Feasibility Robust Optimization via Scenario Generation and Reduction

2018 ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Solution

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

scholarly journals Robust Optimization Approach Using Scenario Concepts for Artillery Firing Scheduling Under Uncertainty

2019 ◽  
Vol 9 (14) ◽  
pp. 2811
Author(s):  
Choi ◽  
Yun ◽  
Kim ◽  
Jin ◽  
Kim
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Numerical Experiments ◽  
Master Problem ◽  
Model Parameters ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Robust Solution ◽  
Reasonable Time ◽  
Scheduling Under Uncertainty

Real wars involve a considerable number of uncertainties when determining firing scheduling. This study proposes a robust optimization model that considers uncertainties in wars. In this model, parameters that are affected by enemy’s behavior and will, i.e., threats from enemy targets and threat time from enemy targets, are assumed as uncertain parameters. The robust optimization model considering these parameters is an intractable model with semi-infinite constraints. Thus, this study proposes an approach to obtain a solution by reformulating this model into a tractable problem; the approach involves developing a robust optimization model using the scenario concept and finding a solution in that model. Here, the combinations that express uncertain parameters are assumed by scenarios. This approach divides problems into master and subproblems to find a robust solution. A genetic algorithm is utilized in the master problem to overcome the complexity of global searches, thereby obtaining a solution within a reasonable time. In the subproblem, the worst scenarios for any solution are searched to find the robust solution even in cases where all scenarios have been expressed. Numerical experiments are conducted to compare robust and nominal solutions for various uncertainty levels to verify the superiority of the robust solution.

scholarly journals Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 211
Author(s):  
Lijun Xu ◽  
Yijia Zhou ◽  
Bo Yu
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Model ◽  
Multi Stage ◽  
Proposed Model ◽  
Dual Forms

In this paper, we focus on a class of robust optimization problems whose objectives and constraints share the same uncertain parameters. The existing approaches separately address the worst cases of each objective and each constraint, and then reformulate the model by their respective dual forms in their worst cases. These approaches may result in that the value of uncertain parameters in the optimal solution may not be the same one as in the worst case of each constraint, since it is highly improbable to reach their worst cases simultaneously. In terms of being too conservative for this kind of robust model, we propose a new robust optimization model with shared uncertain parameters involving only the worst case of objectives. The proposed model is evaluated for the multi-stage logistics production and inventory process problem. The numerical experiment shows that the proposed robust optimization model can give a valid and reasonable decision in practice.

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

2017 ◽  
Vol 34 (2) ◽  
pp. 420-446 ◽  
Author(s):  
Qi Zhou ◽  
Ping Jiang ◽  
Xinyu Shao ◽  
Hui Zhou ◽  
Jiexiang Hu
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Content Type ◽  
Computational Burden ◽  
Design Alternative ◽  
Kriging Metamodel ◽  
On Line

Purpose Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach. Design/methodology/approach In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations. Findings One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty. Originality/value The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.

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>

scholarly journals Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials

2020 ◽  
Author(s):  
Shixin Wang ◽  
Xuan Wang ◽  
Jiawei Zhang
Keyword(s):  
Robust Optimization ◽  
Performance Measures ◽  
Broad Class ◽  
Problem Definition ◽  
Partial Ordering ◽  
Group Index ◽  
Optimization Approach ◽  
Worst Case ◽  
Process Flexibility ◽  
Long Chain

Problem definition: The theoretical investigation of the effectiveness of limited flexibility has mainly focused on a performance metric that is based on the maximum sales in units. However, this could lead to substantial profit losses when the maximum sales metric is used to guide flexibility designs while the products have considerably large profit margin differences. Academic/practical relevance: We address this issue by introducing margin differentials into the analysis of process flexibility designs, and our results can provide useful guidelines for the evaluation and design of flexibility configurations when the products have heterogeneous margins. Methodology: We adopt a robust optimization framework and study process flexibility designs from the worst-case perspective by introducing the dual margin group index (DMGI). Results and managerial implications: We show that a general class of worst-case performance measures can be expressed as functions of a design’s DMGIs and the given uncertainty set. Moreover, the DMGIs lead to a partial ordering that enables us to compare the worst-case performance of different designs. Applying these results, we prove that under the so-called partwise independently symmetric uncertainty sets and a broad class of worst-case performance measures, the alternate long-chain design is optimal among all long-chain designs with equal numbers of high-profit products and low-profit products. Finally, we develop a heuristic based on the DMGIs to generate effective flexibility designs when products exhibit margin differentials.

Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Yanjing Li ◽  
Zhaosong Lu ◽  
Jeremy J. Michalek
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Descent Method ◽  
Quadratic Approximation ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Decomposition Approach ◽  
Diagonal Quadratic Approximation ◽  
Target Cascading ◽  
Nested Loop

Analytical target cascading (ATC) is an effective decomposition approach used for engineering design optimization problems that have hierarchical structures. With ATC, the overall system is split into subsystems, which are solved separately and coordinated via target/response consistency constraints. As parallel computing becomes more common, it is desirable to have separable subproblems in ATC so that each subproblem can be solved concurrently to increase computational throughput. In this paper, we first examine existing ATC methods, providing an alternative to existing nested coordination schemes by using the block coordinate descent method (BCD). Then we apply diagonal quadratic approximation (DQA) by linearizing the cross term of the augmented Lagrangian function to create separable subproblems. Local and global convergence proofs are described for this method. To further reduce overall computational cost, we introduce the truncated DQA (TDQA) method, which limits the number of inner loop iterations of DQA. These two new methods are empirically compared to existing methods using test problems from the literature. Results show that computational cost of nested loop methods is reduced by using BCD, and generally the computational cost of the truncated methods is superior to the nested loop methods with lower overall computational cost than the best previously reported results.

