B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Central European Journal of Operations Research, 7:25--38, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 Maniezzo 1998 [73] ANTS QAP Job shop scheduling Colorni, Dorigo Maniezzo 1994 [20] AS JSP ....

....gets smaller, which obviously favors the exploration of new paths. They found that, when applied to the TSP, MMAS nds signi cantly better tours than AS, although comparable to those obtained with ACS (ACS is an extension of AS discussed in Section 3.1.1. 3) Bullnheimer, Hartl and Strauss [12] proposed yet another modi cation of AS, called AS rank . In AS rank , as it was the case in MMAS, the only pheromone updates are performed by the daemon, that implements the following activities: i) the m ants are ranked by tour length (L 1 (t) L 2 (t) Lm (t) and the arcs which were ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the ant system: a computational study. Technical Report POM-03/97, Institute of Management Science, University of Vienna, 1997. Accepted for publication in the Central European Journal for Operations Research and Economics.

....follows the rules of the ACO metaheuristic. The ACO metaheuristic was proposed to provide a unifying framework for many applications of ant algorithms [5, 4] to combinatorial optimization problems. ACO algorithms have been successfully applied to several NP hard combinatorial optimization problems [1, 4, 5, 6, 10, 13, 15, 16]; we refer to [9] for a recent overview of ACO and its applications. From a high level perspective, ACO is a population based algorithm, where arti cial pheromone trails are used to coordinate a population of simple agents, called (arti cial) ants. Characteristic features of ACO are that (i) ....

....one important focus of research on ACO has been the introduction of algorithmic improvements over AS to achieve much better performance. These improved algorithms include elitist Ant System [3] Ant Colony System (ACS) 6] MAX MIN Ant System (MMAS) 19, 20] the rank based version of Ant System [1], and Best Worst Ant System [2] Typically, these algorithms have been tested again on the TSP [17] and have shown signi cantly better performance that AS in several applications. Only few other successful ant algorithms were proposed for tackling NP hard optimization problems that do not follow ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the Ant System: A computational study. Central European Journal for Operations Research and Economics, 7(1):25-38, 1999.

.... ) min )e = dr (1 ) e: As a nal remark, we note that Ant System, an ACO algorithm particularly important because it is the ancestor of all ACO algorithms [3] 8] 9] as well as some of its variants (for example, elitist Ant System [3] 9] and the rank based version of Ant System [2]) do not belong to ACO min . In fact, in these three algorithms there is no lower bound to the value of pheromone trails that can therefore become null. It is interesting to note that ACS and MMAS were shown to perform better than Ant System and its variants on many standard benchmark problems ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the Ant System: A computational study. Central European Journal for Operations Research and Economics, 7(1):25-38, 1999.

.... 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 Maniezzo 1998 [39] ANTS QAP Vehicle routing Bullnheimer, Hartl Strauss 1996 [9, 5, 7] ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the ant system: a computational study. Technical Report POM-03/97, Institute of Management Science, University of Vienna, 1997. Accepted for publication in the Central European Journal for Operations Research and Economics.

....of possible paths P , but checking if eval(P ) 0 can be done in a polynomial time. 3.5 Pheromone updating The goal of pheromone updating is to concentrate ants on the paths that minimize the value of eval and this can be done in many various ways. Here we choose an elitist and ranking strategy [2] to update the pheromone trails. So, if the colony contains N ants then we obtain a set S of N N di erent paths. If no path has a null evaluation (otherwise a solution is reached) then, we can order S as a sequence of subsets from the better to the worst paths. S = S v1 [ S vn ; 8i ....

B. Bullnheimer, R. Hartl, and C. Strauss. A new rank based version of the ant system  a computational study. Central European Journal of Operations Research, 7(1):2538, 1999.

