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.

Scenario-Based Stochastic Programming Strategy for Microgrid Energy Scheduling Considering Uncertainties

2014 ◽  
Vol 672-674 ◽  
pp. 1322-1328 ◽  
Author(s):  
He Peng Li ◽  
Chuan Zhi Zang ◽  
Peng Zeng ◽  
Hai Bin Yu ◽  
Zhong Wen Li
Keyword(s):  
Stochastic Programming ◽  
Programming Model ◽  
Moving Average ◽  
Arma Model ◽  
Random Variable ◽  
Equivalent Model ◽  
Optimization Strategy ◽  
Renewable Energy Resources ◽  
Scheduling Optimization ◽  
Deterministic Equivalent

The inherent random and intermittence of the renewable energy resources pose a huge challenge to the Microgrid (MG) energy management systems (EMS). In order to mitigate the effects of uncertainties, we propose a novel two-stage stochastic programming model for the energy scheduling optimization by considering the uncertainties in solar and wind generation, and the plug-in electric vehicles (EV). The random nature of uncertainty is characterized by a scenarios generation approach based on autoregressive moving average (ARMA) model according to probability density function of each random variable. By use of the strategy of scenarios simulation, the stochastic problem is decomposed into the deterministic equivalent problem. The firefly algorithm (FA) is used to solve the equivalent model. The effectiveness and robust of proposed stochastic energy scheduling optimization strategy for MG is valid by comparison with the simulation results of deterministic method.

scholarly journals The electric location-routing problem with heterogeneous fleet: Formulation and Benders decomposition approach

2021 ◽  
Vol 131 ◽  
pp. 105251
Author(s):  
Hatice Çalık ◽  
Ammar Oulamara ◽  
Caroline Prodhon ◽  
Said Salhi
Keyword(s):  
Benders Decomposition ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Heterogeneous Fleet ◽  
Location Routing

Two-stage stochastic programming-based capacity optimization for a high-temperature electrolysis system considering dynamic operation strategies

2021 ◽  
Vol 40 ◽  
pp. 102733
Author(s):  
Ruomei Qi ◽  
Yiwei Qiu ◽  
Jin Lin ◽  
Yonghua Song ◽  
Wenying Li ◽  
...  
Keyword(s):  
High Temperature ◽  
Stochastic Programming ◽  
Capacity Optimization ◽  
Two Stage ◽  
Dynamic Operation ◽  
Electrolysis System ◽  
High Temperature Electrolysis

scholarly journals A Two-Stage Neural Network-Based Cold Start Item Recommender

2021 ◽  
Vol 11 (9) ◽  
pp. 4243
Author(s):  
Chieh-Yuan Tsai ◽  
Yi-Fan Chiu ◽  
Yu-Jen Chen
Keyword(s):  
Neural Network ◽  
Recommendation System ◽  
Service Providers ◽  
Cold Start ◽  
Computational Time ◽  
Two Stage ◽  
The Neural Network ◽  
Textual Description ◽  
Recommendation Algorithms ◽  
Content Information

Nowadays, recommendation systems have been successfully adopted in variant online services such as e-commerce, news, and social media. The recommenders provide users a convenient and efficient way to find their exciting items and increase service providers’ revenue. However, it is found that many recommenders suffered from the cold start (CS) problem where only a small number of ratings are available for some new items. To conquer the difficulties, this research proposes a two-stage neural network-based CS item recommendation system. The proposed system includes two major components, which are the denoising autoencoder (DAE)-based CS item rating (DACR) generator and the neural network-based collaborative filtering (NNCF) predictor. In the DACR generator, a textual description of an item is used as auxiliary content information to represent the item. Then, the DAE is applied to extract the content features from high-dimensional textual vectors. With the compact content features, a CS item’s rating can be efficiently derived based on the ratings of similar non-CS items. Second, the NNCF predictor is developed to predict the ratings in the sparse user–item matrix. In the predictor, both spare binary user and item vectors are projected to dense latent vectors in the embedding layer. Next, latent vectors are fed into multilayer perceptron (MLP) layers for user–item matrix learning. Finally, appropriate item suggestions can be accurately obtained. The extensive experiments show that the DAE can significantly reduce the computational time for item similarity evaluations while keeping the original features’ characteristics. Besides, the experiments show that the proposed NNCF predictor outperforms several popular recommendation algorithms. We also demonstrate that the proposed CS item recommender can achieve up to 8% MAE improvement compared to adding no CS item rating.

scholarly journals A simple heuristic for reducing the number of scenarios in two-stage stochastic programming

2010 ◽  
Vol 34 (8) ◽  
pp. 1246-1255 ◽  
Author(s):  
Ramkumar Karuppiah ◽  
Mariano Martín ◽  
Ignacio E. Grossmann
Keyword(s):  
Stochastic Programming ◽  
Two Stage ◽  
Simple Heuristic
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