D. Costa and A. Hertz. (1997). Ant can colour graphs. Journal of Operational Research Society, 48: 295-305.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... [73] ANTS QAP Job shop scheduling Colorni, Dorigo Maniezzo 1994 [20] AS JSP Vehicle routing Bullnheimer, Hartl Strauss 1996 [15, 11, 13] AS VRP Gambardella, Taillard Agazzi 1999 [51] HAS VRP Sequential ordering Gambardella Dorigo 1997 [50] HAS SOP Graph coloring Costa Hertz 1997 [22] ANTCOL Shortest common Michel Middendorf 1998 [76] AS SCS supersequence HAS QAP is an ant algorithm which does not follow all the aspects of the ACO meta heuristic. This is a variant of the original AS QAP. 3.1 Applications of ACO algorithms to static combinatorial optimization ....

....was compared in [76] with the MM [45] 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 resulted to be the best performing algorithm. 3.1. 6 Graph coloring problem Costa and Hertz (1997) [22] have proposed the AS ATP algorithm for assignment type problems. The AS ATP algorithm they de ne is basically the same as AS except that ants need to make two choices: rst they choose an item, then they choose a resource to assign to the previously chosen item. These two choices are made by ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295-305, 1997.

....permanent, but rather evaporates over time. Thus, over time, paths that are not used will become less and less attractive, while those used frequently will attract ever more ants. This approach has been applied to a number of combinatorial optimization problems, such as the Graph Coloring Problem [3], the Quadratic Assignment Problem (e.g. 4] the Travelling Salesman Problem (e.g. 5] 6] the Vehicle Routing Problem ( 7] 8] and the Vehicle Routing Problem with Time Windows ( 9] Recently, a covergence proof for a generalized Ant System has been developed by Gutjahr ( 10] In the ....

Costa, D. and Hertz, A.: Ants can colour graphs. Journal of the Operational Research Society 48(3) (1997) 295--305

....is a form of collective, intelligent agent system. It is similar to other models for swarm intelligence and crowd behavior (e.g. 8, 9] It was first used by Dorigo (e.g. 4] to solve the traveling salesperson problem and has later been used for solving problems ranging from graph coloring [10] to routing and load balancing [11, 12] The method shares a number of conceptual features with models for describing complex behavior such as Braitenberg vehicles [13] or Langton s vant [14] ANTS is very similar to random walk or diffusion based methods for solving optimization problems, but ....

D. Costa and A. Hertz. Ants Can Colour Graphs. J. Oper. Res. Soc., 48:295--305, 1997.

.... [12, 13, 15] AntNet AntNet FA network routing Subramanian, Druschel Chen 1997 [50] Regular ants Heusse, Gu erin, Snyers Kuntz 1998 [33] CAF van der Put Rothkrantz 1998 [51, 52] ABC backward Sequential ordering Gambardella Dorigo 1997 [25] HAS SOP Graph coloring Costa Hertz 1997 [10] ANTCOL Shortest common Michel Middendorf 1998 [42] AS SCS supersequence HAS QAP is an ant algorithm which does not follow all the aspects of the ACO meta heuristic. This is a variant of the original AS QAP. seen a particular case of the QAP: the items are the set of integers between 1 ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295-305, 1997.

....and MAX MIN Ant System [19] Also, ACO solutions have been developed for many other combinatorial optimisation problems. Algorithms have been proposed for the quadratic assignment problem [20, 21] scheduling problems [22, 23] the vehicle routing problem (VRP) 24] the graph colouring problem [25], the shortest common super sequence problem [26] the multiple knapsack problem [27] and many others. Nevertheless, hardly any work has been done using ACO for the BPP and the CSP. In fact, the only publication related to this is a hybrid approach formulated by Bilchev [12] He uses ACO to ....

....problems ACO has been applied to. The TSP is an ordering problem: the aim 5 is to put the different cities in a certain order. This is translated in the meaning of the pheromone trail for the TSP: it encodes the favourability of visiting a certain city j after another city i. Costa and Hertz [25] also use ACO to solve a grouping problem, namely the Graph Colouring Problem (GCP) In the GCP, a set of nodes is given, with undirected edges between them. The aim is to colour the nodes in such a way that no nodes of the same colour are connected. So, in fact, you want to group the nodes into ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997.