....ant algorithm reacts explicitly to this change. In particular, we study an ant algorithm for a Traveling Salesperson Problem (TSP) where an instance may change through the deletion or insertion of a city. Ant algorithms have been applied successfully for the static TSP problem by several authors [5, 6, 7, 8, 9, 10]. In Bonabeau et al. 1] it is suggested that ant algorithms should in general exhibit particularly good performance for dynamic versions of TSP, however they did not con rm this. The simplest way to handle the change of a problem instance would be to restart the ant algorithm after the change ....

....position of the inserted deleted city, all test results are averaged over the insertion respectively deletion of all 101 cities. The parameter values of the ant algorithm were m = 10 ants, 1, 5, q 0 = 0:5, and = 0:01. The heuristic weight of = 5 has been used by several authors (e.g. [5, 12]) for TSP. We also performed all tests with = 1 and q 0 2 f0:0; 0:9g, with equivalent or worse performance. The elitist ant was dropped when the insertion deletion occurred, and redetermined in the rst iteration thereafter. To obtain an understanding for the total amount of equalization done ....

B. Bullnheimer, R.F. Hartl, C. Strauss, \A New Rank Based Version of the Ant System - A Computational Study," CEJOR, 7: 25-38, 1999.

....was not competitive with state of the art algorithms for the TSP. Therefore, one important focus of research on ACO algorithms has been the introduction of algorithmic improvements to achieve a much better performance. Typically, these improved algorithms have been tested again on the TSP [12,47,6]. While they differ mainly in specific aspects of the search control, all these ACO algorithms are based on a stronger exploitation of the search history to direct the ants search process. Recent research on the search space characteristics of some combinatorial optimization problems has shown ....

....condition not met) do ConstructSolutions ApplyLocalSearch optional UpdateTrails end end Fig. 1. Algorithmic skeleton for ACO algorithms applied to static combinatorial problems. 2. 2 Combinatorial optimization problems Traditionally, almost all ACO algorithms have been tested on the TSP [13,14,12,47,6]. In this article we focus on the TSP and the QAP as application domains for MMAS. 2.2.1 The Traveling Salesman Problem The TSP can be represented by a complete graph G = N; A) with N being the set of nodes, also called cities, and A being the set of arcs fully connecting the nodes. Each arc ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank based version of the ant system -- a computational study. Central European Journal for Operations Research and Economics, 7(1):25--38, 1999

....T gb and e is a positive integer. Note that this type of pheromone update is a first example of daemon action as described in Section 3.3. Other improvements, described below, were the rank based version of Ant System (AS rank ) MAX MIN Ant System (MMAS) and Ant Colony System (ACS) AS rank [14] is in a sense an extension of the elitist strategy: it sorts the ants according to the lengths of the tours they generated and, after each tour construction phase, only the (w 1) best ants and the global best ant are allowed to deposit pheromone. The rth best ant of the colony contributes to the ....

.... 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 1998 [62] Maniezzo Colorni AS QAP b 1999 [64] Scheduling problems Colorni, Dorigo ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the Ant System: A computational study. Central European Journal for Operations Research and Economics, 7(1):25--38, 1999.

.... The said common characteristics were the ones that motivated our idea that the integration of some speci c aspects of PBIL, in particular, and of other EAs, in general, could improve the performance of ACO [3] in fact, two ACO models, AS elite and AS rank , based on this idea are to be found in [2]) The new ACO model so developed will be called Best Worst Ant System (BWAS) and will be introduced in this work. To do so, once analyzed the basic operation mode of ACO algorithms and described some speci c models in Section 2, Section 3 will be devoted to brie y introduce the PBIL algorithm. ....

B. Bullnheimer, R.F. Hartl, C. Strauss. A New Rank Based Version of the Ant System: A Computational Study. Central European Journal for Ops. Research and Economics, 7(1):25-38, 1999.

....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 mainly compare two meta heuristics : on the one hand, the PATS ....

....more and more attractive. This fact will be increased by pheromone evaporation. This subtle principle of communication 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 ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. A new rank based version of the ant system: A computational study. Working paper, University of Vienna, Austria, 1997.

