A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In CEC99: Proceedings of the Congress on Evolutionary Computation, pages 1445--1450, July 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to locate administrative functions and employees among a set of offices in a building. In this case, it might be most efficient to minimize the amount of movement (of both people and paperwork) within the building. An ant colony heuristic was developed by Bauer, Bullnheimer, Hartl, and Strauss [2] for the singlemachine total tardiness problem. In this situation, a series of jobs to be performed on one machine must be scheduled. The goal is to minimize the total tardiness of the jobs, where tardiness is defined as the difference between the job s completion time and its due date (or ....

....Passenger seating Body style Wheel size 150, 180, 210 4, 5, 6 coupe, sedan, wagon 14 , 15 , 16 Attribute Levels Table 1. Automobile design example. Tr aveling Salesman Vehicle Routing Single Machine Tardiness Power Economic Dispatch Not tested.Table summarized from data in [2, 4, 5, 12]. Better Better Better Better Same Worse Better Problem Genetic Algorithms Simulated Annealing Tabu Search Neural Networks Table 2. Overall performance of ant approach compared to other techniques for several problems. ator. Artificial ants move from ....

Bauer, A., Bullnheimer, B., Hartl, R. F., and Strauss, C. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999 Congress on Evolutionary Computation (1999), 1445--1450.

....the bigger problems. Examples of these improvements are Ant Colony System [18] 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 ....

A. Bauer, B. Bullnheimer, R. F. Hartl, and C Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999.

....particularly well. 1 Introduction The Ant Colony Optimization (ACO) metaheuristic has recently been applied to several scheduling problems like the Job Shop problem [2, 5, 12] the Flow Shop problem [11] the Single Machine Total Tardiness problem (SMTTP) and its weighted variant the SMTWTP [1, 3, 7], and the Resource Constrained Project Scheduling problem [8] In ACO several generations of arti cial ants search for good solutions. Information exchange between the ants is based on principles of communicative behavior found in real ant colonies (for an introduction and overview see [4] ....

....Springer Verlag, LNCS 2037 (2001) 484 493. near good solutions. In addition to the pheromone values the ants will usually be guided by some problem speci c heuristic for evaluating the possible decisions. It has already been shown that ACO can solve permutation scheduling problems like SMTWTP [1, 3, 7] and Flow Shop [11] very successfully. A comparison between ACO and other heuristics on a set of benchmark problems from [13] for the SMTWTP was done in [3] ACO was able to nd for all 125 test instances with 100 jobs the best known solutions. This was signi cantly better than the best known ....

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A. Bauer, B. Bullnheimer, R.F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the

....the heuristic information ij used by the ants: Earliest Due Date (EDD) This heuristic puts the jobs in non decreasing order of the due dates d j . In this case ij = 1=d j . Modified Due Date (MDD) This heuristic puts the jobs in non decreasing order of the modified due dates mdd j [2] given by mdd j = maxfC p j ; d j g, where C is the sum of the processing times of the already sequenced jobs. In this case ij = 1=mdd j . Apparent Urgency (AU) This heuristic puts the jobs in non decreasing order of the apparent urgency [20] given by au j = w j =p j ) exp( maxfd j C ....

....rule is to make the decision of putting job j on position i less desirable for the other ants so that the exploration of different sequences is favored. 2. 3 Other ACO approaches to scheduling problems An application of ACO to the unweighted single machine total tardiness problem was presented in [2]. Although for this problem heuristic approaches appear not to be very interesting, because the total (unweighted) tardiness problem can be rather efficiently solved by enumerative methods [6] we verified that our approach substantially outperforms this early application. In the literature only ....

A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proc. of CEC'99, pages 1445--1450. IEEE Press, Piscataway, NJ, 1999.

....and then iteratively appends an unscheduled job to the partial sequence constructed so far. The heuristic information the ants use in addition to pheromone is either the jobs apparent urgency [12] or it is based on the modified due date rule which was used in an earlier application of ACO [2] to the unweighted single machine total tardiness problem (the unweighted version is much easier to solve than the weighted one) Local search is applied to all solutions the ants construct in each iteration. To achieve best possible performance we found that local search, candidate lists, and ....

A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC'99), pages 1445--1450. IEEE Press, 1999.

.... ordering problem [Gambardella and Dorigo, 1997] job shop scheduling [van der Zwaan and Marques, 1999] flow shop scheduling [St utzle, 1998] vehicle routing [Bullnheimer et al. 1999; Gambardella et al. 1999] bus driver scheduling [Forsyth and Wren, 1997] tardiness scheduling problems [Bauer et al. 1999; den Besten et al. 2000] and resource constrained project scheduling [Merkle et al. 2000] In most of these cases, the scheduling problem at hand is reduced to a TSPlike problem in which the problem is to find some optimal Job Job Job A A B Figure 2: In the Ant Colony Control (AC 2 ) ....

