B. Bullnheimer, R.F. Hartl, and C. Strauss, Applying the ant system to the vehicle routing problem, In: Voss S., Martello S., Osman I.H., Roucairol C. (eds.) MetaHeuristics: Advances and Trends in Local Search Paradigms for Optimization, Kluwer, Boston, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 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 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 ....

....These results, although not exceptional, are encouraging and suggest that further work could lead to a workable system. Also, a comparison with other approaches is necessary. 3.1. 4 Vehicle routing problem There are many types of vehicle routing problems (VRPs) Bullnheimer, Hartl and Strauss [11, 13, 15] applied an AS like algorithm to the following instance. Let G = N; A; d) be In fact, the TSP can be seen as the problem of assigning to each of n cities a di erent number chosen between 1 and n. QAP, as the TSP, is NP hard [89] HAS QAP is an ant algorithm which, although initially inspired ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the ant system to the vehicle routing problem. In I. H. Osman S. Vo, S. Martello and C. Roucairol, editors, pages 109-120. Kluwer Academics, 1998.

.... 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] AS VRP Gambardella, Taillard Agazzi 1999 [26] HAS VRP Connection oriented Schoonderwoerd, Holland, 1996 [45, 44] ABC network routing Bruten Rothkrantz White, Pagurek Oppacher 1998 [53] ASGA Di Caro Dorigo 1998 [14] AntNet FS Bonabeau, Henaux, Gu erin, 1998 [4] ABC smart ants ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the ant system to the vehicle routing problem. In S. Vo, S. Martello, I. H. Osman, and C. Roucairol, editors, pages 285-296. Kluwer Academics, 1998.

....best path (such as the shortest path) and send out the message. The basic assumption of this technique is that the network is stationary. In a faulty or mobile network, searching for the optimal path using this conventional approach will become very dicult. Ant routing (or ant like routing method) [5], 7] 32] 33] 34] 35] is a recent proposed mobile agent based network routing algorithm particular for use in these environments. The idea of ant routing algorithm mimics the path searching process of an ant. Once a request for sending a message is received from a server, the server will ....

Bullnheimer B., R.F.Hartl and C.Strauss. Applying the ant system to the vehicle routing problem. ########### ## ### ### ############## ############# ########## (MIC-97), Sophia-Antipolis, France.

....the exploration of not yet visited edges and diversity in solution generation. 5. 4 MACS VRPTW for vehicle routing problems with time windows Although VRPs are a relatively direct extensions of the TSP, the first ant system for vehicle routing problems has been designed only very recently by Bullnheimer et al. 1997, 1999) who considered the most elementary version of the problem: the capacitated vehicle routing problem (CVRP) This chapter considers a more elaborated vehicle routing problem with two objective functions: i) the minimization of the number of tours (or vehicles) and (ii) the minimization of the ....

B. Bullnheimer, R. F. Hartl, C. Strauss, Applying the Ant System to the Vehicle Routing Problem, in Metaheuristics: Advances and Trends in Local Search for Optimization, S.Voss, S. Martello, I.H. Osman and C. Roucairol (eds.), Kluwer Academic Publishers, Boston, 1999, 285-296.

....stochastic approaches based on ant colonies for problem solving. This concerns for instance combinatorial optimization problems like the travelling salesman problem (Dorigo and Gambardella 1997) the quadratic assignment problem (Gambardella et al. 1997) routing problems (Di Caro and Dorigo 1997) (Bullnheimer et al. 1997), the bin packing problem (Bilchev 1996) or time tabling problems (Forsyth and Wren 1997) Numerical optimization problems have been tackled also with artificial ants such as in (Bilchev and Parmee 1996) as well as robotics (Deneubourg et al. 1990) Goss and Deneubourg 1991) Data clustering is ....

Bullnheimer B., Hartl R.F. and Strauss C. (1997), Applying the ant system to the vehicle routing problem, Third International Conference on Metaheuristics.