.... 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 Maniezzo 1998 [73] ANTS QAP Job shop scheduling Colorni, Dorigo Maniezzo 1994 [20] AS JSP ....

....gets smaller, which obviously favors the exploration of new paths. They found that, when applied to the TSP, MMAS finds significantly better tours than AS, although comparable to those obtained with ACS (ACS is an extension of AS discussed in Section 3.1.1. 3) Bullnheimer, Hartl and Strauss [12] proposed yet another modification of AS, called AS rank . In AS rank , as it was the case in MMAS, the only pheromone updates are performed by the daemon, that implements the following activities: i) the m ants are ranked by tour length (L 1 (t) L 2 (t) Lm (t) and the arcs which ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the ant system: a computational study. Technical Report POM-03/97, Institute of Management Science, University of Vienna, 1997. Accepted for publication in the Central European Journal for Operations Research and Economics.

....was not competitive with state of the art algorithms for the TSP. Therefore, one important focus of research on ACO algorithms has been the introduction of algorithmic improvements to achieve a much better performance. Typically, these improved algorithms have been tested again on the TSP [12,47,6]. While they differ mainly in specific aspects of the search control, all these ACO algorithms are based on a stronger exploitation of the search history to direct the ants search process. Recent research on the search space characteristics of some combinatorial optimization problems has shown ....

....condition not met) do ConstructSolutions ApplyLocalSearch optional UpdateTrails end end Fig. 1. Algorithmic skeleton for ACO algorithms applied to static combinatorial problems. 2. 2 Combinatorial optimization problems Almost all ACO algorithms have initially been tested on the TSP [13,14,12,47,6]. In this article we focus on the TSP and the QAP as application domains for MMAS. 2.2.1 The Traveling Salesman Problem The TSP can be represented by a complete graph G = N; A) with N being the set of nodes, also called cities, and A being the set of arcs fully connecting the nodes. Each arc ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank based version of the ant system -- a computational study. Central European Journal for Operations Research and Economics, 7 (1999) 25--38.

....chosen less probably by subsequent ants. The modified update rule in ACS is the same as presented later in Section 4.1 using the global best tour to update the trails. Since the first version of this Technical Report another variant of Ant System was proposed, the rank based version of Ant System [5]. Here, the best ants in each iteration and the elitist ants are allowed to modify the trails. The quantity of trail an ant may lay down depends on its rank in the current iteration and the quantity of trail the elitist ant may lay on some arc, see [5] for more details. 4 MAX MIN Ant System ....

....the rank based version of Ant System [5] Here, the best ants in each iteration and the elitist ants are allowed to modify the trails. The quantity of trail an ant may lay down depends on its rank in the current iteration and the quantity of trail the elitist ant may lay on some arc, see [5] for more details. 4 MAX MIN Ant System In initial experiments with Ant System we noted that more greediness improves performance finding good solutions much more quickly. Especially for larger problem instances Ant System without some greedy component gives rather poor results. 5 Initially ....

[Article contains additional citation context not shown here]

Bernd Bullnheimer, Richard F. Hartls, and Christine Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Technical report, University of Viena, Institute of Management Science, 1997.

....to construct tours, guided by the pheromone trail and heuristic information based on intercity distances. Since the work on Ant System, several improvements of the basic algorithm have been proposed including Ant Colony System [9] MAX MIN Ant System [22] and the rank based version of Ant System [3]. Additionally, the performance of ACO algorithms can be significantly enhanced by adding a local search phase in which solutions are improved by a local search procedure [15, 21, 9] Thus, the most efficient ACO algorithms are actually hybrid algorithms consisting of a solution construction ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Technical report, University of Viena, 1997.

....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 1998 [39] ANTS QAP Vehicle routing Bullnheimer, Hartl Strauss 1996 [9, 5, 7] AS VRP ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the ant system: a computational study. Technical Report POM-03/97, Institute of Management Science, University of Vienna, 1997. Accepted for publication in the Central European Journal for Operations Research and Economics.

