An efficient algorithm for a certain class of robust optimization problems

2014 ◽  
Vol 33 (4) ◽  
pp. 1208-1219
Author(s):  
M. Paffrath ◽  
U. Wever
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Convergence Properties ◽  
Content Type ◽  
Good Convergence ◽  
Deterministic Problem ◽  
Function Calls ◽  
Complex Technical Systems ◽  
Set Up ◽  
Absolute Reliability

Purpose – The purpose of this paper is to present an efficient method for the numerical treatment of robust optimization problems with absolute reliability constraints. Design/methodology/approach – Optimization with anti-optimization based on response surface techniques; polynomial chaos for approximation of the stochastic objective function. Findings – The number of function calls is comparable to that of the corresponding deterministic problem. Thus, the method is well suited for complex technical systems. The performance of the method is demonstrated on an optimal design problem for turbochargers. Originality/value – The highlights of this paper are: algorithms for robust and deterministic problems show comparable complexity; no derivatives required; good convergence properties because of special set up of optimization problem; application in complex industrial examples.

scholarly journals Oracle-based algorithms for binary two-stage robust optimization

2020 ◽  
Vol 77 (2) ◽  
pp. 539-569
Author(s):  
Nicolas Kämmerling ◽  
Jannis Kurtz
Keyword(s):  
Robust Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Capital Budgeting ◽  
Hub Location Problem ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Problem ◽  
Objective Uncertainty

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

A multi-objective robust optimization approach for engineering design under interval uncertainty

2018 ◽  
Vol 35 (2) ◽  
pp. 580-603 ◽  
Author(s):  
Qi Zhou ◽  
Xinyu Shao ◽  
Ping Jiang ◽  
Tingli Xie ◽  
Jiexiang Hu ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Content Type ◽  
Computational Burden ◽  
Multi Objective ◽  
Design Alternatives ◽  
Kriging Metamodel

Purpose Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty. Design/methodology/approach In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process. Findings Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties. Originality/value A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

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.

Improving Multi-Objective Robust Optimization Under Interval Uncertainty Using Worst Possible Point Constraint Cuts

2009 ◽  
Author(s):  
W. Hu ◽  
M. Li ◽  
S. Azarm ◽  
S. Al Hashimi ◽  
A. Almansoori ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Master Problem ◽  
Multi Objective ◽  
Acceptable Range ◽  
Function Calls ◽  
Order Of Magnitude

Many real-world engineering design optimization problems are multi-objective and have uncertainty in their parameters. For such problems it is useful to obtain design solutions that are both multi-objectively optimum and robust. A robust design is one whose objective and constraint function variations under uncertainty are within an acceptable range. While the literature reports on many techniques in robust optimization for single objective optimization problems, very few papers report on methods in robust optimization for multi-objective optimization problems. The Multi-Objective Robust Optimization (MORO) technique with interval uncertainty proposed in this paper is a significant improvement, with respect to computational effort, over a previously reported MORO technique. In the proposed technique, a master problem solves a relaxed optimization problem whose feasible domain is iteratively confined by constraint cuts determined by the solutions from a sub-problem. The proposed approach and the synergy between the master problem and sub-problem are demonstrated by three examples. The results obtained show a general agreement between the solutions from the proposed MORO and the previous MORO technique. Moreover, the number of function calls for obtaining solutions from the proposed technique is an order of magnitude less than that from the previous MORO technique.

scholarly journals The trouble with the second quantifier

4OR ◽  
2021 ◽  
Author(s):  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Robust Optimization ◽  
Complexity Theory ◽  
Operational Research ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Theoretical Background ◽  
Research Community ◽  
Universal Quantifier ◽  
Computational Complexity Theory

AbstractWe survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

2020 ◽  
Author(s):  
Amir Ardestani-Jaafari ◽  
Erick Delage
Keyword(s):  
Robust Optimization ◽  
Operations Management ◽  
Optimization Problems ◽  
Close Relation ◽  
Bilinear Programming ◽  
Two Stage ◽  
Bilinear Models ◽  
Robust Counterpart ◽  
Adjustable Robust Counterpart ◽  
Affinely Adjustable Robust Counterpart