An Agent Based Optimization Approach to Manufacturing Process Planning

2001 ◽  
Author(s):  
Saurabh Deshpande ◽  
Jonathan Cagan
Keyword(s):  
Stochastic Optimization ◽  
Process Planning ◽  
Manufacturing Process ◽  
Optimization Problems ◽  
Search Space ◽  
Optimization Techniques ◽  
Process Models ◽  
Optimization Approach ◽  
Agent Based ◽  
Manufacturing Process Planning

Abstract Many optimization problems, such as manufacturing process planning optimization, are difficult problems due to the large number of potential configurations (process sequences) and associated (process) parameters. In addition, the search space is highly discontinuous and multi-modal. This paper introduces an agent based optimization algorithm that combines stochastic optimization techniques with knowledge based search. The motivation is that such a merging takes advantage of the benefits of stochastic optimization and accelerates the search process using domain knowledge. The result of applying this algorithm to computerized manufacturing process models is presented.

Surrogate-Assisted Modeling and Robust Optimization of a Micro Gas Turbine Plant With Carbon Capture

2019 ◽  
Author(s):  
Simone Giorgetti ◽  
Diederik Coppitters ◽  
Francesco Contino ◽  
Ward De Paepe ◽  
Laurent Bricteux ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Gas Turbines ◽  
Carbon Capture ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Aspen Plus ◽  
Optimization Approach ◽  
Co2 Absorption ◽  
Exhaust Gas ◽  
Nsga Ii

Abstract The growing share of wind and solar power in the total energy mix has caused severe problems in balancing the electrical power production. Consequently, in the future, all fossil fuel-based electricity generation will need to be run on a completely flexible basis. Micro Gas Turbines (mGTs) constitutes a mature technology which can offer such flexibility. Even though their greenhouse gas emissions are already very low, stringent carbon reduction targets will require them to be completely carbon neutral: this constraint implies the adoption of post-combustion Carbon Capture (CC) on these energy systems. To reduce the CC energy penalty, Exhaust Gas Recirculation (EGR) can be applied to the mGTs increasing the CO2 content in the exhaust gas and reducing the mass flow rate of flue gas to be treated. As a result, a lower investment and operational cost of the CC unit can be achieved. In spite of this attractive solution, an in-depth study along with a robust optimization of this system has not yet been carried out. Hence, in this paper, a typical mGT with EGR has been coupled with an amine-based CC plant and simulated using the software Aspen Plus®. A rigorous rate-based simulation of the CO2 absorption and desorption in the CC unit offers an accurate prediction; however, its time complexity and convergence difficulty are severe limitations for a stochastic optimization. Therefore, a surrogate-based optimization approach has been used, which makes use of a Gaussian Process Regression (GPR) model, trained using the Aspen Plus® data, to quickly find operating points of the plant at a very low computational cost. Using the validated surrogate model, a robust optimization using a Non-dominated Sorting Genetic Algorithm II (NSGA II) has been carried out, assessing the influence of each input uncertainty and varying several design variables. As a general result, the analysed power plant proves to be intrinsically very robust, even when the input variables are affected by strong uncertainties.

scholarly journals Shape Design Optimization of a Robot Arm Using a Surrogate-Based Evolutionary Approach

2020 ◽  
Vol 10 (7) ◽  
pp. 2223 ◽  
Author(s):  
J. C. Hsiao ◽  
Kumar Shivam ◽  
C. L. Chou ◽  
T. Y. Kam
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Shape Design ◽  
Optimization Approach ◽  
Robot Arm ◽  
Shape Design Optimization ◽  
Robot Arms ◽  
Conflicting Objectives ◽  
Computer Aided

In the design optimization of robot arms, the use of simulation technologies for modeling and optimizing the objective functions is still challenging. The difficulty is not only associated with the large computational cost of high-fidelity structural simulations but also linked to the reasonable compromise between the multiple conflicting objectives of robot arms. In this paper we propose a surrogate-based evolutionary optimization (SBEO) method via a global optimization approach, which incorporates the response surface method (RSM) and multi-objective evolutionary algorithm by decomposition (the differential evolution (DE ) variant) (MOEA/D-DE) to tackle the shape design optimization problem of robot arms for achieving high speed performance. The computer-aided engineering (CAE) tools such as CAE solvers, computer-aided design (CAD) Inventor, and finite element method (FEM) ANSYS are first used to produce the design and assess the performance of the robot arm. The surrogate model constructed on the basis of Box–Behnken design is then used in the MOEA/D-DE, which includes the process of selection, recombination, and mutation, to optimize the robot arm. The performance of the optimized robot arm is compared with the baseline one to validate the correctness and effectiveness of the proposed method. The results obtained for the adopted example show that the proposed method can not only significantly improve the robot arm performance and save computational cost but may also be deployed to solve other complex design optimization problems.

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