New hybrid reliability-based topology optimization method combining fuzzy and probabilistic models for handling epistemic and aleatory uncertainties

Meng, Zeng; Pang, Yongsheng; Pu, Yuxue; Wang, Xuan

doi:10.1016/j.cma.2020.112886

Cited by 96 publications

(25 citation statements)

References 52 publications

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“…the cost is considered for each type (C[z]), instead of considering it for each particular bin (C j ). The total weight of the crisp (original) solution obtained from ( 8) is assumed to be precalculated in the variable P max as in expression (19).…”

Section: Solving Fuzzy Vcsbpp With Partial Packingmentioning

confidence: 99%

“…From the practical point of view, several fuzzy optimization approaches have been recently presented to deal with the real-world conditions in diverse fields, such as: uncertain payoffs in the context of incomplete-information games [6], epistemic and aleatory uncertainties in the context of topology (structural) optimization [19], uncertainty of device parameters and about the network structure (failure and changes) for clustering optimization of wireless ISSN: 1137-3601 (print), 1988-3064 (on-line) c IBERAMIA and the authors ad-hoc networks [20], and uncertainty associated to durations and flexible due dates in job shop scheduling [25]. Recent fuzzy approaches for logistic optimization problems are: the consideration of the uncertainties associated to the cost of stations, demands, prices and distance capacity of each drone in order to minimize the cost of an aerial (drone-based) delivery system [23], the management of an uncertain radius of coverage in location problems [10] and the use of fuzzy numbers to manage uncertainties associated to service time, energy consumption, travel time and recharge in the context of optimizing electric vehicle routing problem [31].…”

Section: Introductionmentioning

confidence: 99%

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fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

Herrera-Franklin¹,

Rosete

García-Borroto

2021

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The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizing the cost of all bins used to pack a set of items. There are many real-life applications of the VCSBPP where the focus is to improve the efficiency of the solution method. In spite of the existence of fuzzy approaches to adapt other optimization problems to real life conditions, VCSBPP has not been extensively studied in terms of relaxations of the crisp conditions. In this sense, the fuzzy approaches for the VCSBPP varies from relaxing the capacity of the bins to the items weights. In this paper we address a non-explored side consisting in relaxing the set of items to be packed. Therefore, our main contribution is a fuzzy version of VCSBPP that allows incomplete packing. The proposed fuzzy VCSBPP is solved by a parametric approach. Particularly, a fast heuristic algorithm is introduced that allows to obtain a set of solutions with interesting trade-offs between cost and relaxation of the original crisp conditions. An experimental study is presented to explore the proposed fuzzy VCSBPP and its solution.

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Section: Solving Fuzzy Vcsbpp With Partial Packingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

Herrera-Franklin¹,

Rosete

García-Borroto

2021

View full text Add to dashboard Cite

show abstract

“…Note that the classical TO methodology is commonly applied under a deterministic assumption in which the inherently uncertain factors, such as manufacturing imperfections, knowledge incompleteness, and environmental loading fluctuations, are resolved deterministically 9,10 . To account for these inevitable uncertainties reasonably, the methodologies of reliability‐based topology optimization (RBTO) 11,12 and robust topology optimization (RTO) 13,14 have been suggested with time requirements. Compared with RBTO, RTO is capable of accounting for uncertain behaviors in the objective function; hence, it is extensively used in well‐known minimum compliance designs of the TO problem 15 .…”

Section: Introductionmentioning

confidence: 99%

“…However, complex engineering systems always contain multisource and nonnegligible uncertainties, which should be taken into account simultaneously in the preliminary design phase. In this context, the hybrid RBTO method was recently proposed by Meng et al 12 to solve the minimum volume problem with uncertain constraints. In the TO field, it should be noted that the minimum compliance design is an important type of optimization problem 19,37 .…”

Section: Introductionmentioning

confidence: 99%

Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties

Meng

Wang

et al. 2021

Numerical Meth Engineering

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Owing to the variations in geometric dimensions, material properties and external loads in engineering applications, robust topology optimization (RTO) has garnered increasing attention in recent years to account for the uncertain behaviors during the preliminary concept design phases. This paper presents a hybrid RTO method to simultaneously resolve the epistemic and aleatory uncertainties. First, based on the probabilistic and fuzzy methodologies, the hybrid RTO model is formulated with nested double optimization loops using Monte Carlo simulations. Second, an efficient iterative method is proposed based on the perturbation method to accelerate the rate of convergence of the proposed hybrid RTO model. The derivatives of the hybrid robust compliance objective function with respect to the deterministic design variables, random parameters, and fuzzy parameters are then derived using the adjoint variable method. Finally, a T-shaped beam design, an L-shaped beam design, and a three-dimensional cantilever beam design are tested to validate the proposed hybrid RTO method.

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“…Several works have been performed considering the same point of view [2,3]. Newly, [4] developed a hybrid method of RBTO with the aim of handling epistemic and aleatory uncertainties. This method consists of an efficient single optimization loop method based on Karush-Kuhn-Tucker optimality condition.…”

Section: Introductionmentioning

confidence: 99%

Linear versus nonlinear reliability-based topology optimization with application to bridge structures

2021

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In general, two types of topology optimization models can be found in literature. The first type is called Deterministic Topology Optimization (DTO) leading to a single layout when considering a given design space. The second type is called Reliability-Based Topology Optimization (RBTO) leading to various solutions. In our previous work, two strategies based on the Inverse Optimum Safety Factors (IOSF) were established and applied simply to the normal (Gaussian or linear) distribution law. In this work, linear and nonlinear (normal and lognormal) distribution RBTO cases are compared. A bridge structure is considered a numerical application to perform this comparison where different layouts at the same level of reliability can be found. The numerical results show that regarding the distribution laws, certain output parameters and safety factor values are affected. This change can affect the resulting topology layouts as well as the output parameter such as the compliance. When rising the values of the reliability index, the values of the compliance become larger and the volume values become lesser for the lognormal distribution when comparing to the normal one.

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New hybrid reliability-based topology optimization method combining fuzzy and probabilistic models for handling epistemic and aleatory uncertainties

Cited by 96 publications

References 52 publications

fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties

Linear versus nonlinear reliability-based topology optimization with application to bridge structures

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