Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning

Li, Mian; Gabriel, Steven A.; Shim, Yohan; Azarm, Shapour

doi:10.1007/s11067-010-9150-7

Cited by 28 publications

(9 citation statements)

References 24 publications

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“…When attempting to survey applications of RO in nonlinear contexts, one might identify the following relevant piece of work. In Li et al (2011), the authors deal with convex and non-convex quadratic problems with interval uncertainty sets, while ellipsoidal uncertainty regions are considered in Takeda et al (2010). In Hsiung et al (2008), the authors tackle a geometric program where they exploit a piece-wise linear approximation of the nonlinear constraints in order to derive a tractable approximation.…”

Section: Related Workmentioning

confidence: 99%

A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study

Delage

Gianoli

Sansò

2018

Operations Research

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Section: Related Workmentioning

confidence: 99%

A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study

Delage

Gianoli

Sansò

2018

Operations Research

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“…Deterministic approaches, on the other hand, incorporate non-statistical index such as gradient information (Taguchi, 1978; Renaud, 1997; Lee and Park, 2001; Kim et al , 2010; Papadimitriou and Giannakoglou, 2013) or sensitivity region information (Gunawan and Azarm, 2004; Gunawan and Azarm, 2005; Li et al , 2009; Li et al , 2010; Li et al , 2011; Zhou et al , 2012; Mortazavi et al , 2013; Cheng et al , 2015) into the original optimization problem to obtain a robust optimum. The interval number programming method is also used as a deterministic approach to obtain a robust optimum under interval uncertainty (Li et al , 2013; Wu et al , 2015a; Wu et al , 2015b).…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Shao

Jiang

et al. 2018

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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.

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“…RO methods can be classified into two types: Probabilistic approaches perform the RO by using the probability distribution of variable variations, usually mean and variance of uncertain variables (Du et al , 2008; Li et al , 2015; Carpinelli et al , 2015; Pedersen et al , 2016). Deterministic approaches , on the other hand, incorporate non-statistical index such as gradient information (Taguchi, 1978; Renaud, 1997; Lee and Park, 2001; Kim et al , 2010; Papadimitriou and Giannakoglou, 2013) or sensitivity region information (SRI) (Gunawan and Azarm, 2004; Gunawan and Azarm, 2005; Li et al , 2009; Li et al , 2010; Li et al , 2011; Zhou et al , 2012; Mortazavi et al , 2013; Cheng et al , 2015) into the original optimization problem to obtain a robust optimum. …”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Jiang

Shao

et al. 2017

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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.

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Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning

Abstract: Robust optimization, Interval uncertainty, Linear programming, Quadratic programming, Mixed-integer linear programming, Mixed-integer quadratic programming,

Cited by 28 publications

References 24 publications

A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study

A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study

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

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

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