.... b 1999 [64] Scheduling problems Colorni, Dorigo Maniezzo AS JSP 1994 [17] Stutzle AS FSP 1997 [80] Bauer et al. ACS SMTTP 1999 [2] den Besten, Stutzle Dorigo ACS SMTWTP 1999 [21] Merkle, Middendorf Schmeck ACO RCPS 2000 [66] Vehicle routing Bullnheimer, Hartl Strauss AS VRP 1997 [12, 13] Gambardella, Taillard Agazzi HAS VRP 1999 [45] Connection oriented Schoonderwoerd et al. ABC 1996 [77, 76] network routing White, Pagurek Oppacher ASGA 1998 [89] Di Caro Dorigo AntNet FS 1998 [26] Bonabeau et al. ABC smart ants 1998 [10] Connection less Di Caro Dorigo AntNet ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the Ant System to the vehicle routing problem. In S. Vo S. Martello, I. H. Osman, and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 285--296. Kluwer Academic Publishers, Dordrecht, 1999.

.... 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 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 ....

....These results, although not exceptional, are encouraging and suggest that further work could lead to a workable system. Also, a comparison with other approaches is necessary. 3.1. 4 Vehicle routing problem There are many types of vehicle routing problems (VRPs) Bullnheimer, Hartl and Strauss [11, 13, 15] applied an AS like algorithm to the following instance. Let G = N, A, d) be 10 In fact, the TSP can be seen as the problem of assigning to each of n cities a di#erent number chosen between 1 and n. QAP, as the TSP, is NP hard [89] 11 HAS QAP is an ant algorithm which, although initially ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the ant system to the vehicle routing problem. In I. H. Osman S. Vo, S. Martello and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 109--120. Kluwer Academics, 1998.

....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, for example, in the ATM ....

Bullnheimer B., R.F. Hartl and C. Strauss, Applying the Ant System to the Vehicle Routing Problem. 2nd Metaheuristics International Conference (MIC-97), Sophia-Antipolis, France, 1997.

.... 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 Gambardella, Taillard Agazzi 1999 [26] HAS VRP Connection oriented Schoonderwoerd, Holland, 1996 [45, 44] ABC network routing Bruten Rothkrantz White, Pagurek Oppacher 1998 [53] ASGA Di Caro Dorigo 1998 [14] AntNet FS Bonabeau, Henaux, Gu erin, 1998 [4] ABC smart ants Snyers, Kuntz ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the ant system to the vehicle routing problem. In I. H. Osman S. Vo, S. Martello and C. Roucairol, editors, MetaHeuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 109--120. Kluwer Academics, 1998.

....the exploration of not yet visited edges and diversity in solution generation. 5. 4 MACS VRPTW for vehicle routing problems with time windows Although VRPs are a relatively direct extensions of the TSP, the first ant system for vehicle routing problems has been designed only very recently by Bullnheimer et al. 1997, 1999) who considered the most elementary version of the problem: the capacitated vehicle routing problem (CVRP) This chapter considers a more elaborated vehicle routing problem with two objective functions: i) the minimization of the number of tours (or vehicles) and (ii) the minimization of the ....

B. Bullnheimer, R. F. Hartl, C. Strauss, Applying the Ant System to the Vehicle Routing Problem, in Metaheuristics: Advances and Trends in Local Search for Optimization, S.Voss, S. Martello, I.H. Osman and C. Roucairol (eds.), Kluwer Academic Publishers, Boston, 1999, 285-296.

....path (or even the shortest path) to send out the message. As searching for the optimal path in a stationary network is already a difficult problem [11] the searching for the optimal path in a faulty network or mobile network will be much more difficult. Ant routing (or ant like routing method) [31, 32, 33, 34, 5, 7] is a recent proposed mobile agent based network routing algorithm for use in these environments. The idea mimic the path searching process of an ant. Once a request for sending message is received from a server, the server will generate a number of mobile agents like ant. These agents will then ....

Bullnheimer B., R.F.Hartl and C.Strauss. Applying the ant system to the vehicle routing problem. Proceedings of the 2nd Metaheuristics International Conference (MIC-97), Sophia-Antipolis, France.

....problems within a reasonable amount of time. Ant Colonies (AC) is a general purpose heuristic (meta heuristic) that has been proposed by Dorigo [1] AC has achieved widespread success in solving different optimization problems (traveling salesman [2] quadratic assignment [3] vehicle routing [4], job shop scheduling [5] telecommunication routing [6] etc. Our aim is to develop parallel models for ACs to solve large combinatorial optimization problems. The parallel AC algorithm has been combined with a local search method based on tabu search. The testbed optimization problem we used ....