A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In CEC99: Proceedings of the Congress on Evolutionary Computation, pages 1445--1450, July 1999.

....have been tested. In this paper we propose an Ant Colony Optimization (ACO) approach for the RCPSP (see (Dorigo and Di Caro, 1999) for an introduction to ACO) The ACO approach has recently been applied to scheduling problems, as Job Shop, Flow Shop, and Single Machine Tardiness problems (see (Bauer et al. 1999; den Besten et al. 1999; Colorni et al. 1994; Merkle and Middendorf, 2000; Stutzle, 1998; van der Zwaan and Marques, 1999) In ACO several generations of artificial ants search for good solutions. Every ant of a generation builds up a solution step by step going through several probabilistic ....

....ants of the next generation are attracted by the pheromone so that they will search in the solution space near good solutions. In addition to the pheromone values the ants will usually be guided by some problem specific heuristic for evaluating the possible decisions. The algorithms proposed in (Bauer et al. 1999) and (Stutzle, 1998) for the single machine total tardiness problem and the flow shop problem respectively use a pheromone matrix T = T ij where pheromone is added to an element T ij of the pheromone matrix when a good solution was found where job j is the ith job on the machine. The ....

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Bauer, A., Bullnheimer, B., Hartl, R., and Strauss, C. (1999). An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC99), 6-9 July Washington D.C., USA, pages 1445--1450.

....the feasible neighborhood N k i of ant k is formed by the still unscheduled jobs. Pheromone trails are defined as follows: ij refers to the desirability of scheduling job j at position i. This definition of the pheromone trails is, in fact, used in most ACO application to scheduling problems [2, 21, 66, 80]. Concerning the heuristic information, in [21] the use of three priority rules allowed to define three different types of heuristic information for the SMTWTP. The investigated priority rules were: i) the earliest due date rule (EDD) which puts the jobs in non decreasing order of the due dates ....

....SMTWTP. The investigated priority rules were: i) the earliest due date rule (EDD) which puts the jobs in non decreasing order of the due dates d j , ii) the modified due date rule (MDD) which puts the jobs in non decreasing order of the modified due dates given by mdd j = maxfC p j ; d j g [2], where C is the sum of the processing times of the already sequenced jobs, and (iii) the apparent urgency rule (AU) which puts the jobs in non decreasing order of the apparent urgency [70] given by au j = w j =p j ) exp( maxfd j C j ; 0g) kp) where k is a parameter of the priority rule. In ....

[Article contains additional citation context not shown here]

A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC'99), pages 1445-- 1450. IEEE Press, Piscataway, NJ, 1999.

....transport networks. In their approach Varela and Sinclair use multiple pheromone types for the different wavelengths in their system. Other ACO inspired algorithms have been applied to problems such as the sequential ordering problem [11] vehicle routing [4] single machine scheduling [1], and resource constrained project scheduling [14] Unlike our system, each of these scheduling applications of ACO deals with a statically defined problem. But the shop floor is a dynamic environment and our approach treats it as such. 3. Our Approach: AC 2 Our system uses a colony of ....

A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In CEC99: Proceedings of the Congress on Evolutionary Computation, pages 1445--1450, July 1999.

....to compute the heuristic information ij used by ants: Earliest Due Date (EDD) This heuristic puts the jobs in non decreasing order of the due dates d j . In this case ij = 1=d j . Modi ed Due Date (MDD) This heuristic puts the jobs in non decreasing order of the modi ed due dates mdd j [2] given by mdd j = maxfC p j ; d j g, where C is the sum of the processing times of the already sequenced jobs. In this case ij = 1=mdd j . Apparent Urgency (AU) This heuristic puts the jobs in non decreasing order of the apparent urgency [21] given by au j = w j p j exp maxfd j C j ....

....rule is to make the decision of putting job j on position i less desirable for the other ants so that the exploration of di erent sequences is favored. 2. 3 Other ACO approaches to scheduling problems An application of ACO to the unweighted single machine total tardiness problem was presented in [2]. Although for this problem heuristic approaches appear not to be very interesting, because the total (unweighted) tardiness problem can be rather eciently solved by enumerative methods [6] we veri ed that our approach substantially outperforms this early application. In the literature only few ....

A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proc. of CEC'99, pages 1445-1450. IEEE Press, Piscataway, NJ, 1999. 12

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A. Bauer, B. Bullnheimer, R. F. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In CEC99: Proceedings of the Congress on Evolutionary Computation, pages 1445--1450, July 1999.

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A. Bauer, B. Bullnheimer, R. Hartl, and C. Strauss. An ant colony optimization approach for the single machine total tardiness problem. In Proceedings of the 1999.

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A. Bauer, B. Bullnheimer, R.F. Hartl, and C. Strauss. An Ant Colony Optimization Approach for the Single Machine Total Tardiness Problem. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC99), 6-9 July Washington D.C., USA, 1445-1450, 1999.

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