A Dantzig–Wolfe decomposition algorithm for linear economic model predictive control of dynamically decoupled subsystems

Sokoler, Leo Emil; Standardi, Laura; Edlund, Kristian; Poulsen, Niels Kjølstad; Madsen, Henrik; Jørgensen, John Bagterp

doi:10.1016/j.jprocont.2014.05.013

Cited by 14 publications

(10 citation statements)

References 27 publications

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“…The maintenance scheduling and routing problem of offshore wind farms has been formulated as a VRP with side constraints by Irawan et al (2017) and solved efficiently using Dantzig-Wolfe decomposition. Dantzig-Wolfe decomposition has been used by Edlund et al (2011) and Sokoler et al (2014) for distributed implementation of the MPC optimization problem, which is an LP problem. Applications of Dantzig-Wolfe decomposition to MILP-MPC are relatively few.…”

Section: Mpc and Distributed Milpmentioning

confidence: 99%

“…Typical remedies for the erratic behaviour of the dual bounds include warm start e.g. (Sokoler et al, 2014), which provides a good dual bound at the beginning of the iteration, and stabilization techniques (Rousseau et al, 2007;Gschwind and Irnich, 2016), which add penalizing terms to (53) to avoid drastic change in the Lagrangian dual bounds. Another improvement of the standard column generation algorithm is the primal-dual column generation technique developed by Gondzio et al (2013), which uses suboptimal primal and dual solutions of the restricted master problem to improve the stability of the iteration.…”

Section: Upper and Lower Boundsmentioning

confidence: 99%

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Integrated condition-based track maintenance planning and crew scheduling of railway networks

Su¹,

Jamshidi

Núñez

et al. 2019

Transportation Research Part C: Emerging Technologies

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We develop a multi-level decision making approach for optimal condition-based maintenance planning of a railway network divided into a large number of sections with independent stochastic deterioration dynamics. At higher level, a chance-constrained Model Predictive Control (MPC) controller determines the long-term section-wise maintenance plan, minimizing condition deterioration and maintenance costs for a finite planning horizon, while ensuring that the deterioration level of each section stays below the maintenance threshold with a given probabilistic guarantee in the presence of parameter uncertainty. The resulting large MPC optimization problem containing both continuous and discrete decision variables is solved using Dantzig-Wolfe decomposition to improve the scalability of the proposed approach. At a lower level, the optimal short-term scheduling of the maintenance interventions suggested by the high-level controller and the optimal routing of the corresponding maintenance crew is formulated as a capacitated arc routing problem, which is solved exactly by transforming it into a node routing problem. The proposed approach is illustrated by a numerical case study on the optimal treatment of squats of a regional Dutch railway network. Simulation results show that the proposed approach is robust, non-conservative, and scalable.

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Section: Mpc and Distributed Milpmentioning

confidence: 99%

Section: Upper and Lower Boundsmentioning

confidence: 99%

Integrated condition-based track maintenance planning and crew scheduling of railway networks

Su¹,

Jamshidi

Núñez

et al. 2019

Transportation Research Part C: Emerging Technologies

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“…The discretized OCP is an MILP. To get well-behaved closedloop solutions, the OCP objective function can be augmented by 1 -and 2 -penalty terms on the input-rate [54]. For 2regularization, the OCP becomes an MIQP.…”

Section: A Standard Formmentioning

confidence: 99%

A Hierarchical Algorithm for Integrated Scheduling and Control With Applications to Power Systems

Sokoler

Dinesen

Jørgensen

2017

IEEE Trans. Contr. Syst. Technol.

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“…Remark 2: Provided that φ (u, x, z) is a convex function and that U is a convex set, u * CE can often be obtained efficiently by special-purpose optimization algorithms [24], [25].…”

Section: Certainty Equivalence Economic Model Predictive Controlmentioning

confidence: 99%

A mean-variance criterion for economic model predictive control of stochastic linear systems

Sokoler

Dammann

Madsen

et al. 2014

53rd IEEE Conference on Decision and Control

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Stochastic linear systems arise in a large number of control applications. This paper presents a mean-variance criterion for economic model predictive control (EMPC) of such systems. The system operating cost and its variance is approximated based on a Monte-Carlo approach. Using convex relaxation, the tractability of the resulting optimal control problem is addressed. We use a power management case study to compare different variations of the mean-variance strategy with EMPC based on the certainty equivalence principle. The certainty equivalence strategy is much more computationally efficient than the mean-variance strategies, but it does not account for the variance of the uncertain parameters. Openloop simulations suggest that a single-stage mean-variance approach yields a significantly lower operating cost than the certainty equivalence strategy. In closed-loop, the single-stage formulation is overly conservative, which results in a high operating cost. For this case, a two-stage extension of the mean-variance approach provides the best trade-off between the expected cost and its variance. It is demonstrated that by using a constraint back-off technique in the specific case study, certainty equivalence EMPC can be modified to perform almost as well as the two-stage mean-variance formulation. Nevertheless, we argue that the mean-variance approach can be used both as a strategy for evaluating less computational demanding methods such as the certainty equivalence method, and as an individual control strategy when heuristics such as constraint back-off do not perform well.Simulations demonstrate that while MV-EMPC(M) outperforms CE-EMPC in open-loop, the back-off based modification of CE-EMPC works almost as well in closed-loop. Nevertheless, the performance of MV-EMPC(M) provides important information that can be utilized to evaluate the performance of less computational demanding control strategies. We also emphasize that the preliminary results presented in this paper are based on a single test system. Other examples may show that the performance gap between MV-EMPC(M) and CE-EMPC can be much larger. 53rd IEEE Conference on Decision and Control

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A Dantzig–Wolfe decomposition algorithm for linear economic model predictive control of dynamically decoupled subsystems

Cited by 14 publications

References 27 publications

Integrated condition-based track maintenance planning and crew scheduling of railway networks

Integrated condition-based track maintenance planning and crew scheduling of railway networks

A Hierarchical Algorithm for Integrated Scheduling and Control With Applications to Power Systems

A mean-variance criterion for economic model predictive control of stochastic linear systems

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