Robust optimization approach for a chance-constrained binary knapsack problem

2015 ◽  
Vol 157 (1) ◽  
pp. 277-296 ◽  
Author(s):  
Jinil Han ◽  
Kyungsik Lee ◽  
Chungmok Lee ◽  
Ki-Seok Choi ◽  
Sungsoo Park
Keyword(s):  
Robust Optimization ◽  
Knapsack Problem ◽  
Optimization Approach

scholarly journals The robust bilevel continuous knapsack problem with uncertain coefficients in the follower’s objective

2022 ◽  
Author(s):  
Christoph Buchheim ◽  
Dorothee Henke
Keyword(s):  
Robust Optimization ◽  
Knapsack Problem ◽  
Bilevel Optimization ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Np Hard ◽  
Worst Case ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
Continuous Knapsack Problem

AbstractWe consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack and the follower chooses an optimal packing according to his own profits, which may differ from those of the leader. To this bilevel problem, we add uncertainty in a natural way, assuming that the leader does not have full knowledge about the follower’s problem. More precisely, adopting the robust optimization approach and assuming that the follower’s profits belong to a given uncertainty set, our aim is to compute a solution that optimizes the worst-case follower’s reaction from the leader’s perspective. By investigating the complexity of this problem with respect to different types of uncertainty sets, we make first steps towards better understanding the combination of bilevel optimization and robust combinatorial optimization. We show that the problem can be solved in polynomial time for both discrete and interval uncertainty, but that the same problem becomes NP-hard when each coefficient can independently assume only a finite number of values. In particular, this demonstrates that replacing uncertainty sets by their convex hulls may change the problem significantly, in contrast to the situation in classical single-level robust optimization. For general polytopal uncertainty, the problem again turns out to be NP-hard, and the same is true for ellipsoidal uncertainty even in the uncorrelated case. All presented hardness results already apply to the evaluation of the leader’s objective function.

Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH

2021 ◽  
pp. 1-19
Author(s):  
ZUOXUN LI ◽  
KAI ZHANG
Keyword(s):  
Model Predictive Control ◽  
Stochastic Model ◽  
Robust Optimization ◽  
Predictive Control ◽  
Attitude Control ◽  
Optimization Approach ◽  
Distributionally Robust Optimization ◽  
Distributionally Robust ◽  
Stochastic Model Predictive Control ◽  
Rendezvous And Docking

Abstract A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.

scholarly journals A Bidding Model for a Virtual Power Plant via Robust Optimization Approach

2017 ◽  
Vol 95 ◽  
pp. 15001
Author(s):  
Tianxiang Geng ◽  
Li Xiang ◽  
Maosheng Ding ◽  
Feng Li
Keyword(s):  
Power Plant ◽  
Robust Optimization ◽  
Optimization Approach ◽  
Virtual Power ◽  
Virtual Power Plant
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