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.

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.

Robust Optimization of Steam Power System

2013 ◽  
Vol 860-863 ◽  
pp. 2606-2609
Author(s):  
Ran Ding ◽  
Guo Xiang Li
Keyword(s):  
Power System ◽  
Robust Optimization ◽  
Optimization Model ◽  
System Optimization ◽  
Uncertain Parameters ◽  
Steam Power ◽  
Power System Optimization ◽  
Steam Power System ◽  
System Optimal ◽  
Simulation Results

In steam power system optimal problems, uncertain parameters should be considered unless the solution will be infeasible. The uncertain parameters and constraints in steam power system optimization model are analyzed. Then the related constraints with uncertain parameters which used to be expressed by joint chance constraints are approximated, and a robust optimization model of steam power system is proposed. The simulation results illustrate the validity of the model.

scholarly journals A robust optimization model for influence maximization in social networks with heterogeneous nodes

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mehrdad Agha Mohammad Ali Kermani ◽  
Reza Ghesmati ◽  
Mir Saman Pishvaee
Keyword(s):  
Social Networks ◽  
Robust Optimization ◽  
Optimization Model ◽  
Text Messaging ◽  
Influence Maximization ◽  
Optimization Approach ◽  
Expected Number ◽  
Influential Nodes ◽  
Heterogeneous Nodes ◽  
Probabilistic Nature

AbstractInfluence maximization is the problem of trying to maximize the number of influenced nodes by selecting optimal seed nodes, given that influencing these nodes is costly. Due to the probabilistic nature of the problem, existing approaches deal with the concept of the expected number of nodes. In the current research, a scenario-based robust optimization approach is taken to finding the most influential nodes. The proposed robust optimization model maximizes the number of infected nodes in the last step of diffusion while minimizing the number of seed nodes. Nodes, however, are treated as heterogeneous with regard to their propensity to pass messages along; or as having varying activation thresholds. Experiments are performed on a real text-messaging social network. The model developed here significantly outperforms some of the well-known existing heuristic approaches which are proposed in previous works.

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.

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 A New Robust Optimization Approach to Deal with Dependent Uncertain Parameters

2020 ◽  
Author(s):  
Amirhossein Mostofi ◽  
Vipul Jian ◽  
Mojtaba Arab Momeni
Keyword(s):  
Robust Optimization ◽  
Optimization Approach ◽  
Uncertain Parameters

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scholarly journals Unconstrained Quadratic Programming Problem with Uncertain Parameters

2021 ◽  
pp. 1-7
Author(s):  
Sie Long Kek ◽  
Fong Peng Lim ◽  
Harley Ooi
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Linear Equations ◽  
Optimal Solution ◽  
Theoretical Work ◽  
Quadratic Programming Problem ◽  
Model Parameters ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Unconstrained Quadratic Programming

In this paper, an unconstrained quadratic programming problem with uncertain parameters is discussed. For this purpose, the basic idea of optimizing the unconstrained quadratic programming problem is introduced. The solution method of solving linear equations could be applied to obtain the optimal solution for this kind of problem. Later, the theoretical work on the optimization of the unconstrained quadratic programming problem is presented. By this, the model parameters, which are unknown values, are considered. In this uncertain situation, it is assumed that these parameters are normally distributed; then, the simulation on these uncertain parameters are performed, so the quadratic programming problem without constraints could be solved iteratively by using the gradient-based optimization approach. For illustration, an example of this problem is studied. The computation procedure is expressed, and the result obtained shows the optimal solution in the uncertain environment. In conclusion, the unconstrained quadratic programming problem, which has uncertain parameters, could be solved successfully.

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