239 |
Distributed optimization by ant colonies
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(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... |

209 |
Scheduling of vehicles from a central depot to a number of delivery points
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(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 ... |

191 | Ant colonies for the traveling salesman problem
- 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... |

186 | Removing the genetics from the standard genetic algorithm
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- 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... |

123 |
Ants 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... |

118 | 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... |

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... |

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... |

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... |

97 |
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... |

80 |
Optimization, Learning and Natural Algorithms (in Italian
- Dorigo
- 1992
(Show Context)
Citation Context ... Lugano Switzerland luca@idsia.ch Keywords ant algorithms, ant colony optimization, swarm intelligence, metaheuristics, natural computation Ant algorithms were first proposed by Dorigo and colleagues =-=[33, 40]-=- as a multi-agent approach to difficult combinatorial optimization problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). There is currently much ongoing act... |

79 | Genetic local search algorithms for solving symmetric and asyimmetric traveling salesman problems
- Freisleben, Merz
- 1996
(Show Context)
Citation Context ...erms of quality of the solutions generated and of CPU time required to generate them, was the best one. ACS-3-opt’s performance was compared to that of the genetic algorithm (with local optimization=-=) [47, 48]-=- that won the First International Contest on Evolutionary Optimization [2]. The two algorithms showed similar performance with the genetic algorithm behaving slightly better on symmetric problems and ... |

78 | Solving symmetric and asymmetric TSPs by ant colonies
- Gambardella, Dorigo
- 1996
(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... |

76 | Applying the ant system to the vehicle routing problem
- Bullnheimer, Hartl, et al.
- 1998
(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... |

72 | Theory and algorithms for plan merging
- Foulser, Li, et al.
- 1992
(Show Context)
Citation Context ...tions; every fixed number of iterations they exchange the best solution found). AS-SCS-LM (i.e., AS-SCS with LM heuristic, lookahead, and island model of computation) was compared in [78] with the MM =-=[46]-=- and LM heuristics, as well as with a recently proposed genetic algorithm specialized for the SCS problem. On the great majority of the test problems AS-SCS-LM turned out to be the best-performing alg... |

66 |
A method for solving traveling salesman problems
- Croes
- 1958
(Show Context)
Citation Context ... 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 of a vehicle and its maximum capacity D. Comparisons on a set of stan... |

56 | New genetic local search operators for the traveling, salesman problem
- Freisleben, Merz
- 1996
(Show Context)
Citation Context ...erms of quality of the solutions generated and of CPU time required to generate them, was the best one. ACS-3-opt’s performance was compared to that of the genetic algorithm (with local optimization=-=) [47, 48]-=- that won the First International Contest on Evolutionary Optimization [2]. The two algorithms showed similar performance with the genetic algorithm behaving slightly better on symmetric problems and ... |

51 | Routing in telecommunications networks with ‘‘Smart’’ ant-like agents (Working paper 98-01-003). Santa Fe, A Comprehensive Overview of the Applications of Artificial LifeK.-J. Kim and S.-B. ChoNM: Santa Fe Institute
- Bonabeau, Henaux, et al.
- 1998
(Show Context)
Citation Context ...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 Connectionless Di Caro & Dorigo 1997 [26, 29, 32] AntNet & network routing AntNet-FA Subramanian, Druschel, & Chen 1997 [100] Regular ants Heusse, Guérin, Sn... |

50 |
Neural Networks for Pattern Recognition. Oxford Univ
- 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 [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... |

48 |
A new rank-based version of the ant system: a computational study
- Bullnheimer, Hartl, et al.
- 1997
(Show Context)
Citation Context ... 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 [53, 54] HAS-QAPa Stützle & Hoos 1998 [99] MMAS-QAP Maniezzo & Colorni 1998 [76] AS-QAPb ... |

47 | Mobile agents for adaptive routing - Caro, Dorigo - 1998 |

42 |
From Natural to Artificial Swarm Intelligence
- Bonabeau, Dorigo, et al.
- 1999
(Show Context)
Citation Context ... the quadratic assignment problem (QAP). There is currently much ongoing activity in the scientific community to extend and apply ant-based algorithms to many different discrete optimization problems =-=[5, 21]-=-. Recent applications cover problems such as vehicle routing, sequential ordering, graph coloring, routing in communications networks, and so on. Ant algorithms were inspired by the observation of rea... |

