Dorigo, M. & Gambardella, L. M. (1997), `Ant colonies for the traveling salesman problem', BioSystems 43, 73--81.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....more pheromone on the same trail, causing even more ants to be attracted. In essence, therefore, swarm intelligence paradigms use positive reinforcement as a search strategy. The Ant Colony System (ACS) algorithm, a swarm based optimization procedure, was first proposed by Dorigo and Gambardella [5] for solving the celebrated traveling salesman problem (TSP) Experimental studies carried out by the authors indicate that the ACS algorithm outperforms other evolutionary techniques like simulated annealing, elastic nets and self organizing maps on the TSP. Before describing the ACS procedure ....

....(t) # = pheromone decay coe#cient, # (0, 1] q = uniformly distributed random variable over the interval [0,1] q 0 = tunable parameter, q 0 [0, 1] Note that the local visibility parameter, # ij , is defined to be the inverse of P ij and not d ij (see eqn. 1) as was used by Dorigo et al. [5] for solving the TSP. This definition allows for the e#ect of the channel loss factor, #, to be incorporated into local visibility. IV. TREE BUILDING BY AN ANT We begin by defining the following sets: V = set of all nodes in the network s = transmission step number = new nodes reached in ....

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) Dorigo M. and L. M. Gambardella , "Ant Colonies for the Traveling Salesman Problem," BioSystems

....AS has more recently been used on the Quadratic Assignment Problem [12] and the Vehicle Routing Problem [2] Ant Colony System. To improve upon the results of the Ant System on various optimization problems, the Ant Colony System (ACS) was developed. The rst use of the ACS was also on the TSP [5, 6]. An ACS is a colony of ants. Just as in the AS, ants form solutions by moving from one city to another city until all cities have been visited. They still prefer cities that are connected by short edges containing a high amount of pheromone. In the ACS, however, edges are updated after an ant has ....

M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. Biosystems, 43:73-81, 1997.

....application inspired by ants and perhaps by any insect society. Their initial Ant System (AS) Colorni et al. 1992b; 1992a; Dorigo et al. 1996] showed promising results with the Traveling Salesperson Problem (TSP) And they later refined their approach in their Ant Colony System (ACS) Dorigo and Gambardella, 1997a; 1997b] and through the addition of some local search procedures this ACS is competitive with some of the best known heuristics for the TSP. The general idea behind the class of ACO algorithms for the TSP is as follows (also see Figure 1) Begin by laying some initial quantities of artificial ....

....combinatorial optimization problems. One area particularly important to manufacturing where there has been a lot of work is scheduling. There is at least one ACObased approach to almost any scheduling problem you can think of. Some of these include: the sequential ordering problem [Gambardella and Dorigo, 1997] , job shop scheduling [van der Zwaan and Marques, 1999] flow shop scheduling [St utzle, 1998] vehicle routing [Bullnheimer et al. 1999; Gambardella et al. 1999] bus driver scheduling [Forsyth and Wren, 1997] tardiness scheduling problems [Bauer et al. 1999; den Besten et al. 2000] ....

M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--89, 1997.

....return journey more often. The pheromone on the shorter path will therefore be more strongly reinforced and will eventually become the preferred route for the stream of ants. The works of Colorni, Dorigo Maniezzo, 1991] Dorigo, Maniezzo Colorni, 1991] Dorigo, Maniezzo Colorni, 1996] Dorigo Gambardella, 1997], Dorigo Di Caro, 1999] offer detailed information on the workings of the algorithm and the choice of the various parameters. We use an ant colony optimization metaheuristic to treat the complex problem that we have described, and we will show how the multiple objectives of the scheduler may ....

Dorigo M., Gambardella L.M. [1997], Ant colonies for the traveling salesman problem, BioSystems, 43, 73-81.

....Dorigo Gambardella [1997] The improvements concern the transition rule, the trail updating rules, the use of local improvement rules and the use of a restricted candidate list. These extensions have been included in the algorithm proposed in this article. Transition rule Gambardella Dorigo [1997] have suggested a modification to the original transition rule described by equation (1) They suggest that the ant at city i should choose the next city j to visit according to the modified rule presented in equation (3) of Figure 1. In this equation, q is a random number and q 0 is a ....

Dorigo and F. Glover Editors, New Ideas in Optimization, McGraw-Hill. Dorigo M., Gambardella L.M., [1997], Ant colonies for the traveling salesman problem, BioSystems, 43, 73-81.

....paths immediatly after these ants have returned, stimulating nestmates to choose the shortest path. Taking advantage of this antbased optimizing principle combined with pheromone evaporation to avoid early convergence to bad solutions, Colorni ## ### (1991, 1992, 1993) Dorigo ## ### (1996) Dorigo and Gambardella (1997a, 1997b; Gambardella and Dorigo, 1995) and Gambardella ## ### (1997) have proposed a remarkable optimization method, # To whom correspondence should be sent. c # 1998 HERMES 150 Botee and Bonabeau Ant Colony Optimization (ACO) which they applied to classical NP hard combinatorial optimization ....

