Confidence structural robust optimization by non‐linear semidefinite programming‐based single‐level formulation

Guo, Xu; Du, Juanjuan; Gao, Xixin

doi:10.1002/nme.3083

Cited by 22 publications

(9 citation statements)

References 39 publications

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“…With the relations in Equations (17) and (19) in mind, by applying the lemmas in convex analysis (see the Appendix for details) as in other works, 13,[21][22][23][24] it can be concluded that the sensitivity u l / a i is bounded in terms of…”

Section: Interval Methods For Sensitivity Boundingmentioning

confidence: 94%

“…Table 6 presents the calculated lower and upper sensitivity bounds of u 13y / A i (i = 1, … , 51) with use of the proposed iterative interval sensitivity bounding method. It can be found that, among totally 51 binary discrete variables, the optimal values of 18 0-1 variables (x i , i ∈ I 1 = {5, 9,10,14,15,17,19,22,24,27,28,32,33,38,40,43,45, 50}) can be determined directly in the first-round sensitivity bounding analysis. With these obtained values being fixed another 15 values of x i , i ∈ I 2 = {1, 4,12,13,18,20,23,26,29,34,35,37, 39, 48, 51} can be found from monotonic analysis in the second-round sensitivity bounding process.…”

Section: A 51-bar Truss Arch Bridgementioning

confidence: 99%

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Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique

Wei

et al. 2018

Numerical Meth Engineering

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In the present paper, finding the exact bound of structural response for truss structures is considered under bounded interval type uncertainty. This problem is challenging since seeking the exact bound corresponds to locating the global optima of a multivariate function (generally nonconvex). Traditional treatment of this problem involves the solution of a linear mixed 0-1 programming problem, which is a highly computationally demanding task especially when large-scale structures are taken into consideration. In order to alleviate the computational effort, a sensitivity bounding technique is developed in this work using the tools from convex analysis to disclose the monotonicity of concerned structural response function with respect to 0-1 variables. It is shown that this technique can not only reduce the number of 0-1 variables substantially but also change the computational complexity of the considered problem from nondeterministic polynomial-hard to nondeterministic polynomial-hard in some cases. The proposed approach provides the possibility of finding the exact bound of structural response for large-scale truss structures within a reasonable time, and its effectiveness is demonstrated through several numerical examples. KEYWORDS bounds of structural response, global optimization, interval uncertainty, linear mixed 0-1 programming, sensitivity bounding Int J Numer Methods Eng. 2018;116:21-42. wileyonlinelibrary.com/journal/nmewhere x, f (x), and g i (x; p) are the design variable vector, objective function, and ith constraint, respectively. p denotes the vector of uncertain parameters and U p is the corresponding uncertainty set. It is clear that the objective of a WCDO problem is essentially to optimize the performance of a design while ensuring the its safety under the worst combination of uncertain parameters. Therefore, Equation (1) is actually a nested bilevel program. The upper level program aims at finding the best design by selection of optimal design variables, while the lower level program identifies the worst-case structural responses and determines the feasibility of a given design. To predict the extreme structural response with respect to the uncertain parameter efficiently, interval analysis technique or convex modeling methods cooperating with sensitivity analysis and gradient-based algorithms are commonly adopted in literatures. [8][9][10][11][12] It should be pointed out that the lower level program in Equation (1) must be solved with global optimality; otherwise, the feasibility of an "optimal solution" cannot be fully guaranteed. 13 This issue, however, cannot been guaranteed by the general gradient-based algorithms used in most related literature studies, especially for WCDO problems involving nonconvex objective/constraint functions, which are ubiquitous in practical engineering applications. Under this circumstance, the obtained solution may be totally meaningless since the worst-case structural response may be severely underestimated. Actually, it is very difficult to find the global ...

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Section: Interval Methods For Sensitivity Boundingmentioning

confidence: 94%

Section: A 51-bar Truss Arch Bridgementioning

confidence: 99%

Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique

Wei

et al. 2018

Numerical Meth Engineering

Self Cite

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“…In the following, we add (24) to problem (23). It is worth noting that a truss design involving a chain is infeasible for the presented robust optimization problem, because it is unstable and cannot be in equilibrium with uncertain forces applied to an intermediate node of the chain.…”

Section: Treatment Of Members Lying On a Linementioning

confidence: 99%

“…By relaxing the 0-1 constraints into linear inequality constraints, we obtain an SDP relaxation. Since SDP can be solved efficiently with a primal-dual interior-point method, we can find a global optimal solution of problem (23) with a branch-and-bound method [59].…”

Section: Review Of Existing Formulationmentioning

confidence: 99%

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Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach

Kanno

2018

Comput Optim Appl

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The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very time-consuming. This paper presents an alternative formulation, semidefinite programming with complementarity constraints, and proposes an efficient heuristic. The proposed method is based upon the convex-concave procedure for DC (difference-of-convex) programming. It is shown that the method can often find a practically reasonable truss design within the computational cost of solving some dozen of convex optimization subproblems. . 1 A truss is an assemblage of straight bars (called members) connected by pin-joints (called nodes) that do not transfer moment. See section 2 for some concrete examples. 2 The compliance of a truss, formally defined by (16), is equivalent to the twice strain energy of the truss at the equilibrium state under the prescribed boundary conditions. It can be regarded as a global measure of the displacements, and hence by minimizing the compliance the global stiffness of the truss is maximized.

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A semidefinite programming approach to robust truss topology optimization under uncertainty in locations of nodes

Hashimoto

Kanno

2014

Struct Multidisc Optim

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Confidence structural robust optimization by non‐linear semidefinite programming‐based single‐level formulation

Cited by 22 publications

References 39 publications

Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique

Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique

Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach

A semidefinite programming approach to robust truss topology optimization under uncertainty in locations of nodes

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