.... et al. 4] van der Put, Rothkrantz [48] network routing ACS Dorigo, Ganbardella [16] TSP, VRP AntNet Di Caro, Dorigo [6] 7] network 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 ....

....more and more rarely by the ants, until they reach the min value. The min and max parameters are used to counteract premature stagnation of search, maintaining at the same time some kind of elitist strategy. When applied to TSP, MMAS performs better than AS. Bullnheimer, Hartl and Strauss [5] proposed yet another modi cation of AS, called AS rank , introducing a rank based version of the probability distribution to limit the danger of over emphasized trails caused by many ants using sub optimal solutions. The idea is the following. At each iteration, when all solutions are completed ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R.F. Hartl, and C. Strauss, A new rank-based version of the ant system: a computational study, Technical Report POM-03/97, Institute of Management Science, University of Vienna, 1997, Accepted for publication in the Central European Journal for Operations Research and Economics.

....the ACO meta heuristic and, therefore, we will call these algorithms also ACO algorithms. The first ACO algorithm, called Ant System (AS) 18, 14, 19] has been applied to the Traveling Salesman Problem (TSP) Starting from Ant System, several improvements of the basic algorithm have been proposed [21, 22, 17, 51, 53, 7]. Typically, these improved algorithms have been tested again on the TSP. All these improved versions of AS have in common a stronger exploita To appear in K. Miettinen, M. Makela, P. Neittaanmaki and J. Periaux, editors, Evolutionary Algorithms in Engineering and Computer Science: Recent ....

....studied in literature [29, 31, 45] and has attracted since a long time a considerable amount of research e#ort. The TSP also plays an important role in Ant Colony Optimization since the first ACO algorithm, called Ant System [18, 14, 19] as well as many of the subsequently proposed ACO algorithms [21, 17, 52, 53, 7] have initially been applied to the TSP. The TSP was chosen for many reasons: i) it is a problem to which ACO algorithms are easily applied, ii) it is an NP hard [26] optimization problem, iii) it is a standard test bed for new algorithmic ideas and a good performance on the TSP is often ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Central European Journal for Operations Research and Economics. To appear.

....the ACO meta heuristic and, therefore, we will call these algorithms also ACO algorithms. The first ACO algorithm, called Ant System (AS) 18, 14, 19] has been applied to the Traveling Salesman Problem (TSP) Starting from Ant System, several improvements of the basic algorithm have been proposed [21, 22, 17, 51, 53, 7]. Typically, these improved algorithms have been tested again on the TSP. All these improved versions of AS have in common a stronger exploitay To appear in K. Miettinen and M.M. Makela, P. Neittaanmaki, J. Periaux, editors, Evolutionary Algorithms in Engineering and Computer Science: Recent ....

....in literature [29, 31, 45] and has attracted since a long time a considerable amount of research effort. The TSP also plays an important role in Ant Colony Optimization since the first ACO algorithm, called Ant System [18, 14, 19] as well as many of the subsequently proposed ACO algorithms [21, 17, 52, 53, 7] have initially been applied to the TSP. The TSP was chosen for many reasons: i) it is a problem to which ACO algorithms are easily applied, ii) it is an NP hard [26] optimization problem, iii) it is a standard test bed for new algorithmic ideas and a good performance on the TSP is often taken ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Central European Journal for Operations Research and Economics. To appear.

....and heuristic information based on intercity distances. Since the work on Ant System several extensions of the basic algorithm have been proposed, among those are Ant ColonySystem (Dorigo and Gambardella, 1997) MAX MIN Ant System (Stutzle and Hoos, 1998) and the rank based version of Ant System (Bullnheimer et al. 1997). Here, in particular, we consider the application of MAX MIN Ant System (MMAS) to the FSP. 1 The performance of ACO approaches with respect to solution quality and convergence speed can be further enhanced by adding a local search phase (Stutzle and Hoos, 1997; Dorigo and Gambardella, 1997) ....