.... [16] Local search has also been used successfully within a memetic algorithm to do real world exam timetabling [3] Although several ant colony optimization (ACO) algorithms [2, 11, 21] have been previously proposed for other constraint satisfaction problems [18] including vertex coloring [8], a full timetabling problem has not been tackled before using ACO. The work presented here arises out of the Metaheuristics Network (MN) a European Commission project undertaken jointly by five European institutes which seeks to compare metaheuristics on di#erent combinatorial ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997.

....as a heuristic for choosing values to be assigned to variables. A. The ant colony optimization metaheuristic ACO is a stochastic approach that has been proposed to solve di erent hard combinatorial optimization problems such as traveling salesman problems [6] 10] 9] graph colouring problems [4], quadratic assignment problems [12] 20] and vehicle routing problems [1] 13] The main idea of ACO is to model the problem as the search for a minimum cost path in a graph. Arti cial ants walk through this graph, looking for good paths. Each ant has a rather simple behaviour so that it will ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295-305, 1997.

....is to put the di erent cities in a certain order. This is translated in the meaning of the pheromone trail: it encodes the favourability of visiting a certain city j after another city i. To our knowledge, there is only one ACO application for a grouping problem. It is Costa and Hertz AntCol ([6]) an ACO solution for the Graph Colouring Problem (GCP) In the GCP, a set of nodes is given, with undirected edges between them. The aim is to colour the nodes in such a way that no nodes of the same colour are connected. So, in fact, you want to group the nodes into colours. Costa and Hertz use ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295-305, 1997.

.... the most successful examples of swarm intelligent systems and have been applied to many types of problems, including the traveling salesman problem [6, 5] the problem of task allocation [1] the problems of discrete optimization [3, 4] the vehicle routing problem [7] the graph coloring problem [2], and the graph partitioning problem [13] 4 ANT COLONY PROGRAMMING FOR APPROXIMATION PROBLEMS 4.1 EXPRESSION APPROACH In this approach ant colony programming is applied for generating arithmetic expressions of a single variable which are represented in the pre x notation. The ant colony ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295-305,

....for choosing values to be assigned to variables. The Ant Colony Optimization meta heuristic Ant Colony Optimization (ACO) is a stochastic approach that has been proposed to solve di erent hard combinatorial optimization problems such as traveling salesman problems [6] graph colouring problems [7], quadratic assignment problems [8] or vehicle routing problems [9] ACO is a distributed and collective approach. The main idea is to model the problem as the search of a best path through a graph. Arti cial ants walk through this graph, looking for good paths. Each ant has a rather simple ....

D. Costa and A. Hertz, \Ants can colour graphs," Journal of the Operational Research Society, vol. 48, pp. 295-305, 1997.

.... Dorigo et al. 1996) has been used to solve a variety of NP hard combinatorial optimization problems, e.g. the vehicle routing problem (Bullnheimer et al. 1999a, 1999b) Gambardella et al. 1999) the travelling salesman problem (Dorigo and Gambardella (1997) the graph coloring problem (Costa and Hertz (1997)) and the quadratic assignment problem (Stutzle and Dorigo (1999) Dorigo et al. 1999) provide a thorough overview over problems solved with ACO. Gutjahr (2000) presented a convergence proof for a generalized ant system. Inspired by the behavior of real ants searching for food, its main idea is ....

Costa, D., A. Hertz. 1997. Ants can colour graphs. Journal of the Operational Research Society 48(3), 295--305.

....and other practical problems including register allocation,the design and operation of flexible manufacturing systems [15] frequency assignment (see [2] and references there) etc. It is well known that the problem of determining the chromatic number is NP hard on arbitrary graphs. Costa and Hertz [5] recently proposed an evolutionary algorithm which imitates the ants behaviour for solving the graph coloring problem. The evolutionary methods use the collective properties of a group of distinguishable solutions, called population. There are many other aproaches to color a graph [9] In this ....

