A New Characterization of Relevant Intervals for Energetic Reasoning

Derrien, Alban; Petit, Thierry

doi:10.1007/978-3-319-10428-7_22

Cited by 17 publications

(18 citation statements)

References 9 publications

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“…This test is based on the so-called energetic reasoning [10] and is an adaptation on the well-known "left-shift/right-shift" test of Baptiste et al [3] for the CuSP. We also extend to the CECSP the results of Derrien and Petit [8]. A previous version of the test for the CECSP with identity function was proposed in [2].…”

Section: Energetic Reasoningmentioning

confidence: 73%

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

et al. 2015

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International audienceThis paper addresses a scheduling problem with a continuously-divisible, cumulative and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with a non-decreasing and continuous function. The goal is to find a feasible schedule, which is already NP-complete, and then to minimize the resource consumption. For the case where all functions are linear, we present two new Mixed Integer Linear Programs (MILP), as well as improvements of an existing formulation. We also present a detailed version of the adaptation of the well-known "left-shift/right-shift" satisfiability test for the cumulative constraint and the associated time-window adjustments to our problem. For this test, three ways of computing relevant intervals are described. Finally, a hybrid branch-and-bound using both the satisfiability test and the MILP is presented with a new heuristic for choosing the variable on which the branching is done. Computational experiments on randomly generated instances are reported in order to compare all of these solution methods

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Section: Energetic Reasoningmentioning

confidence: 73%

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

et al. 2015

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“…This work extends the work of [13] for linear processing rate functions. The full characterization of relevant intervals for the time-bound adjustments is also provided, extending the result for the cumulative constraint [4]. This characterization was not presented in [13].…”

Section: Energetic Reasoningmentioning

confidence: 85%

Cumulative scheduling with variable task profiles and concave piecewise linear processing rate functions

2017

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“…We added some improvements proposed by Derrien et Petit to reduce the number of considered intervals [5]; -Not-First-Not-Last (NFNL) is implemented with a O(n 3 ) variant of the algorithm proposed by Schutt et al [14].…”

Section: Algorithm 3: Refinement Of Pushing and Pushed With O(n) Overmentioning

confidence: 99%

Time-Table Disjunctive Reasoning for the Cumulative Constraint

Hartert

Schaus

2015

Integration of AI and OR Techniques in Constraint Programming

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Abstract. Scheduling has been a successful domain of application for constraint programming since its beginnings. The cumulative constraint -which enforces the usage of a limited resource by several tasks -is one of the core components that are surely responsible of this success. Unfortunately, ensuring bound-consistency for the cumulative constraint is already NP-Hard. Therefore, several relaxations were proposed to reduce domains in polynomial time such as Time-Tabling, Edge-Finding, Energetic Reasoning, and Not-First-Not-Last. Recently, Vilim introduced the Time-Table Edge-Finding reasoning which strengthens Edge-Finding by considering the time-table of the resource. We pursue the idea of exploiting the time-table to detect disjunctive pairs of tasks dynamically during the search. This new type of filtering -which we call time-table disjunctive reasoning -is not dominated by existing filtering rules. We propose a simple algorithm that implements this filtering rule with a O(n 2 ) time complexity (where n is the number of tasks) without relying on complex data structures. Our results on well known benchmarks highlight that using this new algorithm can substantially improve the solving process for some instances and only adds a marginally low computation overhead for the other ones.

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A New Characterization of Relevant Intervals for Energetic Reasoning

Cited by 17 publications

References 9 publications

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

Cumulative scheduling with variable task profiles and concave piecewise linear processing rate functions

Time-Table Disjunctive Reasoning for the Cumulative Constraint

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