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the ant system to the vehicle routing problem. In 2nd Metaheuristics Int. Conf. MIC'97, Sophia-Antipolis, France, July 1997.

....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 messages have two ....

Bullnheimer B., R.F. Hartl and C. Strauss, Applying the Ant System to the Vehicle Routing Problem. 2nd Metaheuristics International Conference (MIC-97), SophiaAntipolis, France, 1997.

....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, Hartl, and Strauss [8, 6]. They obtained good computational results for standard benchmark instances, slightly worse than the best performing Tabu Search algorithms. A recent application by Gambardella, Taillard, and Agazzi to vehicle routing problems with time windows, improves the best known solutions for some benchmark ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. Applying the Ant System to the Vehicle Routing Problem. In S. Voss, S. Martello, I.H. Osman, and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 285--296. Kluwer, Boston, 1999.

....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, Hartl, and Strauss [8, 6]. They obtained good computational results for standard benchmark instances, slightly worse than the best performing Tabu Search algorithms. A recent application by Gambardella, Taillard, and Agazzi to vehicle routing problems with time windows, improves the best known solutions for some benchmark ....

B. Bullnheimer, R.F. Hartl, and C. Strauss. Applying the Ant System to the Vehicle Routing Problem. In S. Voss, S. Martello, I.H. Osman, and C. Roucairol, editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 285--296. Kluwer, Boston, 1999.

....and new solutions are successively generated by the ants. In particular let us mention successful hybrid ant system implementations applied to symmetric and asymmetric TSPs [14, 21, 46] sequential ordering problems [22] quadratic assignment problems [23, 46, 55] and vehicle routing problems [6]. 3 Adaptive memory programming Although the methods presented in the previous section may look very different at first glance, an analysis of a number of implementations, and especially the most efficient and recent ones, shows that they are sometimes extremely close in their working ....

Bullnheimer B., R.F. Hartl and C. Strauss (1997), "Applying the Ant System to the Vehicle Routing Problem", Presented at the 2nd Metaheuristic International Conference, Sophia-Antipolis, France.

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Bullnheimer, B., R. F. Hartl and C. Strauss (1997): Applying the Ant System to the Vehicle Routing Problem, Workin Paper POM-WP 4/97, University of Vienna.

....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 sequential tour building approach, which ....

.... (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 sequential tour building approach, which utilized a parametrized savings criterion. The main idea of our new approach is to transfer the simultaneous tour construction mechanism proposed in [11] into a rank based Ant System. Our computational ....

[Article contains additional citation context not shown here]

Bullnheimer, B., Hartl, R. F. and Strauss, Ch.: Applying the ant system to the vehicle routing problem. In: Voss, S., Martello, S., Osman, I. H. and Roucairol, C. (Eds.): Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer, Boston (1999)

....an adaptive memory represents the pheromone trails. The artificial ants are additionally equiped with a local heuristic function to guide their search through the set of feasible solutions. The application of the Ant System to Traveling Salesman [10] Quadratic Assignment [14] Vehicle Routing [3], Job Shop Scheduling [6] and Graph Coloring [7] is evidence for the methods versatility. As problem size increases performance becomes a crucial criteria in combinatorial optimization problems. Several attempts on parallelizing heuristics for combinatorial optimization problems have been ....

Bullnheimer, B.; Hartl, R.F.; Strauss, C.: Applying the Ant System to the Vehicle Routing Problem. Paper presented at 2 nd International Conference on Metaheuristics (MIC'97), Sophia-Antipolis, France, 1997.

....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 ....

.... ae 0 (5) with the initial trail intensity 0 = 1 n Delta TEDD where TEDD is the total tardiness for a processing sequence generated according to the EDD rule. 4. 3 Local Search Ant Colony Optimization algorithms have been shown to work very well if combined with a local search procedure [4, 5, 14, 32]. In such a case, a local search procedure is applied to the solutions generated by the artificial ants before updating the pheromone trails. For our ant approach to the SMTTP a pairwise swap was considered. The pairwise swap is a 2 opt like strategy that may either be applied to the set of all ....

