# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 123-134     https://doi.org/10.1007/s11709-018-0478-2
 RESEARCH ARTICLE |
Border-search and jump reduction method for size optimization of spatial truss structures
1. Department of Civil Engineering, Velayat University, Iranshahr 9911131311, Iran
2. Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan 9816745845, Iran
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 Abstract This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried. Corresponding Authors: Babak DIZANGIAN Just Accepted Date: 24 April 2018   Online First Date: 29 May 2018    Issue Date: 04 January 2019
 Cite this article: Babak DIZANGIAN,Mohammad Reza GHASEMI. Border-search and jump reduction method for size optimization of spatial truss structures[J]. Front. Struct. Civ. Eng., 2019, 13(1): 123-134. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-018-0478-2 http://journal.hep.com.cn/fsce/EN/Y2019/V13/I1/123
 Fig.1  An efficient random strategy Fig.2  The flow chart of border-search operator (BSO) Fig.3  Flow chart of proposed optimization method. MSV: Most sensitive variables Fig.4  Space degradation strategy (SDS) Fig.5  Stair-wise step-by-step formulation Fig.6  Sequential BSOs and JOs to find local optimums, Phase 2 Fig.7  22-bar space truss, Example 1 [33] (unit: in, 1 in=2.54 cm) Tab.1  Loading conditions for 22-bar space truss Tab.2  Allowable stresses and member grouping data for the 22-bar space truss Fig.8  First sensitivity analysis at $Xstepp1$ for the 22-bar space truss Tab.3  Comparing optimal designs for the 22-bar space truss Tab.4  Weights and the number of analyses Fig.9  Convergence history of best weight for 22-bar space truss Fig.10  72-bar space truss [33] (unit: in, 1 in=2.54 cm) Fig.11  First sensitivity analysis at $Xste pp1$ for the 72-bar truss Fig.12  Convergence history of best weight of 72-bar space truss Tab.5  Comparing optimal designs for the 72-bar space truss Tab.6  Weights and the number of analyses Fig.13  120-bar dome truss [33] Tab.7  Comparing optimal designs for the 120-bar dome truss Tab.8  Weights and the number of analyses Fig.14  First sensitivity analysis at $Xs tepp1$ for the 120-bar dome truss Fig.15  Convergence history of best weight of 120-bar dome truss