A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure

2021 ◽  
Author(s):  
Haodong Yu ◽  
Jie Sun ◽  
Yanjun Wang
Keyword(s):  
Stochastic Optimization ◽  
Decomposition Method ◽  
Benders Decomposition ◽  
Tree Structure ◽  
Scenario Tree ◽  
Distributionally Robust

Robust Stochastic Optimization Made Easy with RSOME

2020 ◽  
Vol 66 (8) ◽  
pp. 3329-3339 ◽  
Author(s):  
Zhi Chen ◽  
Melvyn Sim ◽  
Peng Xiong
Keyword(s):  
Robust Optimization ◽  
Stochastic Optimization ◽  
Linear Optimization ◽  
Mixture Distribution ◽  
Scenario Tree ◽  
Distributionally Robust Optimization ◽  
Clustering And Classification ◽  
Stochastic Linear Optimization ◽  
Distributionally Robust ◽  
Generalized Moments

We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided. This paper was accepted by David Simchi-Levi, optimization.

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anton Ochoa Bique ◽  
Leonardo K. K. Maia ◽  
Ignacio E. Grossmann ◽  
Edwin Zondervan
Keyword(s):  
Stochastic Optimization ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Cost Minimization ◽  
Water Electrolysis ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Strong Impact ◽  
Hydrogen Supply

Abstract A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

scholarly journals Long-Term Expansion Planning of the Transmission Network in India under Multi-Dimensional Uncertainty

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7813
Author(s):  
Spyros Giannelos ◽  
Anjali Jain ◽  
Stefan Borozan ◽  
Paola Falugi ◽  
Alexandre Moreira ◽  
...  
Keyword(s):  
Energy Storage ◽  
Stochastic Optimization ◽  
Economic Benefit ◽  
Benders Decomposition ◽  
Investment Decision ◽  
Transport Sector ◽  
Transmission Network ◽  
Expansion Planning ◽  
Investment Decision Making ◽  
Wide Scale

Considerable investment in India’s electricity system may be required in the coming decades in order to help accommodate the expected increase of renewables capacity as part of the country’s commitment to decarbonize its energy sector. In addition, electricity demand is geared to significantly increase due to the ongoing electrification of the transport sector, the growing population, and the improving economy. However, the multi-dimensional uncertainty surrounding these aspects gives rise to the prospect of stranded investments and underutilized network assets, rendering investment decision making challenging for network planners. In this work, a stochastic optimization model is applied to the transmission network in India to identify the optimal expansion strategy in the period from 2020 until 2060, considering conventional network reinforcements as well as energy storage investments. An advanced Nested Benders decomposition algorithm was used to overcome the complexity of the multistage stochastic optimization problem. The model additionally considers the uncertainty around the future investment cost of energy storage. The case study shows that deployment of energy storage is expected on a wide scale across India as it provides a range of benefits, including strategic investment flexibility and increased output from renewables, thereby reducing total expected system costs; this economic benefit of planning with energy storage under uncertainty is quantified as Option Value and is found to be in excess of GBP 12.9 bn. The key message of this work is that under potential high integration of wind and solar in India, there is significant economic benefit associated with the wide-scale deployment of storage in the system.

Efficient joint power and admission control in underlay cognitive networks using Benders’ decomposition method

2018 ◽  
Vol 129 ◽  
pp. 19-31 ◽  
Author(s):  
Fahime Khoramnejad ◽  
Mehdi Rasti ◽  
Hossein Pedram ◽  
Mehdi Monemi
Keyword(s):  
Admission Control ◽  
Decomposition Method ◽  
Benders Decomposition ◽  
Cognitive Networks ◽  
Joint Power

A modified Benders decomposition method for efficient robust optimization under interval uncertainty

2011 ◽  
Vol 44 (2) ◽  
pp. 259-275 ◽  
Author(s):  
Sauleh Siddiqui ◽  
Shapour Azarm ◽  
Steven Gabriel
Keyword(s):  
Robust Optimization ◽  
Decomposition Method ◽  
Benders Decomposition ◽  
Interval Uncertainty

Coordinated and Priority‐based Surgical Care: An Integrated Distributionally Robust Stochastic Optimization Approach

2021 ◽  
Author(s):  
Esmaeil Keyvanshokooh ◽  
Pooyan Kazemian ◽  
Mohammad Fattahi ◽  
Mark P. Van Oyen
Keyword(s):  
Stochastic Optimization ◽  
Surgical Care ◽  
Optimization Approach ◽  
Distributionally Robust
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