Column generation for the discrete UC problem with min-stop ramping constraints

Dupin, Nicolas

doi:10.1016/j.ifacol.2019.11.186

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…Table 2 shows that the quality of the lower bounds of the extended DW reformulation outperforms compact formulations at the LP relaxation and also at the root noot of the B&B tree considering the generic cuts implemented in Cplex. Note that this was not the case in [79], and these results are coherent with the known results for the class of vehicle routing problems [11].…”

Section: Results With Extended Dw Reformulationsupporting

confidence: 89%

“…There is a theoretical advantage in computing the LP relaxation of the extended formulation ( 27)-( 29) instead of one of the LP relaxation of the compact formulations [78]. However, it is possible to have equality among these LP relaxations in the case of a tight formulation existing for sub-problems, as in [79]. It is a numerical issue to test if an improvement of the LP relaxation is obtained considering the DW extended formulation and if it compensates the higher computation times to process the CG algorithm.…”

Section: Dual Bounds Derived From Cgmentioning

confidence: 99%

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Matheuristics and Column Generation for a Basic Technician Routing Problem

Dupin

Parize²,

Talbi

2021

Algorithms

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This paper considers a variant of the Vehicle Routing Problem with Time Windows, with site dependencies, multiple depots and outsourcing costs. This problem is the basis for many technician routing problems. Having both site-dependency and time window constraints lresults in difficulties in finding feasible solutions and induces highly constrained instances. Matheuristics based on Mixed Integer Linear Programming compact formulations are firstly designed. Column Generation matheuristics are then described by using previous matheuristics and machine learning techniques to stabilize and speed up the convergence of the Column Generation algorithm. The computational experiments are analyzed on public instances with graduated difficulties in order to analyze the accuracy of algorithms for ensuring feasibility and the quality of solutions for weakly to highly constrained instances. The results emphasize the interest of the multiple types of hybridization between mathematical programming, machine learning and heuristics inside the Column Generation framework. This work offers perspectives for many extensions of technician routing problems.

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Section: Results With Extended Dw Reformulationsupporting

confidence: 89%

Section: Dual Bounds Derived From Cgmentioning

confidence: 99%

Matheuristics and Column Generation for a Basic Technician Routing Problem

Dupin

Parize²,

Talbi

2021

Algorithms

Self Cite

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“…That said, we naturally associate (6) with D-W decomposition and CG -see e.g., [35]. However, solving a large UC problem with CG does not yet seem promisingsee e.g., a recent work [43]. Fortunately, we remind the reader that our goal is not to solve this integer problem, but the LD (2).…”

Section: D-w Characterization and Cg Algorithmmentioning

confidence: 99%

Computation of Convex Hull Prices in Electricity Markets with Non-Convexities using Dantzig-Wolfe Decomposition

Andrianesis¹,

Bertsimas²,

Caramanis³

et al. 2020

Preprint

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The presence of non-convexities in electricity markets has been an active research area for about two decades. The -inevitable under current marginal cost pricing -problem of guaranteeing that no truthful-bidding market participant incurs losses in the day-ahead (DA) market is addressed in current practice through make-whole payments a.k.a. uplift. Alternative pricing rules have been studied to deal with this problem. Among them, Convex Hull (CH) prices associated with minimum uplift have attracted significant attention. Several US Independent System Operators (ISOs) have considered CH prices but resorted to approximations, mainly because determining exact CH prices is computationally challenging, while providing little intuition about the price formation rational. In this paper, we describe CH price estimation problem by relying on Dantzig-Wolfe decomposition and Column Generation. Moreover, the approach provides intuition on the underlying price formation rational. A test bed of stylized examples elucidate an exposition of the intuition in the CH price formation. In addition, a realistic ISO dataset is used to suggest scalability and validate the proofof-concept.

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