....coloring problem. The evolutionary methods use the collective properties of a group of distinguishable solutions, called population. There are many other aproaches to color a graph [9] In this paper, we have choosen two in order to compare with the ants algorithm. The ants algorithm proposed in [5] uses the algorithm called Recursive Largest First (RLF) as a subroutine. Therefore it is natural to compare the ants algorithm with a simple repetition of RLF within the same time bounds. The algorithm RLF belongs to the class of constructive methods. They build feasible solutions by starting ....

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D. Costa and A. Hertz, Ants can colour graphs, Journal of the Operational Research Society 48, (1997), 295-305.

.... nodes (nodes in the set J ) to agent nodes (nodes in the set I) without repeating any task node but using possibly several times an agent node (several tasks may be assigned to a same agent) At each step of the construction process, an ant has to make one of the following two basic decisions [19]: i) it has to decide which task to assign next and (ii) it has to decide to which agent a chosen task should be assigned. Pheromone trail and heuristic information can be associated with both tasks. With respect to the first step the pheromone information can be used to learn an appropriate ....

.... Dorigo AntNet AntNet FA 1997 [23, 25, 28] network routing Subramanian, Druschel Chen Regular ants 1997 [86] Heusse et al. CAF 1998 [54] van der Put Rothkrantz ABC backward 1998 [88] Sequential ordering Gambardella Dorigo HAS SOP 1997 [43, 44] Graph coloring Costa Hertz ANTCOL 1997 [19] Shortest common Michel Middendorf AS SCS 1998 [67, 68] supersequence Frequency assignment Maniezzo Carbonaro ANTS FAP 1998 [63] Generalized assignment Ramalhinho Lourenco Serra MMAS GAP 1998 [73] Multiple knapsack Leguizamon Michalewicz AS MKP 1999 [59] Optical networks routing ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997.

.... paths using a stochastic decision policy based only on local information represented by the pheromone trail deposited by other ants [3] Algorithms that take inspiration from ants behavior in finding shortest paths have recently been successfully applied to several discrete optimization problems [2, 4, 5, 6, 7, 8, 9]. In ant colony optimization each one of a set of concurrent artificial ants makes use of a stochastic local search strategy to build a solution to the combinatorial problem under consideration. The whole set of ants collectively search for high quality solutions by a cooperative effort mediated ....

D. Costa and A. Hertz, Ants can colour graphs, Journal of the Operational Research Society, 48, 1997, 295--305.

.... ants, have recently been successfully applied to several discrete optimization problems #Dorigo, Maniezzo, Colorni, 1991; Dorigo, 1992; Dorigo, Maniezzo, Colorni, 1996; Dorigo Gambardella, 1997; Schoonderwoerd, Holland, Bruten, Rothkrantz, 1996; Schoonderwoerd, Holland, Bruten, 1997; Costa Hertz, 1997#. In all these algorithms a set of arti#cial ants collectively solve the problem under consideration through a cooperative e#ort. This e#ort is mediated by indirect communication of information on the problem structure the ants concurrently collect while building solutions by using a stochastic ....

Costa, D., & Hertz, A. #1997#. Ants can colour graphs. Journal of the Operational Research Society, 48, 295#305.

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D. Costa and A. Hertz. (1997). Ant can colour graphs. Journal of Operational Research Society, 48: 295-305.

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D. Costa and A. Hertz, Ants can colour graphs, Journal of the Operations Research Society 48, pp. 295-305, 1997.

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Costa D. and A. Hertz (1997). Ants Can Colour Graphs. Journal of the Operational Research Society, 48, 295-305.

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D. Costa, A. Hertz. "Ants can Colour Graphs". Journal of Operational Research Society 48, 1997, 295-305.

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D. Costa D and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997.

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D. Costa and A. Hertz. Ants Can Colour Graphs. J. Oper. Res. Soc., 48:295--305, 1997.

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D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997.

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Costa, D. and Hertz, A.: Ants can colour graphs. Journal of the Operational Research Society 48(3) (1997) 295--305

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D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295-305, 1997.

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Costa, D. and A. Hertz (1997): Ants can Colour Graphs, Journal of the Operational Research Society 48 pp. 295-305.

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