Algorithms for Non-Linear and Stochastic Resource Constrained Shortest Paths

Parmentier, Axel

doi:10.48550/arxiv.1504.07880

Cited by 2 publications

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“…This new algorithm is able to solve industrial instances with all their technical constraints within the time limit of 5 milliseconds. To that purpose, we have extended the RCSP framework recently introduced by the second author [13] to be able to deal with constraints on subpaths and have modeled the single unit commitment problem in this extended framework. We have then leveraged on the framework to design efficient solution algorithm.…”

Section: Contributions and Planmentioning

confidence: 99%

“…In this section, we follow [15] to briefly introduce the resource constrained shortest path framework of [13]. A digraph D is a pair (V, A), where V is the set of vertices and A is the set of arcs of D.…”

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

“…The proof being rather technical, we only sketch it here to underline the main ideas. Details are available in the preamble of Section 8 in [13]. Practical choices of key and tests are given after the proof.…”

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

“…The lattice ordered monoid framework is not required to use this test and this key. The main advantage of this framework is that it enables to use the practically efficient algorithm in [13] to compute good quality lower bounds b v on the resource q Q of all the v-d paths Q for each vertex v in V . When these bounds are computed, we can use the lower bound test (Low), and the key c(q P ⊕ b v ).…”

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

“…As we will see in Section 5, on our problem, the introduction of the lower bound test and of this new key both lead to a drastic speed-up with respect to the traditional choice mentioned above. This speed-up is not specific to our problem [13,15], and probably comes from the fact that (Low) discards many paths and c(q P ⊕ b v ) is a good evaluation of how promising a path P is. Furthermore, on our problem, computing the bounds takes around 8% (0.15ms) percent of the total solving time of the fastest enumeration algorithm.…”

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

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Resource constrained shortest path algorithm for EDF short-term thermal production planning problem

Kruber,

Parmentier,

Benchimol

2018

Preprint

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Unit commitment problem on an electricity network consists in choosing the production plan of the plants (units) of a company in order to meet demand constraints. It is generally solved using a decomposition approach where demand constraints are relaxed, resulting in one pricing subproblem for each unit. In this paper we focus on the pricing subproblem for thermal units at EDF, a major French electricity producer. Our objective is to determine an optimal two-day production plan that minimizes the overall cost while respecting several non-linear operational constraints. The pricing problem is generally solved by dynamic programming. However, due to the curse of dimensionality, dynamic programming reaches its limits when extra-constraints have to be enforced. We model the subproblem as a resource constrained shortest path (RCSP) problem. Leveraging on RCSP algorithms recently introduced by the second author, we obtain an order of magnitude speed-up with respect to traditional RCSP algorithms.

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Section: Contributions and Planmentioning

confidence: 99%

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

Section: Ordered Monoid Frameworkmentioning

confidence: 99%

See 3 more Smart Citations

Resource constrained shortest path algorithm for EDF short-term thermal production planning problem

Kruber,

Parmentier,

Benchimol

2018

Preprint

Self Cite

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Aircraft routing and crew pairing: Updated algorithms at Air France

Parmentier

Meunier

2020

Omega

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Aircraft routing and crew pairing problems aims at building the sequences of flight legs operated respectively by airplanes and by crews of an airline. Given their impact on airlines operating costs, both have been extensively studied for decades. Our goal is to provide reliable and easy to maintain frameworks for both problems at Air France. We propose simple approaches to deal with Air France current setting. For routing, we introduce a compact MIP formulation that can be solved by current MIP solvers in at most a few minutes even on Air France largest instances. Regarding crew pairing, we provide a standard methodology to model the column generation pricing subproblem within a new resource constrained shortest path framework recently introduced by the first author. This new framework, which can be used as a black-box, leverages on bounds on paths' resource to discard partial solutions and speed-up the resolution. The resulting approach enables to solve to optimality Air France largest instances. Recent literature has focused on integrating aircraft routing and crew pairing problems. As a side result, we have been able to solve to near optimality large industrial instances of the integrated problem by combining the aforementioned algorithms within a simple cut generating method.

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Algorithms for Non-Linear and Stochastic Resource Constrained Shortest Paths

Cited by 2 publications

References 0 publications

Resource constrained shortest path algorithm for EDF short-term thermal production planning problem

Resource constrained shortest path algorithm for EDF short-term thermal production planning problem

Aircraft routing and crew pairing: Updated algorithms at Air France

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