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 ....

[Article contains additional citation context not shown here]

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.

.... simulated annealing (Kirkpatrick et al. 1983) Others have followed the path, and 6 have either extended the original method (Bullnheimer et al. 1997a; Sttzle Hoos, 1997) or applied ant based optimization to the vehicle routing problem (Bullnheimer et al. 1997b) the graph coloring problem (Costa Hertz, 1997) and the search of continuous spaces (Bilchev Parmee, 1995; Wodrich, 1996) Schoonderwoerd et al. s (1997; Schoonderwoerd, 1996) application to routing and load balancing in telecommunications networks is derived from the same metaphor: however, the formulation of their algorithm, the dynamic ....

Costa, D. & Hertz, A. (1997). Ants can colour graphs. J. Op. Res. Soc. 48, 295-305.

....for solving CSPs As in [6] we first define an ant system on which we can build the ant algorithm. It is a more theoretical layer that defines the necessary formulae needed by the algorithm. Another related ant system, used for solving assignment problems like graph coloring, is presented in [2]. 3.1 The ant system Suppose we have a CSP instance corresponding to a constraint graph G. Let t ij be the intensity of trail on the constraint between variables i and j at time t as in [6] and [5] The trails are in fact laid on the edges of the constraint graph G and are recalculated after ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997. 8

.... Real ants are able to find shortest paths using as only information the pheromone trail deposited by other ants [1] Ant colony optimization (ACO) algorithms which take inspiration from ants behavior in finding shortest paths have recently been successfully applied to combinatorial optimization [3,6,11,12,13]. In ant colony optimization a set of artificial ants collectively solve a combinatorial problem by a cooperative effort. This effort is mediated by stigmergetic communication [3, 14] that is, a form of indirect communication of information on the problem structure ants collect while building ....

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

....their environment. Real ants have been shown to be able to find shortest paths using as only information the pheromone trail deposited by other ants [2] Algorithms that take inspiration from ants behavior in finding shortest paths have recently been successfully applied to discrete optimization [4, 7, 11, 12, 13, 14, 18]. In ant colony optimization a set of artificial ants collectively solve a combinatorial problem by a cooperative effort. This effort is mediated by indirect communication of information on the problem structure they collect while building solutions. Similarly, in AntNet, the algorithm we propose ....

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

....machines) We propose an algorithm using a co operative approach based on the model of the ants colonies presented for the first time by Dorigo and al. Dor92] This approach was applied successfully to a number of algorithms (travelling salesman problem (TSP) DMC96] graph coloring problem [CH97], solving real function [BP95] vehicle routing problem [BHS97] load balancing in telecommunications networks [SHBR97] Our study is applied to the quadratic assignment problem [KB57] QAP) which is known to be among one of most complex NP hards problems [SG76a] In this article, we ....

.... has been used as a guideline for the design of heuristics dedicated to some combinatorial optimization problems, notably the TSP in [DMC96,GD95,DG96] vehicule routing problems [BHS97] load balancing in communication networks [CD97] real functions optimization [BP95] graph coloring problems [CH97], Several works have also been targeted at the QAP, for example Stuzle s Min Max algorithm [Stu97] or Gamberdella et al. s HAS QAP [GTD98] 3.1 From ants to ANTabu ANTabu is inspired by the natural model, but slightly deviates on some points. In nature, ants have a constructive behavior, ....

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

.... [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 a HAS QAP is an ant algorithm which does not follow all the aspects of the ACO meta heuristic. b 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. 14 The AS ATP algorithm they define is basically the same as AS except that ants need to make two choices: first they choose an item, then they choose a resource to assign to the previously chosen item. These two choices are made ....

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

....problem solving technique is generally attributed to Dorigo [6] However, since his early work on the Travelling Salesman Problem (TSP) and Asymmetric TSP, the technique has been applied to several other problem domains. These include the Quadratic Assignment Problem (QAP) 15, 19] graph coloring [5], vehicle routing [2] and, as we shall see in the next section, communications network routing. 3. Routing and Connection Management Many strategies have been proposed and researched for network routing, a problem related to connection management. Connection management problems can be found, ....

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

....discouraged some students from taking the class, however there does not seem to be any reasonable or effective way around this barrier. 3 Anticipated Changes One addition to the syllabus the next time this course is taught will be the subject of ant colony methods as founded by Dorigo and others [2 4]. This is an important new paradigm of evolutionary computation that involves cooperative behavior. A smaller section might be added on particle swarm techniques as put forth by Kennedy and others [11 13] These have a similar theme of cooperation among agents, but balance individual and group ....