Bullnheimer, B., Hartl, R. F., and Strauss, C. (1997). A New Rank Based Version of the Ant System --- A Computational Study. Technical report, University of Viena, Institute of Management Science.

....fact will be increased by pheromone evaporation. Fig. 1. Ants facing an obstacle This subtle principle of communication 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] 1.3 A brief overview of this ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. A new rank based version of the ant system: A computational study. Working paper, University of Vienna, Austria, 1997.

....Ant System only for rather small problems good results may be obtained. This is the main reason why several extensions of the basic algorithm have been proposed. Among those are Ant Q [20] Ant Colony System (ACS) 21, 14] MAX MIN Ant System [36, 38] and the rank based version of Ant System [5]. Additionally, the performance of ACO algorithms can be improved significantly by adding a local search phase [29, 36, 37, 14] in which the solutions are improved by a local search procedure. Thus, the best performing ACO algorithms are in fact hybrid algorithms consisting of a solution ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Technical report, University of Viena, Institute of Management Science, 1997.

....by the pheromone trail and heuristic information based on intercity distances. Since the work on Ant System, several extensions of the basic algorithm have been proposed, among those are Ant Q [14] Ant Colony System [15] MAX MIN Ant System [32, 34] and the rank based version of Ant System [5]. All these extensions are in some sense greedier than Ant System, but differ significantly in main aspects of the search control. MAX MIN Ant System [34, 32] yields a significantly better solution quality than Ant System for TSPs if only tour constructions are allowed. Additionally, the ....

....differences between MAX MIN Ant System and Ant System are that in MMAS only one ant 1 is allowed to provide a feedback mechanism by updating 1 Choosing only one ant for trail update was proposed also for Ant Q and ACS. Other possibilities like choosing several of the best ants as proposed in [5] may also be used. Sophia Antipolis, France, July 21 24, 1997 INRIA PRiSM Versailles 4 2ND INTERNATIONAL CONFERENCE ON METAHEURISTICS MIC97 the trails and that the trails are limited to an interval between some maximum and minimum possible values max and min . A minor difference is that ....

B. Bullnheimer, R. Hartl, and C. Strauss. A New Rank Based Version of the Ant System: A Computational Study. POM Working Paper 3/97, University of Viena, 1997.

....construct tours, guided by the pheromone trail and heuristic information based on intercity distances. Since the work on Ant System, several improvements of the basic algorithm have been proposed including Ant Colony System [10] MAX MIN Ant System [24] and the rank based version of Ant System [4]. Additionally,the performance of ACO algorithms can be significantly enhanced by adding a local search phase in which solutions are improved by a local search procedure [10, 23, 16] Thus, the most efficient ACO algorithms are actually hybrid algorithms consistingof a solutionconstruction ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Technical report, University of Viena, 1997.

....chosen less probably by subsequent ants. The modified update rule in ACS is the same as presented later in Section 4.1 using the global best tour to update the trails. Since the first version of this Technical Report another variant of Ant System was proposed, the rank based version of Ant System [5]. Here, the best ants in each iteration and the elitist ants are allowed to modify the trails. The quantity of trail an ant may lay down depends on its rank in the current iteration and the quantity of trail the elitist ant may lay on some arc, see [5] for more details. 4 MAX MIN Ant System ....

....the rank based version of Ant System [5] Here, the best ants in each iteration and the elitist ants are allowed to modify the trails. The quantity of trail an ant may lay down depends on its rank in the current iteration and the quantity of trail the elitist ant may lay on some arc, see [5] for more details. 4 MAX MIN Ant System In initial experiments with Ant System we noted that more greediness improves performance finding good solutions much more quickly. Especially for larger problem instances Ant System without some greedy component gives rather poor results. 3 Initially ....