....increase the performance of ACO algorithms, and con rm that ACO is more than an exotic metaheuristic as it compares well with existing algorithms on popular benchmark problems. 2. ACO algorithm for the TSP In this section we brie y describe Ant Colony System (ACS) an ACO algorithm introduced by Dorigo and Gambardella (1997a, 1997b) Let us consider a symmetric TSP with # cities. Let # be the total number of ants, assumed constant over time. For an ant located on city #, the transition from city # to city # depends on: 1) Whether or not city # has already been visited. Eachant has a tabu list that contains all the cities ....

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Dorigo, M. and Gambardella, L.M. (1997). Ant Colonies for the Traveling Salesman Problem. BioSystems ##, 73-81.

....a tour as short as possible, visiting every cities. It has been studied intensively, notably in the EA community. Evolutionary inspired methods seem to be among the best heuristic schemes nowadays. Algorithms like Inver over Operator [14] the Repair and Brood Selection [15] Ant Colony Systems [16, 10], and the Edge Assembly Crossover [17, 18] are certainly among the most powerful heuristics for this problem. 4.1 PROBLEMS ARISING FROM NON BINARY REPRESENTATION The case of non binary search space is a tricky problem for designing an attractor repoussoir algorithm. We face several problems: ....

M. Dorigo and L. Gambardella. Ant colonies for the traveling salesman problem. Technical Report TR/IRIDIA/1996-3, IRIDIA, Universit'e Libre de Bruxelles, Belgium, 1996.

.... fonlupt lil.univ littoral.fr Figure 1: Ants facing an obstacle 1 Introduction There has been a recent interest in the field of the Ant Colony Optimization (ACO) The basic idea is to imitate the cooperative behavior of an ant colony in order to solve large combinatorial optimization problems [1, 2, 3, 4]. The ants based algorithms have been introduced with Marco Dorigo s PhD. It is based on the principle that using very simple communication mechanisms, an ant group is able to find the shortest path between any two points. During the trip a chemical trail (pheromone) is left on the ground. The ....

M. Dorigo and L. Gambardella. Ant colonies for the traveling salesman problem. Technical Report TR/IRIDIA/1996-3, IRIDIA, Universit'e Libre de Bruxelles, Belgium, 1996.

....to collect many references, the list is certainly not complete. However, the underlying bibliography will be continuously updated. D R A F T January 6, 1999, 11:26am D R A F T 22 Reference Design Implementation Optimization problem [2] HRH(GA AC) sequential traveling salesman (het,glo,spe) [3] LCH(GA(LS LS) sequential scheduling for (hom,glo,gen) het,glo,gen) landing aircraft [6] LCH (GA(LS) sequential function optimization (het,glo,gen) 1] HCH(SA) parallel static VLSI design (hom,glo,gen) 10] HCH(LCH(GA(LS) parallel traveling salesman (het,glo,gen) hom,glo,gen) 7] HCH(GA) ....

M. Dorigo and L. Gambardella. Ant colonies for the traveling salesman problem. Technical Report TR/IRIDIA/1996-3, IRIDIA, Universit'e Libre de Bruxelles, Belgium, 1996.

....Table 1. List of applications of ACO algorithms to static combinatorial optimization problems. Classi cation by application and chronologically ordered. Traveling salesman Dorigo, Maniezzo Colorni 1991 [33, 39, 40] AS Gambardella Dorigo 1995 [48] Ant Q Dorigo Gambardella 1996 [36, 37, 49] ACS ACS 3 opt St utzle Hoos 1997 [92, 93] MMAS Bullnheimer, Hartl Strauss 1997 [12] AS rank Quadratic assignment Maniezzo, Colorni Dorigo 1994 [75] AS QAP Gambardella, Taillard Dorigo 1997 [52] HAS QAP St utzle Hoos 1998 [94] MMAS QAP Maniezzo Colorni 1998 [74] AS QAP ....

....evaporation and o ine pheromone updating. They found that this new procedure improves signi cantly the quality of the results obtained with AS. 3.1.1. 3 Ant colony system (ACS) ACS 3 opt, and Ant Q The Ant Colony System (ACS) algorithm has been introduced by Dorigo and Gambardella (1996) [36, 37, 49] to improve the performance of AS, that was able to nd good solutions within a reasonable time only for small problems. ACS is based on AS but presents some important di erences. First, the daemon updates pheromone trails o ine: at the end of an iteration of the algorithm, once all the ants have ....

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M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73-81, 1997.

....to combinatorial optimization problems. Classi cation by application and chronologically ordered. Problem name Authors Year Main references Algorithm name Traveling salesman Dorigo, Maniezzo Colorni 1991 [16, 21, 22] AS Gambardella Dorigo 1995 [23] Ant Q Dorigo Gambardella 1996 [19, 20, 24] ACS ACS 3 opt St utzle Hoos 1997 [47, 48] MMAS Bullnheimer, Hartl Strauss 1997 [6] AS rank Quadratic assignment Maniezzo, Colorni Dorigo 1994 [41] AS QAP Gambardella, Taillard Dorigo 1997 [27] HAS QAP St utzle Hoos 1998 [49] MMAS QAP Maniezzo Colorni 1998 [40] AS QAP ....

