MIDAS: A mixed integer dynamic approximation scheme

Philpott, Andy; Wahid, F.; Bonnans, J. Frédéric

doi:10.1007/s10107-019-01368-1

Cited by 24 publications

(16 citation statements)

References 17 publications

(11 reference statements)

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“…Another new and promising method that can be used to solve the nonconvex MTHS problem is reported in [28]. As SDDiP it is an extension of SDDP for handling nonconvexities.…”

Section: B Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Hjelmeland

Zou

Helseth

et al. 2019

IEEE Trans. Sustain. Energy

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Hydropower producers rely on stochastic optimization when scheduling their resources over long periods of time. Due to its computational complexity, the optimization problem is normally cast as a stochastic linear program. In a future power market with more volatile power prices, it becomes increasingly important to capture parts of the hydropower operational characteristics that are not easily linearized, e.g. unit commitment and nonconvex generation curves.Stochastic dual dynamic programming (SDDP) is a stateof-the-art algorithm for long-and medium-term hydropower scheduling with a linear problem formulation. A recently proposed extension of the SDDP method known as stochastic dual dynamic integer programming (SDDiP) has proven convergence also in the nonconvex case. We apply the SDDiP algorithm to the medium-term hydropower scheduling (MTHS) problem and elaborate on how to incorporate stagewise dependent stochastic variables on the right-hand sides and the objective of the optimization problem. Finally, we demonstrate the capability of the SDDiP algorithm on a case study for a Norwegian hydropower producer.The case study demonstrates that it is possible but timeconsuming to solve the MTHS problem to optimality. However, the case study shows that a new type of cut, known as strengthened Benders cut, significantly contributes to closing the optimality gap compared to classical Benders cuts.

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“…Another new and promising method that can be used to solve the nonconvex MTHS problem is reported in [28]. As SDDiP it is an extension of SDDP for handling nonconvexities.…”

Section: B Stochastic Dual Dynamic Programmingmentioning

confidence: 99%

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Hjelmeland

Zou

Helseth

et al. 2019

IEEE Trans. Sustain. Energy

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“…Only recently, some substantial progress has been made in generalizing the Benders decomposition idea to multistage problems with non-convex value functions directly. In [36], step functions are used, instead of cutting-planes, to approximate the value functions, presuming their monotonicity.…”

Section: Introductionmentioning

confidence: 99%

Non-convex nested Benders decomposition

Füllner

Rebennack

2022

Math. Program.

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We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an $$\varepsilon $$ ε -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size.

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“…A considerable amount of research has been conducted for solving the nonconvex MTHS problem, such as [8][9][10][11]. Except [10], which proposed a novel approach that uses step functions to model a nonconvex EFP function, they all rely on solving some relaxation of the original problem. This is also the case for the SB cuts applied in this work.…”

Section: Introductionmentioning

confidence: 99%

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

2019

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We propose a model for medium-term hydropower scheduling (MTHS) with variable head and uncertainty in inflow, reserve capacity, and energy price. With an increase of intermittent energy sources in the generation mix, it is expected that a flexible hydropower producer can obtain added profits by participating in markets other than just the energy market. To capture this added potential, the hydropower system should be modeled with a higher level of detail. In this context, we apply an algorithm based on stochastic dual dynamic programming (SDDP) to solve the nonconvex MTHS problem and show that the use of strengthened Benders (SB) cuts to represent the expected future profit (EFP) function provides accurate scheduling results for slightly nonconvex problems. A method to visualize the EFP function in a dynamic programming setting is provided, serving as a useful tool for a priori inspection of the EFP shape and its nonconvexity.

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MIDAS: A mixed integer dynamic approximation scheme

Cited by 24 publications

References 17 publications

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Non-convex nested Benders decomposition

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

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