Costa, D. and A. Hertz, "Ants can colour graphs," Journal of the Operational Research Society, 48, 1997, 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 a HAS QAP is an ant algorithm which does not follow all the aspects of the ACO meta heuristic. b This is a variant of the original AS QAP. 19 seen a particular case of the QAP: the items are the set of integers ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295--305, 1997. 22

....algorithm using 125 benchmark problems and present computational results. 1 Introduction Ant Colony Optimization (ACO) is a rather new meta heuristic introduced in the early nineties (cf. 6, 7, 11, 15] and has successfully been applied to several combinatorial optimization problems (cf. e.g. [4, 5, 8, 9, 16, 21, 25]) In this paper we apply ACO to the Single Machine Total Tardiness Problem y We would like to thank Herbert Dawid and Marco Dorigo for their contributions to this research. Financial support from the Austrian Science Foundation under Grant F 01005 Adaptive Information Systems and Modelling in ....

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

.... Ant Colony Optimization (ACO) is a meta heuristic that dates back to the early nineties and was first introduced by Dorigo et al. cf. 8, 9, 14, 18] Since then ACO has been applied to a variety of classic combinatorial optimization problems and has generated very good results (cf. e.g. [5, 6, 10, 11, 19, 24, 29, 38]) In recent work simplifications and generalizations of the original approach are performed [15, 16] Ant Colony Optimization models a nature based, multi agent process in order to solve hard combinatorial optimization problems. Real ants searching for food are capable to find the shortest path ....

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

....then it is covered within time 2n. 1 Introduction Ant algorithms are computing methods that make use of ideas from the world of real ant colonies in the context of optimization problems. Some examples for such applications are the traveling salesman problem (TSP) e.g. DMC96] graph coloring [CH97], quadratic assignment [SD99] and routing in communication networks (e.g. SHBR97] see [DD99] and [D93] for a list of references to such applications. Both theoretical [AG92] and experimental [G95] studies show that ants continuously and very effectively forage uncharted territories in search ....

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

.... routing ANTS Maniezzo [31] Maniezzo, Carbonaro [32] QAP, FAP AS Colorni, Dorigo, Maniezzo [10] 11] 17] TSP, QAP, JSP ASrank Bullnheimer, Hartl, Strauss [5] TSP, VRP HAS Gambardella, Taillard, Dorigo [20] 19] QAP, VRP, SOP MMAS Stuetzle, Hoos (1998) 42] TSP, QAP Costa, Hertz (1997) [12] GCP Michel, Middendorf (1998) 36] SCS ANT COLONY OPTIMIZATION: AN OVERVIEW 11 The variety of the contributions testi es both the exibility of the approach and the infancy of the eld, where no evidence of the superiority of a particular technique over the other has so far emerged. In ....

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

....in any respect. The study confirms the positive experience that was made by applying the ant system to other problems of combinatorial optimization such as the job shop scheduling problem [5] the quadratic assignment problem [17] the vehicle routing problem [2] and the graph colouring problem [6]. Directions for future research should be the analysis of parameter settings in a problem specific as well as a general framework. Furthermore the ant system algorithm seems to be well suited for parallelization and for the application to other problems in the field of combinatorial ....

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

....memory corresponds to the pheromone trails. In addition, the artificial ants are equiped with a local heuristic function to guide their search through the set of feasible solutions. The ant system has been applied to the Job Shop Scheduling Problem in [7] to the Graph Colouring Problem in [8], to the Quadratic Assignment Problem in [18] and to the Vehicle Routing Problem in [2] In this paper we present an improved ant system algorithm for the Vehicle Routing Problem (VRP) with one central depot and identical vehicles and show that the ant paradigm can be used to produce competitive ....

D. Costa and A. Hertz, Ants can colour graphs, J. Oper. Res. Soc. 48(1997)295.

....be increased by the evaporation stage. This principle of communicating ants has been used as a framework for solving combinatorial optimization problems like the TSP [2, 5, 6] routing problems, load balancing in communication networks [7] real function optimization [8] graph coloring problem [9], In this paper, we show how we transpose this mechanism to a parallel hybrid parallel ants method called ANTabu to solve the well known QAP and how we achieve very good results by improving the Gambardella, Taillard and Dorigo scheme [10] This paper is organized as follows: Section 2 deals ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of Operation Research Socoety, (48):295--305, 1997.

.... Dorigo and Maniezzo [6] 10] 12] is a new distributed metaheuristic for hard combinatorial optimization problems and was first used on the well known Traveling Salesman Problem (TSP) It has further been applied to the Job Shop Scheduling Problem in [7] to the Graph Colouring Problem in [8] and to the Quadratic Assignment Problem in [18] Observations on real ants searching for food were the inspiration to imitate the behaviour of ant colonies for solving combinatorial optimization problems. Real ants are able to communicate information concerning food sources via an aromatic ....

