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.

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.

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 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 Dynamic Scheduling Model of Bike-Sharing considering Invalid Demand

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Liu He ◽  
Tangyi Guo ◽  
Kun Tang
Keyword(s):  
Optimization Model ◽  
Dynamic Scheduling ◽  
Demand Forecasting ◽  
Optimal Solution ◽  
Coupling Model ◽  
Service Level ◽  
Demand Prediction ◽  
Dynamic Relationship ◽  
Proposed Model ◽  
Bike Sharing

System resources allocation optimization through dynamic scheduling is key to improving the service level of bike-sharing. This study innovatively introduces three types of invalid demand with negative effect including waiting, transfer, and abandoning, which consists of the total demand of bike-sharing system. Through exploring the dynamic relationship among users’ travel demands, the quantity and capacity of bikes at the rental points, the records of bicycles borrowed and returned, and the vehicle scheduling schemes, a demand forecasting model for bike-sharing is established. According to the predicted bikes and the maximum capacity limit at each rental point, an optimization model of scheduling scheme is proposed to reduce the invalid demand and the total scheduling time. A two-layer dynamic coupling model with iterative feedback is obtained by combining the demand prediction model and scheduling optimization model and is then solved by Nicked Pareto Genetic Algorithm (NPGA). The proposed model is applied to a case study and the optimal solution set and corresponding Pareto front are obtained. The invalid demand is greatly reduced from 1094 to 26 by an effective scheduling of 3 rounds and 96 minutes. Empirical results show that the proposed model is able to optimize the resource allocation of bike-sharing, significantly reduce the invalid demand caused by the absence of bikes at the rental point such as waiting in a place, walking to other rental points, and giving up for other travel modes, and effectively improve the system service level.

scholarly journals The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Liyan Xu ◽  
Bo Yu ◽  
Wei Liu
Keyword(s):  
Robust Optimization ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Uncertain Parameters ◽  
Distributionally Robust Optimization ◽  
Worst Case ◽  
Nonnegativity Constraints ◽  
Distributionally Robust ◽  
Stochastic Linear Complementarity Problem

We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linear mapping being nonnegative is not less than a given probability level. Applying the cone dual theory and S-procedure, we show that the distributionally robust counterpart of the uncertain complementarity problem can be conservatively approximated by the optimization with bilinear matrix inequalities. Preliminary numerical results show that a solution of our method is desirable.

A Bi-Objective Order Allocation Optimization Model for Horizontal Manufacturing Collaborative Alliance

2010 ◽  
Vol 102-104 ◽  
pp. 836-840 ◽  
Author(s):  
Fang Qi Cheng
Keyword(s):  
Genetic Algorithm ◽  
Optimization Model ◽  
Optimal Solution ◽  
Order Allocation ◽  
Nsga Ii ◽  
Manufacturing Enterprises ◽  
Proposed Model ◽  
Optimal Solution Set ◽  
Simulation Results ◽  
Enterprise Community

Horizontal manufacturing collaborative alliance is a dispersed enterprise community consisting of several enterprises which produce the same kind of products. To correctly assign order among member companies of horizontal manufacturing collaborative alliance is one of the most important ways to improve the agility and competitiveness of manufacturing enterprises. For the order allocation problem, a bi-objective optimization model is developed to minimize the comprehensive cost and balance the production loads among the selected manufacturing enterprises. Non-dominated sorting genetic algorithm (NSGA-II) is applied to solve the optimization functions. The optimal solution set of Pareto is obtained. The simulation results indicate that the proposed model and algorithm is able to obtain satisfactory solutions.

A One to Multiple Order Allocation Optimization Model of Horizontal Manufacturing Collaborative Alliance

2012 ◽  
Vol 201-202 ◽  
pp. 996-999
Author(s):  
Jin Gao
Keyword(s):  
Optimization Model ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Order Allocation ◽  
Nsga Ii ◽  
Manufacturing Enterprises ◽  
Proposed Model ◽  
Optimal Solution Set ◽  
Simulation Results ◽  
Enterprise Community

Horizontal manufacturing collaborative alliance is a dispersed enterprise community consisting of several enterprises which produce the same kind of products. To correctly assign order among member companies of horizontal manufacturing collaborative alliance is one of the most important ways to improve the agility and competitiveness of manufacturing enterprises. For the order allocation problem, a multi-objective optimization model is developed to minimize the comprehensive cost and balance the production loads among the selected manufacturing enterprises. Non-dominated sorting genetic algorithm (NSGA-II) is applied to solve the optimization functions. The optimal solution set of Pareto is obtained. The simulation results indicate that the proposed model and algorithm is able to obtain satisfactory solutions.

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 Robust Optimization Model for Bi-objective Emergency Medical Service Design Problem with Demand Uncertainty

2019 ◽  
Vol 20 (2) ◽  
pp. 95
Author(s):  
Diah Chaerani ◽  
Siti Rabiatul Adawiyah ◽  
Eman Lesmana
Keyword(s):  
Robust Optimization ◽  
Emergency Medical Service ◽  
Design Problem ◽  
Medical Service ◽  
Optimal Solution ◽  
Service Design ◽  
Mixed Integer ◽  
Worst Case ◽  
Robust Counterpart ◽  
Emergency Medical

Bi-objective Emergency Medical Service Design Problem is a problem to determining the location of the station Emergency Medical Service among all candidate station location, the determination of the number of emergency vehicles allocated to stations being built so as to serve medical demand. This problem is a multi-objective problem that has two objective functions that minimize cost and maximize service. In real case there is often uncertainty in the model such as the number of demand. To deal the uncertainty on the bi-objective emergency medical service problem is using Robust Optimization which gave optimal solution even in the worst case. Model Bi-objective Emergency Medical Service Design Problem is formulated using Mixed Integer Programming. In this research, Robust Optimization is formulated for Bi-objective Emergency Medical Service Design Problem through Robust Counterpart formulation by assuming uncertainty in demand is box uncertainty and ellipsoidal uncertainty set. We show that in the case of bi-objective optimization problem, the robust counterpart remains computationally tractable. The example is performed using Lexicographic Method and Branch and Bound Method to obtain optimal solution. 

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