[Article contains additional citation context not shown here]

B. Bullnheimer, Richard F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Technical report, University of Viena, Institute of Management Science, 1997.

No context found.

Bullnheimer, B., Hartl, R. F. and Strauss, Ch.: A new rank based version of the ant system: a computational study. Central European Journal of Operations Research 7(1) (1999) 25--38

No context found.

Bullnheimer, B., R. F. Hartl and C. Strauss (1997): A New Rank Based Version of the Ant System - A Computational Study, Working Paper POM-WP 3/97, University of Vienna.

....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 previous approaches for the VRP ( 7] 8] the construction of solutions was based on a ....

....and iteratively exchanges two edges with 2 new edges until no further improvements are possible. Pheromone update After all ants have constructed their solutions, the phero mone trails are updated on the basis of the solutions found by the ants. According to the rank based scheme proposed in [6] and [8] the pheromone update is as follows new ij = ## old ij # 1 =1 ## ij ### # ij (4) where 0 1 is the trail persistance and # is the number of elitists. Using this scheme two kinds of trails are laid. First, the best solution found during the process is updated as if # ants ....

Bullnheimer, B., Hartl, R. F. and Strauss, Ch.: A new rank based version of the ant system: a computational study. Central European Journal of Operations Research 7(1) (1999) 25--38

....and assignment of processes after several global or local exchanges. Again, thorough testing will be needed to discover the most promising configuration. Furthermore, recent publications addressing adaptive memory and trail update improved the general Ant System algorithm considerably. In [2] the ants are ranked according to solution quality and only the best ranked ants contribute to the trail update, whereas in [9] and [19] only the very best ant is considered. In addition to that, they use local search to improve the solution generated by the artificial ants. Such combination of ....

....problems of combinatorial optimization such as Quadratic Assignment, Vehicle Routing, Job Shop, Scheduling and Graph Coloring using sequential implementations of the Ant System algorithm. The Ant System shows good worst case results for large problems compared to other classical meta heuristics [2] and can be improved by using candidate lists [4] The desired application of the Ant System to large scale problems and the distributed, modular structure of the algorithm were the motivation to parallelize the algorithm. We developed two parallelization strategies, the Synchronous Parallel ....

Bullnheimer, B.; Hartl, R.F.; Strauss, C.: A New Rank Based Version of the Ant System - A Computational Study. Working Paper No. 1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna, 1997.

....trail added to ij by the ants. As for the heuristic information, there are several possibilities regarding the quantity Delta ij in ACO algorithms. In early versions [16] each ant contributed to the trail update, whereas later versions suggested to rank ants according to quality (AS rank ) [3], or to restrict the update to the best ant (ACS) 14] possibly combined with an upper and lower bound for the trail levels (MMAS) 32] In this paper we followed the ant colony system (ACS) idea, i.e. only the best ant contributes to the pheromone trail update. Thus, we have Delta ij (t) ....

Bullnheimer, B., R.F. Hartl and C. Strauss (1997): A New Rank Based Version of the Ant System - A Computational Study, Working Paper No. 1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, to appear in CEJOR.

....there are various possibilities of pheromone decay Delta ij in ACO algorithms. In early versions [19] each ant contributed to the trail update, whereas later versions suggested a ranking of solutions concerning their quality and let only some best ants contribute to the pheromone trails [7]. Other approaches restricted the update to the best ant [17] possibly combined with an upper and lower bound for the trail levels [39] In this paper we follow the ant colony system (ACS) idea, i.e. only the best solution contributes to the pheromone trail update. Thus, we have Delta ij (t) ....

Bullnheimer, B., R.F. Hartl and C. Strauss (1999): A New Rank Based Version of the Ant System - A Computational Study, Central European Journal of Operations Research 7 (1) pp. 25-38.