Bullnheimer, B., R.F. Hartl and C. Strauss (1998): Applying the Ant System to the Vehicle Routing Problem, in: S. Voss, S. Martello, I. H. Osman and C. Roucairol, eds, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, Kluwer, Boston, pp. 109120.

.... 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 ....

.... Delta 0 (7) with the initial trail intensity 0 = 1 n Delta TEDD where TEDD is the total tardiness for a processing sequence generated according to the EDD rule. 4. 3 Local Search In several other applications ACO algorithms have worked very well if a local search procedure is integrated [5, 6, 17, 39]. Such a local search procedure is applied to the solutions generated by the artificial ants before updating the pheromone trails. We considered pairwise swapping and transposition as two local search alternatives to be part of the ACO approach for the SMTTP 1 . Both strategies are similar to a ....

Bullnheimer, B., R.F. Hartl and C. Strauss (1998): Applying the Ant System to the Vehicle Routing Problem, in: S. Voss, S. Martello, I. H. Osman and C. Roucairol, eds, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, Kluwer, Boston, pp. 109120.

....based version outperformed the others 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 ....

Bullnheimer, B. and Strauss, C.: Applying the ant system to the vehicle routing problem. Working paper, University of Vienna, 1996.

....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 results. The remainder of the paper is organized as follows. First we briefly describe ....

....2 Omega 0 otherwise (1) This probability distribution is biased by the parameters ff and fi that determine the relative influence of the trails and the visibility, respectively. For the TSP Dorigo et al. 12] define the visibility as the reciprocal of the distance. The same is done for the VRP in [2] where the selection probability is then further extended by problem specific information. There, the inclusion of savings and capacity utilization both lead to better results. On the other hand, the latter is relative costly in terms of computation time (as it has to be calculated in each step of ....

[Article contains additional citation context not shown here]

B. Bullnheimer, R.F. Hartl and C. Strauss, Applying the Ant System to the Vehicle Routing Problem, Paper presented at 2nd International Conference on Metaheuristics, SophiaAntipolis, France (1997).

....version outperformed the others 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 ....

Bullnheimer, B., Hartl, R.F. and Strauss, C.: Applying the Ant System to the Vehicle Routing Problem. 2nd International Conference on Metaheuristics (MIC'97), Sophia-Antipolis, France, 1997.

....and an adaptive memory represents the pheromone trails. The artificial ants are additionally equiped with a local heuristic function to guide their search through the set of feasible solutions. The application of the Ant System to Traveling Salesman [10] Quadratic Assignment [13] Vehicle Routing [4], Job Shop Scheduling [6] Graph Coloring [7] and Timetabling [2] is evidence for the methods versatility. As problem size increases performance becomes a crucial criteria. Furthermore, the structure of the Ant System algorithm is highly suitable for parallelization. Both mentioned considerations ....

Bullnheimer, B.; Hartl, R.F.; Strauss, C.: Applying the Ant System to the Vehicle Routing Problem. Paper presented at 2 nd International Conference on Metaheuristics (MIC'97), Sophia-Antipolis, France, 1997.

No context found.

B. Bullnheimer, R.F. Hartl, and C. Strauss, Applying the ant system to the vehicle routing problem, In: Voss S., Martello S., Osman I.H., Roucairol C. (eds.) MetaHeuristics: Advances and Trends in Local Search Paradigms for Optimization, Kluwer, Boston, 1999.

No context found.

B. Bullnheimer, R. F. Hartl, and C. Strauss. Applying the ant system to the vehicle routing problem. In 2nd Metaheuristics Int. Conf. MIC'97, Sophia-Antipolis, France, July 1997.

No context found.

Bullnheimer, B., Hartl, R. F. & Strauss, C. (1997b). Applying the ant system to the vehicle routing problem. 2nd Intnl Conf. on Metaheuristics (MIC'97).

No context found.

Bullnheimer B., R.F. Hartl and C. Strauss (1997), Applying the Ant System to the Vehicle Routing Problem. 2nd Metaheuristics International Conference (MIC-97), SophiaAntipolis, France.

No context found.

Bullnheimer B., R.F. Hartl and C. Strauss. 1997, Applying the Ant System to the Vehicle Routing Problem. 2nd Metaheuristics International Conference (MIC-97), Sophia-Antipolis, France.

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