scholarly journals Constraint Generation Algorithm for the Minimum Connectivity Inference Problem

2019 ◽  
pp. 167-183
Author(s):  
Édouard Bonnet ◽  
Diana-Elena Fălămaş ◽  
Rémi Watrigant
Keyword(s):  
Inference Problem ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Connectivity Inference

scholarly journals A column-and-constraint generation algorithm for two-stage stochastic programming problems

Top ◽  
2021 ◽  
Author(s):  
Denise D. Tönissen ◽  
Joachim J. Arts ◽  
Zuo-Jun Max Shen
Keyword(s):  
Stochastic Programming ◽  
Benders Decomposition ◽  
Equivalent Model ◽  
Computational Time ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Equivalent ◽  
Location Routing ◽  
Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

scholarly journals Oracle-based algorithms for binary two-stage robust optimization

2020 ◽  
Vol 77 (2) ◽  
pp. 539-569
Author(s):  
Nicolas Kämmerling ◽  
Jannis Kurtz
Keyword(s):  
Robust Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Capital Budgeting ◽  
Hub Location Problem ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Problem ◽  
Objective Uncertainty

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

An improved flow-based formulation and reduction principles for the minimum connectivity inference problem

Optimization ◽  
2018 ◽  
Vol 68 (10) ◽  
pp. 1963-1983 ◽  
Author(s):  
Muhammad Abid Dar ◽  
Andreas Fischer ◽  
John Martinovic ◽  
Guntram Scheithauer
Keyword(s):  
Inference Problem ◽  
Connectivity Inference

SU-F-T-15: Evaluation of 192Ir, 60Co and 169Yb Sources for High Dose Rate Prostate Brachytherapy Inverse Planning Using An Interior Point Constraint Generation Algorithm

2016 ◽  
Vol 43 (6Part12) ◽  
pp. 3464-3465
Author(s):  
E Mok Tsze Chung ◽  
H Safigholi ◽  
A Nicolae ◽  
M Davidson ◽  
A Ravi ◽  
...  
Keyword(s):  
Dose Rate ◽  
Interior Point ◽  
High Dose Rate ◽  
High Dose ◽  
Prostate Brachytherapy ◽  
Inverse Planning ◽  
Generation Algorithm ◽  
Constraint Generation
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