....the solution. In early ant system approaches all ants contributed to the trail update (see [2] 12] In more recent papers on the TSP, better results were obtained for update rules where only the best ant contributes to the pheromone trails (see [11] 23] In another paper Bullnheimer et al. [1] suggest to rank the ants according to solution quality and to use only the best ranked ants as well as so called elitist ants to update the pheromone trails. For the VRP this update rule is as follows new ij = ae old ij oe Gamma1 X =1 Delta ij oe Delta ij (2) where ae is ....

....ff = fi = 5 and ae = 0:75. For the other parameters we found f = g = 2 as a good setting. For all problems I max = 2 Delta n iterations were simulated with oe = 6 elitist ants. Thus, the five best ants of an iteration further contributed to the pheromone trail update, which is also proposed in [1]. The candidate list size was set to bn=4c, i.e. only one fourth of the locations, namely the closest ones, were considered 3 . Figure 2 depicts the 50 customer problem (C1) and the corresponding candidate sets (each of size 12) for two selected customers. Customer v 11 and its candidates are ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R.F. Hartl and C. Strauss, A new rank based version of the ant system: a computational study, Working Paper No.1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna (1997).

....one and a half hours for the largest problem. 6 Discussion and conclusion The presented contribution shows the application and the improvement of an ant system algorithm to the VRP. The computational results confirm the positive experiences made with the ant system by applying it to the TSP [1], 11] 23] Although some very good solutions for the VRP instances were obtained, the best known solutions for the fourteen test problems could not be improved. For practical purposes deviations up to 5 are more than acceptable as uncertainty about travel costs, demands, service times etc. ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. A new rank based version of the ant system: a computational study. Working Paper No.1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna, 1997.

....selection and assignment processes after several global or local exchanges. Again, thorough testing will be needed to discover the most promising configuration. Furthermore, recent publications addressing adaptive memory and trail update improved the general Ant System algorithm considerably. In [3] the ants are ranked according to solution quality and only the best ranked ants contribute to the trail update, whereas in [9] and [16] only the very best ant is considered. In addition to that, they use local search to improve the solution generated by the artificial ants. Such combination of ....

....Traveling Salesman Problem, and has later been applied successfully to other standard problems of combinatorial optimization such as Quadratic Assignment, Vehicle Routing, Job Shop, Scheduling, Graph Coloring and Timetabling using sequential implementations of the Ant System algorithm. As shown in [3] the Ant System shows good worst case results for large problems compared to other classical metaheuristics. The desired application of the Ant System to large scale problems and the distributed, modular structure of the algorithm were the motivation to parallelize the algorithm. We developed two ....

Bullnheimer, B.; Hartl, R.F.; Strauss, C.: A New Rank Based Version of the Ant System - A Computational Study. Working Paper No. 1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna, 1997.

No context found.

B. Bullnheimer, R.F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System --- A Computational Study. Central European Journal of Operations Research, 7:25--38, 1999.

No context found.

B. Bullnheimer, R. F. Hartl, and C. Strauss. A New Rank Based Version of the Ant System: A Computational Study. Pom-03/97, Institute of Management Science, University of Vienna, Austria, 1997.

No context found.

B. Bullnheimer, R.F. Hartl, and C. Strauss, A new rank-based version of the ant system: a computational study, Central European Journal of Operations Research 7 (1) (1999), 25--38.

No context found.

B. Bullnheimer, R. F. Hartl, and C. Strauss. A new rank-based version of the Ant System: A computational study. Central European Journal for Operations Research and Economics, 7(1):25-38, 1999.

No context found.

Bullnheimer, B., Hartl, R. F. & Strauss, C. (1997a). A new rank based version of the ant system: a computational study. Working paper #1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna.

No context found.

B. Bullnheimer, R. F. Hartl, & C. Strauss. 1997b. A New Rank-Based Version of the Ant System: A Computational Study. Tech. rept. POM-03/97. Institute of Management Science, University of Vienna, Austria. Accepted for publication in the Central European Journal for Operations Research and Economics.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC