A practical guide to robust optimization

Gorissen, Bram L.; Yanıkoğlu, İhsan; Hertog, Dick den

doi:10.1016/j.omega.2014.12.006

Cited by 454 publications

(274 citation statements)

References 45 publications

Supporting

Mentioning

256

Contrasting

Unclassified

Order By: Relevance

“…More general robust inventory problems have been considered, see for instance [20], however the inventory problems usually assume the time is discretized into a nite set of time periods, which contrasts with our problem where the time is considered continuous. For recent overviews on robust optimization see [13,15,34,33].…”

Section: The Resulting Problem Is Called a Maritime Inventory Routingmentioning

confidence: 99%

See 1 more Smart Citation

Robust Optimization for a Maritime Inventory Routing Problem

Agra

Christiansen

Hvattum

et al. 2018

Transportation Science

View full text Add to dashboard Cite

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous eet and multiple production and consumption ports with limited storage capacity.Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely inuenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set.In the recourse model, the routing, the order of port visits, and the quantities to load and unload are xed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.

show abstract

Section: The Resulting Problem Is Called a Maritime Inventory Routingmentioning

confidence: 99%

“…Within robust optimization such approaches became popular recently, see [8,10,21,49,50]. This procedure is also known as the Adversarial approach [34].…”

Section: Solution Methodsmentioning

confidence: 99%

Robust Optimization for a Maritime Inventory Routing Problem

Agra

Christiansen

Hvattum

et al. 2018

Transportation Science

View full text Add to dashboard Cite

show abstract

“…In Gorissen et al (2015), the authors briefly discuss two ways of dealing with uncertain equality constraints with adjustable variables. Either one can eliminate those equality constraints, or one can apply LDRs.…”

Section: Mve Of General Polytopementioning

confidence: 99%

Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

Zhen

Hertog

2015

SSRN Journal

Self Cite

View full text Add to dashboard Cite

We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard. Our approach does not require an explicit description of the projection, and can easily be generalized to find a maximally sized convex body of a polytopic projection. Our obtained MVE is an inner approximation of the projected polytope, and its center is a centralized relative interior point of the projection. Since FME may produce many redundant constraints, we apply an LP-based procedure to keep the description of the projected polytopes at its minimal size. Furthermore, we propose an upper bounding scheme to evaluate the quality of the inner approximations. We test our approach on a simple polytope and a color tube design problem, and observe that as more auxiliary variables are eliminated, our inner approximations and upper bounds converge to optimal solutions.

show abstract

“…Robust optimization is popular because of its computational tractability for many classes of uncertainty sets and problem types. It has been widely applied to the domains of inventory and logistics, finance, machine learning, energy systems, scheduling, etc [17][18][19]. Although the first relevant study dates back to 1973 [20], robust optimization has been mainly developed in the last 15 years.…”

Section: Related Workmentioning

confidence: 99%

Sensor Network Deployment under Distance Uncertainty with Robust Optimization

Qiao¹,

Liu²,

Zhang³

et al. 2015

Int. J. Onl. Eng.

View full text Add to dashboard Cite

Abstract-We consider the sensor deployment problem in the context of distance uncertainty. It is characterized by differentiated arrangement of specific detection probability thresholds at different locations. The problem is formulated as an integer linear programming (ILP) model firstly, aiming at optimizing the number of sensors and their locations. Based on the robust discrete optimization methodology, the uncertain model is transformed into an equivalent ILP problem considering distance uncertainty. The proposed approach can control the tradeoff between optimality and robustness by varying the parameters named protection levels. Uniform and non-uniform event detection probabiliy distributions are considered in the experiment. The results show that, as the distance uncertainty increases, the constraint violation can be avoided in the robust model and the robust solution can provide a significant improvement at the expense of a small loss in optimality when compared to the optimal solution of a deterministic scenario.

show abstract

A practical guide to robust optimization

Cited by 454 publications

References 45 publications

Robust Optimization for a Maritime Inventory Routing Problem

Robust Optimization for a Maritime Inventory Routing Problem

Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

Sensor Network Deployment under Distance Uncertainty with Robust Optimization

Contact Info

Product

Resources

About