M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73-81, 1997.

....given by maxf0; w rg while the global best tour reinforces the pheromone trails with weight w. Equation 2 becomes therefore: ij (t 1) 1 ) ij (t) w 1 X r=1 (w r) r ij (t) w gb ij (t) 2a) where r ij (t) 1=L r (t) and gb ij (t) 1=L gb . ACS [42, 34, 33] improves over AS by increasing the importance of exploitation of information collected by previous ants with respect to exploration of the search space. 9 This is achieved via two mechanisms. First, a strong elitist strategy is used to update pheromone trails. Second, ants choose the next city ....

....of ACO algorithms. Applications are listed by class of problems and in chronological order. Problem name Authors Algorithm name Year Main references Traveling salesman Dorigo, Maniezzo Colorni AS 1991 [29, 37, 38] Gambardella Dorigo Ant Q 1995 [41] Dorigo Gambardella ACS ACS 3 opt 1996 [33, 34, 42] Stutzle Hoos MMAS 1997 [84, 82, 85] Bullnheimer, Hartl Strauss AS rank 1997 [14] Cordon, et al. BWAS 2000 [18] Quadratic assignment Maniezzo, Colorni Dorigo AS QAP 1994 [65] Gambardella, Taillard Dorigo HAS QAP a 1997 [46] Stutzle Hoos MMAS QAP 1997 [79, 85] Maniezzo ANTS QAP ....

M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--81, 1997.

....to static combinatorial optimization problems. Classification by application and chronologically ordered. Problem name Authors Year Main references Algorithm name Traveling salesman Dorigo, Maniezzo Colorni 1991 [33, 39, 40] AS Gambardella Dorigo 1995 [48] Ant Q Dorigo Gambardella 1996 [36, 37, 49] ACS ACS 3 opt Stutzle Hoos 1997 [92, 93] MMAS Bullnheimer, Hartl Strauss 1997 [12] AS rank Quadratic assignment Maniezzo, Colorni Dorigo 1994 [75] AS QAP Gambardella, Taillard Dorigo 1997 [52] HAS QAP a Stutzle Hoos 1998 [94] MMAS QAP Maniezzo Colorni 1998 [74] AS QAP b ....

....evaporation and o#ine pheromone updating. They found that this new procedure improves significantly the quality of the results obtained with AS. 14 3.1.1. 3 Ant colony system (ACS) ACS 3 opt, and Ant Q The Ant Colony System (ACS) algorithm has been introduced by Dorigo and Gambardella (1996) [36, 37, 49] to improve the performance of AS, that was able to find good solutions within a reasonable time only for small problems. ACS is based on AS but presents some important di#erences. First, the daemon updates pheromone trails o#ine: at the end of an iteration of the algorithm, once all the ants ....

[Article contains additional citation context not shown here]

M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--81, 1997.

....algorithms to combinatorial optimization problems. Classification by application and chronologically ordered. Problem name Authors Year Main references Algorithm name Traveling salesman Dorigo, Maniezzo Colorni 1991 [16, 21, 22] AS Gambardella Dorigo 1995 [23] Ant Q Dorigo Gambardella 1996 [19, 20, 24] ACS ACS 3 opt Stutzle Hoos 1997 [47, 48] MMAS Bullnheimer, Hartl Strauss 1997 [6] AS rank Quadratic assignment Maniezzo, Colorni Dorigo 1994 [41] AS QAP Gambardella, Taillard Dorigo 1997 [27] HAS QAP a Stutzle Hoos 1998 [49] MMAS QAP Maniezzo Colorni 1998 [40] AS QAP b Maniezzo ....

M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--81, 1997.

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M. Dorigo, L. M. Gambardella, Ant Colonies for the Traveling Salesman Problem, BioSystems 43, 1997b, 7381.

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Dorigo, M. & Gambardella, L. M. (1997), `Ant colonies for the traveling salesman problem', BioSystems 43, 73--81.

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M. Dorgio and L. Gambardella, "Ant colonies for the traveling salesman problem," BioSystems, 1997.

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M. Dorigo and L.M. Gambardella, Ant colonies for the traveling salesman problem. Biosystems 43, 73-81. 1997.

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M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--89, 1997.

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M. Dorigo and L. M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--81, 1997.

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M. Dorigo and L. M. Gambardella. Ant colonies for the Traveling Salesman Problem. Biosystems, 43:73--81, 1997.

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M. Dorigo and L.M. Gambardella. Ant colonies for the traveling salesman problem. BioSystems, 43:73--81, 1997.

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M. Dorigo and L.M. Gambardella. (1996). Ant colonies for the traveling salesman problem. Universit'e Libre de Bruxelles, Belgium, IRIDIA, Technical Report TR/IRIDIA/1996-3.

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Dorigo, M. and L.M. Garbardella, \Ant colonies for the traveling salesman problem", BioSystems 43, 73-81, 1997.

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Dorigo M. and Gambardella L. (1997). Ant Colonies for the traveling salesman problem. Biosystems. 43: 73-81.

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