Medium Term Production Scheduling of a Hydro-thermal System under Uncertainty using Nested Benders Decomposition (Produktionsplanung eines hydro-thermischen Kraftwerkssystems unter Unsicherheit für mittlere Planungshorizonte unter Anwendung der Nested Benders Decomposition)

2008 ◽  
Vol 56 (4/2008) ◽  
Author(s):  
Kristian Nolde ◽  
Markus Uhr ◽  
Manfred Morari
Keyword(s):  
Production Scheduling ◽  
Benders Decomposition ◽  
Thermal System ◽  
Medium Term ◽  
Nested Benders Decomposition

scholarly journals Non-convex nested Benders decomposition

2022 ◽  
Author(s):  
Christian Füllner ◽  
Steffen Rebennack
Keyword(s):  
Benders Decomposition ◽  
Unit Commitment ◽  
Piecewise Linear ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Global Optimality ◽  
Value Functions ◽  
State Variables ◽  
Lipschitz Continuous ◽  
Nested Benders Decomposition

AbstractWe 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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