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 ....

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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.

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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