Generalized Benders’ Decomposition for topology optimization problems

Muñoz, Eduardo; Stolpe, Mathias

doi:10.1007/s10898-010-9627-4

Cited by 21 publications

(8 citation statements)

References 29 publications

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“…The second category of methods separate the binary and continuous variables into different sub-problems, by iteratively determining one of them with the other fixed in a subproblem. The representative methods include the Discrete Variable Topology Optimization via Canonical Relaxation Algorithm (DVTOCRA) [26], the Topology Optimization of Binary Structures (TOBS) method [27], and the GBD method [28]. The DVTOCRA method employs a sequential linear/quadratic approximation to separate the binary and continuous variables into different sub-problems [26].…”

Section: Preliminary a A Continuum Topology Optimization Problemmentioning

confidence: 99%

“…It is also anticipated to converge faster than the SIMP or TOBS method, because the GBD formulation permits to use all the material layouts generated from previous iterations in each new iteration, while other methods like the SIMP or TOBS can only take into account the material layout yield from the last iteration. The GBD method was first introduced to TO by Muñoz et al [28] for solving discrete TO problems. In the present paper, we extend it to address a continuum TO problem, as discussed in Section II-B.…”

Section: Preliminary a A Continuum Topology Optimization Problemmentioning

confidence: 99%

“…However, those inequality constraints are not independent, and we do not need to include them all when solving the master problem. To accelerate the solution process, we further introduce the Pareto optimal cuts [28], as defined by:…”

Section: B Generalized Benders' Decompositionmentioning

confidence: 99%

“…As the field variables nonlinearly depend on the design variables, it results in a large-scale, mixed integer nonlinear programming (MINLP) problem, subject to equality and/or inequality constraints. This type of problem is intrinsically NP-hard [24], namely unable to be solved in polynomial time, and hence is challenging to be handled using classical approaches [25]- [28].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Topology Optimization via Quantum Annealing

Qian

Pan

2023

IEEE Trans. Quantum Eng.

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We present a quantum annealing-based solution method for topology optimization (TO).In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed functions, referred to as continuum TO problems. According to the problem's properties and structure, we formulate appropriate sub-problems that can be solved on an annealing-based quantum computer. The methodology established can effectively tackle continuum TO problems formulated as mixed-integer nonlinear programs. To maintain the resulting sub-problems small enough to be solved on quantum computers currently accessible with small numbers of qubits and limited connectivity, we further develop a splitting approach that splits the problem into two parts: the first part can be efficiently solved on classical computers, and the second part with a reduced number of variables is solved on a quantum computer. By such, a practical continuum TO problem of varying scales can be handled on the D-Wave quantum annealer. More specifically, we concern the minimum compliance, a canonical TO problem that seeks an optimal distribution of materials to minimize the compliance with desired material usage. The superior performance of the developed methodology is assessed and compared with the stateof-the-art heuristic classical methods, in terms of both solution quality and computational efficiency. The present work hence provides a promising new avenue of applying quantum computing to practical designs of topology for various applications.

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Section: Preliminary a A Continuum Topology Optimization Problemmentioning

confidence: 99%

Section: Preliminary a A Continuum Topology Optimization Problemmentioning

confidence: 99%

Section: B Generalized Benders' Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Topology Optimization via Quantum Annealing

Qian

Pan

2023

IEEE Trans. Quantum Eng.

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“…Some of them are deterministic, e.g. the application of the branch and bound method for minimal mass problems with a buckling constraint [30,32,59], or the benders decomposition method for the optimization of tailored fiber orientation composites [58]. These methods guarantee in general to find a global solution provided that the problem satisfies certain conditions such as convexity.…”

Section: Introductionmentioning

confidence: 99%

Stacking sequence and shape optimization of laminated composite plates via a level-set method

Allaire

Delgado

2016

Journal of the Mechanics and Physics of Solids

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We consider the optimal design of composite laminates by allowing a variable stacking sequence and in-plane shape of each ply. In order to optimize both variables we rely on a decomposition technique which aggregates the constraints into one unique constraint margin function. Thanks to this approach, an exactly equivalent bi-level optimization problem is established. This problem is made up of an inner level represented by the combinatorial optimization of the stacking sequence and an outer level represented by the topology and geometry optimization of each ply. We propose for the stacking sequence optimization an outer approximation method which iteratively solves a set of mixed integer linear problems associated to the evaluation of the constraint margin function. For the topology optimization of each ply, we lean on the level set method for the description of the interfaces and the Hadamard method for boundary variations by means of the computation of the shape gradient. Numerical experiments are performed on an aeronautic test case where the weight is minimized subject to different mechanical constraints, namely compliance, reserve factor and buckling load.

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