Nested Benders Decomposition and Dynamic Programming for Reservoir Optimisation

1999 ◽  
Vol 50 (5) ◽  
pp. 468 ◽  
Author(s):  
T. W. Archibald ◽  
C. S. Buchanan ◽  
K. I. M. McKinnon ◽  
L. C. Thomas
Keyword(s):  
Dynamic Programming ◽  
Benders Decomposition ◽  
Nested Benders Decomposition

Nested Benders decomposition and dynamic programming for reservoir optimisation

1999 ◽  
Vol 50 (5) ◽  
pp. 468-479 ◽  
Author(s):  
T W Archibald ◽  
C S Buchanan ◽  
K I M McKinnon ◽  
L C Thomas
Keyword(s):  
Dynamic Programming ◽  
Benders Decomposition ◽  
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.

scholarly journals New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

OR Spectrum ◽  
2021 ◽  
Author(s):  
Heiko Diefenbach ◽  
Simon Emde ◽  
Christoph H. Glock ◽  
Eric H. Grosse
Keyword(s):  
Dynamic Programming ◽  
Benders Decomposition ◽  
Computational Study ◽  
Programming Approach ◽  
Routing Problem ◽  
Solution Approach ◽  
Dynamic Programming Approach ◽  
Storage Assignment ◽  
Sweep Algorithm ◽  
Optimality Gap

AbstractThis paper develops new solution procedures for the order picker routing problem in U-shaped order picking zones with a movable depot, which has so far only been solved using simple heuristics. The paper presents the first exact solution approach, based on combinatorial Benders decomposition, as well as a heuristic approach based on dynamic programming that extends the idea of the venerable sweep algorithm. In a computational study, we demonstrate that the exact approach can solve small instances well, while the heuristic dynamic programming approach is fast and exhibits an average optimality gap close to zero in all test instances. Moreover, we investigate the influence of various storage assignment policies from the literature and compare them to a newly derived policy that is shown to be advantageous under certain circumstances. Secondly, we investigate the effects of having a movable depot compared to a fixed one and the influence of the effort to move the depot.

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