Time-Table Disjunctive Reasoning for the Cumulative Constraint

Hartert, Renaud; Schaus, Pierre

doi:10.1007/978-3-319-18008-3_11

Cited by 7 publications

(3 citation statements)

References 14 publications

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“…We believe that the usage of range min query may be useful for subsequent research on scheduling, for instance in time-table disjunctive reasoning [8]. We introduced simple but scalable O(n 2 ) filtering for the cumulative constraint.…”

Section: Resultsmentioning

confidence: 99%

Simple and Scalable Time-Table Filtering for the Cumulative Constraint

Hartert

Schaus

2015

Lecture Notes in Computer Science

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Abstract. Cumulative is an essential constraint in the CP framework, and is present in scheduling and packing applications. The lightest filtering for the cumulative constraint is time-tabling. It has been improved several times over the last decade. The best known theoretical time complexity for time-table is O(n log n) introduced by Ouellet and Quimper. We show a new algorithm able to run in O(n), by relying on range min query algorithms. This approach is more of theoretical rather than practical interest, because of the generally larger number of iterations needed to reach the fixed point. On the practical side, the recent synchronized sweep algorithm of Letort et al, with a time-complexity of O(n 2 ), requires fewer iterations to reach the fix-point and is considered as the most scalable approach. Unfortunately this algorithm is not trivial to implement. In this work we present a O(n 2 ) simple two step alternative approach: first building the mandatory profile, then updating all the bounds of the activities. Our experimental results show that our algorithm outperforms synchronized sweep and the time-tabling implementations of other open-source solvers on large scale scheduling instances, sometimes significantly.Keywords: Constraint programming, Large-Scale, Scheduling, Cumulative Constraint, Time-table. PreliminariesIn this paper, we focus on a single cumulative resource with a discrete finite capacity C ∈ N and a set of n tasks Ω = {1, . . . , n}. Each task i has a start time s i ∈ Z, a fixed duration d i ∈ N, and an end time e i ∈ Z such that the equality s i + d i = e i holds. Moreover, each task i consumes a fixed amount of resource c i ∈ N during its processing time. Tasks are non-preemptive, i.e., they cannot be interrupted during their processing time. In the following, we denote by s i and s i the earliest and the latest start time of task i and by e i and e i the earliest and latest end time of task i (see Fig. 1). The cumulative constraint [1] ensures that the accumulated resource consumption does not exceed the maximum capacity C at any time t (see Fig. 2): ∀t ∈ Z : i∈Ω : si≤t

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Section: Resultsmentioning

confidence: 99%

Simple and Scalable Time-Table Filtering for the Cumulative Constraint

Hartert

Schaus

2015

Lecture Notes in Computer Science

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“…As future work, we would like to integrate into CPChecker properties of scheduling filtering algorithms [12] such as edgefinder, not-first not-last, time-table consistency, energy filtering, etc. for testing the most recent implementation of scheduling algorithms [13,14,15,16,17,18].…”

Section: Discussionmentioning

confidence: 99%

Testing Global Constraints

Aurélie¹,

Valentin²,

Schaus³

2018

Preprint

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Every Constraint Programming (CP) solver exposes a library of constraints for solving combinatorial problems. In order to be useful, CP solvers need to be bug-free. Therefore the testing of the solver is crucial to make developers and users confident. We present a Java library allowing any JVM based solver to test that the implementations of the individual constraints are correct. The library can be used in a test suite executed in a continuous integration tool or it can also be used to discover minimalist instances violating some properties (arc-consistency, etc) in order to help the developer to identify the origin of the problem using standard debuggers.

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“…We analyzed the Energetic Reasoning propagator for the cumulative constraint [1,5,10,11] on Resource Constrained Project Scheduling Problems (RCPSP) instances. This is one of the strongest propagator for cumulative in terms of performed inference, but it comes with a quite high complexity, O(n 3 ).…”

Section: Constraint Programmingmentioning

confidence: 99%

A Visual Web Tool to Perform What-If Analysis of Optimization Approaches

Cauwelaert¹,

Lombardi²,

Schaus³

2017

Preprint

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In Operation Research, practical evaluation is essential to validate the efficacy of optimization approaches. This paper promotes the usage of performance profiles as a standard practice to visualize and analyze experimental results. It introduces a Web tool to construct and export performance profiles as SVG or HTML files. In addition, the application relies on a methodology introduced in [18] to estimate the benefit of hypothetical solver improvements. Therefore, the tool allows one to employ what-if analysis to screen possible research directions, and identify those having the best potential. The approach is showcased on two Operation Research technologies: Constraint Programming and Mixed Integer Linear Programming.

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Time-Table Disjunctive Reasoning for the Cumulative Constraint

Cited by 7 publications

References 14 publications

Simple and Scalable Time-Table Filtering for the Cumulative Constraint

Simple and Scalable Time-Table Filtering for the Cumulative Constraint

Testing Global Constraints

A Visual Web Tool to Perform What-If Analysis of Optimization Approaches

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