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

A Unified Approach to Robust Farkas-Type Results with Applications to Robust Optimization Problems

2017 ◽  
Vol 27 (2) ◽  
pp. 1075-1101 ◽  
Author(s):  
N. Dinh ◽  
T. H. Mo ◽  
G. Vallet ◽  
M. Volle
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Unified Approach

Washington will engage more with South-east Asia

2021 ◽  
Keyword(s):  
United States ◽  
East Asia ◽  
The United States ◽  
South East Asia ◽  
National Unity ◽  
Content Type ◽  
Key Issues ◽  
Set Up

Significance She addressed two key issues during her trip: tensions in post-coup Myanmar and China’s growing regional footprint. Shortly after she left the region, the United States announced that it would donate unused COVID-19 vaccines abroad, including to South-east Asia. Impacts Washington will tighten its sanctions on the Myanmar military while supporting ASEAN’s five-point plan to ease the country’s crisis. The National Unity Government, a parallel administration to Myanmar’s junta set up by its opponents, will try to attract greater US backing. Manila and Washington may extend negotiations over renewing their Visiting Forces Agreement to prevent the pact expiring in August.

Using transfer learning for diabetic retinopathy stage classification

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Enas M.F. El Houby
Keyword(s):  
Diabetic Retinopathy ◽  
Transfer Learning ◽  
Grade Level ◽  
Design Methodology ◽  
Content Type ◽  
Stage Classification ◽  
Set Up ◽  
Retinal Fundus ◽  
Automated Methods

PurposeDiabetic retinopathy (DR) is one of the dangerous complications of diabetes. Its grade level must be tracked to manage its progress and to start the appropriate decision for treatment in time. Effective automated methods for the detection of DR and the classification of its severity stage are necessary to reduce the burden on ophthalmologists and diagnostic contradictions among manual readers.Design/methodology/approachIn this research, convolutional neural network (CNN) was used based on colored retinal fundus images for the detection of DR and classification of its stages. CNN can recognize sophisticated features on the retina and provides an automatic diagnosis. The pre-trained VGG-16 CNN model was applied using a transfer learning (TL) approach to utilize the already learned parameters in the detection.FindingsBy conducting different experiments set up with different severity groupings, the achieved results are promising. The best-achieved accuracies for 2-class, 3-class, 4-class and 5-class classifications are 86.5, 80.5, 63.5 and 73.7, respectively.Originality/valueIn this research, VGG-16 was used to detect and classify DR stages using the TL approach. Different combinations of classes were used in the classification of DR severity stages to illustrate the ability of the model to differentiate between the classes and verify the effect of these changes on the performance of the model.

Research from China finds no significant difference in impact of public service motivation (PSM) in public and private sectors

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Keyword(s):  
Public Sector ◽  
Private Sector ◽  
Employee Performance ◽  
Intention To Leave ◽  
Public And Private ◽  
Content Type ◽  
The Public ◽  
Significant Difference ◽  
Set Up ◽  
The Impact

Purpose The authors assumed PSM would be higher in the public sector, but they set up a trial to find out if this was the case. Design/methodology/approach To test their theories, the authors conducted two independent surveys. The first consisted of 220 usable responses from public sector employees in Changsha, China. The second survey involved 260 usable responses from private sector employees taking an MBA course at a university in the Changsha district. A questionnaire was used to assess attitudes. Findings The results found no significant difference between the impact of public sector motivation (PSM) on employee performance across the public and private sectors. The data showed that PSM had a significant impact on self-reported employee performance, but the relationship did not differ much between sectors. Meanwhile, it was in the private sector that PSM had the greatest impact on intention to leave. Originality/value The authors said the research project was one of the first to test if the concept of PSM operated in the same way across sectors. It also contributed, they said, to the ongoing debate about PSM in China.

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