Lagrangean relaxation

Guignard, Monique

doi:10.1007/bf02579036

Cited by 245 publications

(172 citation statements)

References 49 publications

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“…Duality theory establishes that v ≥ v LD [11]. In particular, for nonconvex cases such as MILP models, we may have that v > v LD , which implies the existence of a duality gap.…”

Section: Lagrangean Decomposition Approachmentioning

confidence: 99%

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A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

Oliveira

Gupta

Hamacher

et al. 2013

Computers & Chemical Engineering

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We present a scenario decomposition framework based on Lagrangean decomposition for the multi-product, multi-period, supply investment planning problem considering network design and discrete capacity expansion under demand uncertainty. We also consider a risk measure that allows us to reduce the probability of incurring in high costs while preserving the decomposable structure of the problem. To solve the resulting large-scale two-stage mixed-integer stochastic linear programming problem, we propose a novel Lagrangean decomposition scheme. In this context, we compare different formulations for the non-anticipativity conditions. In addition to that, we present a new hybrid algorithm for updating the Lagrangean multiplier set, based on the combination of cutting-plane, subgradient and trust-region strategies. Numerical results suggests that different formulations of the non-anticipativity conditions have a significant effect on the performance of the algorithm. Moreover, we observe that the proposed hybrid approach has superior performance when compared with the traditional subgradient algorithm in terms of faster computational times for the problem addressed in this work.

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“…Duality theory establishes that v ≥ v LD [11]. In particular, for nonconvex cases such as MILP models, we may have that v > v LD , which implies the existence of a duality gap.…”

Section: Lagrangean Decomposition Approachmentioning

confidence: 99%

“…Nevertheless, it is widely known that the Lagrangean dual represents a relaxation of the original problem for any given set of Lagrange multipliers [11]. In this sense, we can concentrate our efforts in finding better multipliers sets, i.e.…”

Section: Proposed Strategy For Solving the Lagrangean Dualmentioning

confidence: 99%

A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

Oliveira

Gupta

Hamacher

et al. 2013

Computers & Chemical Engineering

View full text Add to dashboard Cite

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“…Moreover, even when such a solution can be computed, it may require large computational times and special initialization and solution procedures. In fact, presently the MIDO solution of complex and large scale problems seems to be feasible only if special optimization decomposition procedures are used [8], [9], [10], [11], [12].…”

Section: Mido Solution Strategymentioning

confidence: 99%

Simultaneous Scheduling and Control of Multiproduct Continuous Parallel Lines

Flores‐Tlacuahuac

Grossmann

2010

Ind. Eng. Chem. Res.

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In this work we propose a simultaneous scheduling and control optimization formulation to address both optimal steady-state production and dynamic product transitions in multiproduct parallel continuous stirred tank reactors. The simultaneous scheduling and control problem for multiproduct parallel continuous reactors is cast as a Mixed-Integer Dynamic Optimization (MIDO) problem.The reactor dynamic behavior is described by a set of nonlinear ordinary differential equations that are combined with the set of mixed-integer algebraic equations representing the optimal scheduling production model. We claim that the proposed simultaneous scheduling and control approach avoids suboptimal solutions, that are obtained when both problems are solved in a decoupled way. Hence, the proposed optimization strategy can yield improved optimal solutions. The simultaneous approach for addressing the solution of dynamic optimization problems, based on orthogonal collocation on finite elements, is used to transform the set of ordinary differential equations into a Mixed-Integer Nonlinear Programming (MINLP) problem. The proposed simultaneous scheduling and control formulation is tested using three multiproduct continuous stirred tank reactors featuring different nonlinear behavior characteristics.2

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“…Lagrangean relaxation, usually coupled with a nondifferentiable optimization technique (such as subgradient optimization), is a popular approach to solve combinatorial optimization problems (Guignard, 2003). We also adopt this approach to solve SCLP, not only due to its simplicity, but also to the fact that it allows the problem to be decomposed to exploit its special structure.…”

Section: The Lagrangean Relaxation and Decomposition Frameworkmentioning

confidence: 99%

“…Hence, the bound provided by the Lagrangean relaxation may be better than that of the linear programming relaxation of formulation SCLP (see, e.g., Guignard, 2003).…”

Section: Subproblemmentioning

confidence: 99%

Lagrangean‐based solution approaches for the generalized problem of locating capacitated warehouses

Bektaş

Bulgak

2008

Int Trans Operational Res

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The traditional capacitated warehouse location problem consists of determining the number and the location of capacitated warehouses on a predefined set of potential sites such that the demands of a set of customers are met. A very common assumption made in modeling this problem in almost all of the existing research is that the total capacity of all potential warehouses is sufficient to meet the total demand. Whereas this assumption facilitates to define a well-structured problem from the mathematical modeling perspective, it is in fact restrictive, not realistic, and hence rarely held in practice. The modeling approach presented in this paper breaks away from the existing research in relaxing this very restrictive assumption. This paper therefore investigates the generalized problem of locating warehouses in a supply chain setting with multiple commodities with no restriction on the total capacity and the demand. A new integer programming formulation for this problem is presented, and an algorithm based on Lagrangean relaxation and decomposition is described for its solution. Three Lagrangean heuristics are proposed. Computational results indicate that reasonably good solutions can be obtained with the proposed algorithms, without having to use a general purpose optimizer.

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Lagrangean relaxation

Abstract: Integer programming, Lagrangean relaxation, column generation, 90C11, 90-02,

Cited by 245 publications

References 49 publications

A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

Simultaneous Scheduling and Control of Multiproduct Continuous Parallel Lines

Lagrangean‐based solution approaches for the generalized problem of locating capacitated warehouses

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