41 | Two ant colony algorithms for best-effort routing in datagram networks
- Caro, Dorigo
- 1998
(Show Context)
Citation Context ...rantz White, Pagurek, & Oppacher 1998 [105] ASGA Di Caro & Dorigo 1998 [30] AntNet-FS Bonabeau, Henaux, Guérin, 1998 [6] ABC-smart Snyers, Kuntz, & Theraulaz ants Connectionless Di Caro & Dorigo 1997=-= [26, 29, 32] -=-AntNet & network routing AntNet-FA Subramanian, Druschel, & Chen 1997 [100] Regular ants Heusse, Guérin, Snyers, & Kuntz 1998 [64] CAF van der Put & Rothkrantz 1998 [102, 103] ABC-backward Artificial... |

31 |
Parallelization strategies for the ant system
- Bullnheimer, Kotsis, et al.
- 1997
(Show Context)
Citation Context ...peed-up was nearly linear when increasing the number of processors, and this behavior did not change significatively for increasing problem dimensions. More recently, Bullnheimer, Kotsis, and Strauss =-=[14]-=- proposed two coarse-grained parallel versions of AS. The first one, called Synchronous Parallel Implementation (SPI), is basically the same as the one implemented by Bolondi and Bondanza [4], while t... |

29 |
New ideas in optimization
- Dorigo, Caro
- 1999
(Show Context)
Citation Context ... the quadratic assignment problem (QAP). There is currently much ongoing activity in the scientific community to extend and apply ant-based algorithms to many different discrete optimization problems =-=[5, 21]-=-. Recent applications cover problems such as vehicle routing, sequential ordering, graph coloring, routing in communications networks, and so on. Ant algorithms were inspired by the observation of rea... |

29 | Ant colonies for adaptive routing in packet-switched communications networks - Caro, Dorigo - 1998 |

25 |
Results of the first international contest on evolutionary optimisation (1st ICEO
- Bersini, Dorigo, et al.
- 1996
(Show Context)
Citation Context ... them, was the best one. ACS-3-opt’s performance was compared to that of the genetic algorithm (with local optimization) [47, 48] that won the First International Contest on Evolutionary Optimizatio=-=n [2]-=-. The two algorithms showed similar performance with the genetic algorithm behaving slightly better on symmetric problems and ACS-3-opt on asymmetric ones. To conclude, we mention that ACS was the dir... |

23 |
Parallel genetic algorithms: Introduction and overview of the current research
- Dorigo, Maniezzo
- 1993
(Show Context)
Citation Context ... in other populationbased algorithms can be easily adapted to the ACO structure (e.g., migration and 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... |

19 |
Why the ant trails look so straight and nice
- Bruckstein
- 1993
(Show Context)
Citation Context ...e 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 et al. =-=[9, 10] c-=-onsider the shortest path-finding problem in absence of obstacles for ants driven by visual clues and not by pheromones and prove the convergence of the ants’ path to the straight line. Artificial L... |

18 | An adaptive multi-agent routing algorithm inspired by ants behavior
- Caro, Dorigo
- 1998
(Show Context)
Citation Context ...rformance in terms of both throughput and packet delays. Moreover, it appears to be very robust to the ant production rate and its impact on network resources is almost negligible. Di Caro and Dorigo =-=[27, 30] r-=-ecently developed an enhanced version of AntNet, called AntNet-FA. 21 AntNet-FA is the same as AntNet except for the following two aspects. First, forward ants are substituted by so-called “flying a... |

18 | A study of some properties of Ant-Q
- Dorigo, Gambardella
- 1996
(Show Context)
Citation Context ...owed similar performance with the genetic algorithm behaving slightly better on symmetric problems and ACS-3-opt on asymmetric ones. To conclude, we mention that ACS was the direct successor of Ant-Q =-=[36, 49],-=- an algorithm that tried to merge AS and Q-learning [104] properties. In fact, Ant-Q differs from ACS only in the value τ0 used by ants to perform online step-by-step pheromone updates. The idea was ... |