D. Costa, and A. Hertz. Ants can colour graphs. J. Oper. Res. Soc. 48 (1997), pages 295-305.

....in any respect. The study confirms the positive experience that was made by applying the ant system to other problems of combinatorial optimization such as the job shop scheduling problem [6] the quadratic assignment problem [19] the vehicle routing problem [2] and the graph colouring problem [7]. Directions for future research should be the analysis of parameter settings in a problem specific as well as a general framework. Furthermore the ant system algorithm seems to be well suited for parallelization [3] and for the application to other problems in the field of combinatorial ....

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

....to Dorigo [9] It is considered central to our work. However, since Dorigo s early work on the Travelling Salesman Problem (TSP) and Asymmetric TSP, the technique has been applied to several other classes of problem. These include the Quadratic Assignment Problem (QAP) 16, 22] graph coloring [7], vehicle routing [6] and, as we shall see in the later sections, communications network routing. 3. Agent System Architecture In our system, ant like agents solve problems by moving over the nodes and links in a network and interacting with chemical messages deposited in that network. Chemical ....

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

.... ant colony algorithms have been successfully applied to the solution of symmetric and asymmetric traveling salesman problems (Dorigo, Maniezzo and Colorni, 1991; 1996; Dorigo and Gambardella, 1997) quadratic assignment problems (Gambardella, Taillard and Dorigo, 1997) graph coloring problems (Costa and Hertz, 1997), and telecommunications routing problems (Di Caro and Dorigo, 1997; 1998) In this paper we have presented an application of an hybrid algorithm, HAS SOP, which combines an ant colony algorithm with local search to solve the sequential ordering problem. HAS SOP has been evaluated experimentally ....

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

....algorithms. More recently, MMAS has been applied to the flow shop scheduling problem (FSP) in [47] The computational results have shown that MMAS outperforms earlier proposed Simulated Annealing algorithms and performs comparably to Tabu Search algorithms applied to the FSP. Costa and Herz [11] have proposed an extension of AS to assignment type problems and present an application of their approach to the graph coloring problem obtaining results comparable to those obtained by other heuristic approaches. Applications of AS rank to vehicle routing problems are presented by Bullnheimer, ....

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

....algorithms. More recently, MMAS has been applied to the flow shop scheduling problem (FSP) in [47] The computational results have shown that MMAS outperforms earlier proposed Simulated Annealing algorithms and performs comparably to Tabu Search algorithms applied to the FSP. Costa and Herz [11] have proposed an extension of AS to assignment type problems and present an application of their approach to the graph coloring problem obtaining results comparable to those obtained by other heuristic approaches. Applications of AS rank to vehicle routing problems are presented by Bullnheimer, ....

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

....with the order of the graph. In [2] it is shown that the ant algorithm clearly outperforms other classical methods such as simulated annealing and genetic algorithms. On the other hand, in Table 1 we present a comparison between our algorithm and another ant algorithm proposed by Costa and Hertz [3]. The ant algorithm was tested on random graphs with 100, 300, 500 and 1000 nodes (ten graphs for each order) in which there exists an edge between any pair of nodes with a probability 0.5. The better performance of our algorithm may come from the fact that the ants move over the graph instead ....

....move over the graph instead of the solution space, and by the simple way used by any ant to remember former actions of the algorithm. nodes 100 300 500 1000 C H 15.2 35.7 55.6 111.0 ants 14.9 34.8 53.9 99.5 Table 1: A comparison between our algorithm, ants, and Costa and Hertz ant algorithm [3]. We give the average of the number of colours used in each case. One important concern for any algorithm is the extent of its possible applications. Although it is possible to design specific algorithms for most combinatorial problems, there are some general schemes, such as tabu search, ....

[Article contains additional citation context not shown here]

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

.... 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) parallel static neural network (hom,glo,gen) design [8] HCH(TS) sequential graph partitioning (hom,glo,gen) [9] HRH(GA TS) sequential circuit partitioning (het,glo,gen) VLSI design [19] HCH(GA) parallel static 0 1 integer (hom,glo,gen) linear programming [22] HCH(SA) sequential traveling salesman (hom,glo,gen) 17] HCH(GA) sequential royal road (hom,glo,gen) function optimization [14] HCH(TS) parallel ....

D. Costa and A. Hertz. Ants can colour graphs. Journal of Operation Research Socoety, (48):295--305, 1997.

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

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