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...is aim we will also develop a new serializer. We consider two problems in this section. Both are used as standard benchmark problems for scheduling. The first one is called ABZ6 and was introduced in =-=[1]-=-. The second one is the famous MT10 and was introduced in [12]. MT10 was considered as an especially hard problem for several years. It took more than 25 years that the optimality of a found makespan ...

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...t S est T dur S dur T holds, T must be last. edge-finding Similar rules can be formulated if T is contained in S. For this kind of reasoning, the term edge-finding was coined in =-=[2]-=-. There are several variations of this idea in [5], [2], [6], [11] for the Operations Research community and in [13], [7], [3], [14] for the constraint programming community; they differ in the amount...

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... T must be last. edge-finding Similar rules can be formulated if T is contained in S. For this kind of reasoning, the term edge-finding was coined in [2]. There are several variations of this idea in =-=[5]-=-, [2], [6], [11] for the Operations Research community and in [13], [7], [3], [14] for the constraint programming community; they differ in the amount of propagation and which sets S are considered fo...

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... last. edge-finding Similar rules can be formulated if T is contained in S. For this kind of reasoning, the term edge-finding was coined in [2]. There are several variations of this idea in [5], [2], =-=[6]-=-, [11] for the Operations Research community and in [13], [7], [3], [14] for the constraint programming community; they differ in the amount of propagation and which sets S are considered for edge-fin...

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.... edge-finding Similar rules can be formulated if T is contained in S. For this kind of reasoning, the term edge-finding was coined in [2]. There are several variations of this idea in [5], [2], [6], =-=[11]-=- for the Operations Research community and in [13], [7], [3], [14] for the constraint programming community; they differ in the amount of propagation and which sets S are considered for edge-finding. ...

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... problems in this section. Both are used as standard benchmark problems for scheduling. The first one is called ABZ6 and was introduced in [1]. The second one is the famous MT10 and was introduced in =-=[12]-=-. MT10 was considered as an especially hard problem for several years. It took more than 25 years that the optimality of a found makespan was proven [5]. 94 Chapter 11. Scheduling Figure 11.17: A sear...

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...ned in S. For this kind of reasoning, the term edge-finding was coined in [2]. There are several variations of this idea in [5], [2], [6], [11] for the Operations Research community and in [13], [7], =-=[3]-=-, [14] for the constraint programming community; they differ in the amount of propagation and which sets S are considered for edge-finding. The resulting propagators do a lot of propagation, but are a...

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... Post precedence constraints 78a {Schedule.serializedDisj TasksOnRes Start Dur} Order tasks 81a Assign start times 78b end end 11.2 Constructing a Bridge The following problem is taken from =-=[4]-=- and is used as a benchmark in the constraint programming community. The problem is to schedule the construction of the bridge shown in Figure 11.10. Problem Specification The problem is specified as ...

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...ontained in S. For this kind of reasoning, the term edge-finding was coined in [2]. There are several variations of this idea in [5], [2], [6], [11] for the Operations Research community and in [13], =-=[7]-=-, [3], [14] for the constraint programming community; they differ in the amount of propagation and which sets S are considered for edge-finding. The resulting propagators do a lot of propagation, but ...

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...:3 constraints: [ before(4 11) before(5 10) before(6 11) disjoint(1 [2 3 5 7 8 10]) disjoint(2 [3 4 7 8 9 11]) disjoint(3 [5 6 8]) disjoint(4 [6 8 10]) disjoint(6 [7 10]) disjoint(7 [8 9]) disjoint(8 =-=[10]-=-) ] ) 42 Chapter 6. Minimizing a Cost Function 7Propagators for Redundant Constraints For some problems, the performance of a script can be drastically improved by introducing propagators for redundan...

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...ull tree contains more than 47000 choice nodes. A variant of this task-oriented serializer is especially designed to find good solutions. To this aim Oz provides Schedule.taskIntervalsDistO (see also =-=[8]-=-). To find the optimal solution and to prove its optimality with this strategy we need 2979 choice nodes. But be aware that the use of this strategy may also lead to deep search trees which result in ...