14 |
Parallelizzazione di un algoritmo per la risoluzione del problema del commesso viaggiatore. Master’s thesis, Dipartimento di Elettronica e Informazione, Politecnico di
- Bolondi, Bondanza
- 1993
(Show Context)
Citation Context ... 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 Optimization Experimental results showed that communication overhead can be a major pr... |

14 | Improved heuristics and a genetic algorithm for finding short supersequences. OR-Spektrum
- Branke, Middendorf, et al.
- 1998
(Show Context)
Citation Context ...e value returned by the lookahead function takes the place of the heuristic value η in the probabilistic decision rule (Equation 3). Also, in AS-SCS the value returned by a simple heuristic called LM=-= [7]-=- is factorized in the pheromone trail term. Michel and Middendorf [78,79] further improved their algorithm by the use of an island model of computation (i.e., different colonies of ants work on the sa... |

12 |
Positive feedback as a search strategy, Tech. Rep. 91016, Dipartimento di Elettronica, Politecnico di
- Dorigo, Maniezzo, et al.
- 1991
(Show Context)
Citation Context ... Lugano Switzerland luca@idsia.ch Keywords ant algorithms, ant colony optimization, swarm intelligence, metaheuristics, natural computation Ant algorithms were first proposed by Dorigo and colleagues =-=[33, 40]-=- as a multi-agent approach to difficult combinatorial optimization problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). There is currently much ongoing act... |

12 |
An inexact algorithm for the sequential ordering problem
- Escudero
- 1988
(Show Context)
Citation Context ...n. Artificial Life Volume 5, Number 2 155sM. Dorigo, G. Di Caro, and L. M. Gambardella Ant Algorithms for Discrete Optimization 3.1.7 Sequential Ordering Problem The sequential ordering problem (SOP) =-=[42]-=- consists of finding a minimum weight Hamiltonian path on a directed graph with weights on the arcs and on the nodes, subject to precedence constraints among nodes. It is very similar to an asymmetric... |

11 | Probabilistic pursuits on the grid
- Bruckstein, Mallows, et al.
- 1997
(Show Context)
Citation Context ...e 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 et al. =-=[9, 10] c-=-onsider the shortest path-finding problem in absence of obstacles for ants driven by visual clues and not by pheromones and prove the convergence of the ants’ path to the straight line. Artificial L... |

11 |
Extending AntNet for best-effort Quality-ofService routing. Unpublished presentation at ANTS’98
- Caro, Dorigo
(Show Context)
Citation Context ...ear 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 Connectionless Di Caro & Dorigo 1997 [26, 29, 32] AntNet & network routing AntNet-FA Subramanian, Druschel, & Ch... |

7 |
Embedding of a sequential algorithm within an evolutionary algorithm for coloring problems in graphs
- Costa, Hertz, et al.
- 1995
(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... |

7 |
Parallel ant system: An experimental study. Unpublished manuscript
- Dorigo
- 1993
(Show Context)
Citation Context ...n fact, the algorithm’s behavior was not impressive and scaled up very badly when increasing the problem dimensions. Better results were obtained on a coarsegrained parallel network of 16 transputer=-=s [4, 34]-=-. The idea here was to divide the colony into p subcolonies, where p is the number of available processors. Each subcolony acts as a complete colony and therefore implements a standard AS algorithm. A... |

4 |
Tourenplanung mit dem ant system
- Bullnheimer, Strauss
- 1996
(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... |

4 |
Parallel architectures and intrinsically parallel algorithms: Genetic algorithms
- Campanini, Caro, et al.
- 1994
(Show Context)
Citation Context ... in other populationbased algorithms can be easily adapted to the ACO structure (e.g., migration and 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... |

4 | A simple learning algorithm for the traveling salesman problem
- Chen
- 1997
(Show Context)
Citation Context ...evel of stochasticity in signal propagation play the role of a learning rate, controlling the balance between exploration and exploitation. Finally, it is worth making a reference to the work of Chen =-=[17]-=-, who proposed a neural network approach to TSP that bears important similarities with the ACO approach. Like in ACO algorithms, Chen builds a tour in an incremental way, according to synaptic strengt... |