Comparative study of four penalty-free constraint-handling techniques in structural optimization using harmony search
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ORIGINAL ARTICLE
Comparative study of four penalty‑free constraint‑handling techniques in structural optimization using harmony search Hongyou Cao1 · Yupeng Chen1 · Yunlai Zhou2 · Shuang Liu3 · Shiqiang Qin1 Received: 26 May 2020 / Accepted: 28 August 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This study investigates the search capability, stability, and computational efficiency of four improved penalty-free constrainthandling techniques (CHTs), including the death penalty, the Deb rule, the filter method, and the mapping strategy, in structural optimization using harmony search (HS). The first three general-purpose CHTs have been improved by hybridizing with a structural analysis filter strategy to enhance their computational efficiency based on the characteristics of structural optimization and the solution updating rule of the HS. This study also has modified the mapping operator of the mapping strategy to handle size and shape optimization with Euler buckling constraints. Four numerical examples examine the performances of these CHTs. The comparative results show that the mapping strategy exhibits apparent superiority both in search capability and stability among the four. However, it also demands the most computational cost, and the improved Deb rule becomes the most competitive method while considering computational efficiency. The difference between the death penalty and the Deb rule method is that the feasible solution initialization process required by the death penalty method will deteriorate its computational efficiency in problems with small feasible space. The filter method always reserves some infeasible solutions to guide the search in the iteration process. However, its performances are inferior to the other three approaches in four benchmark problems. Keywords Constraint-handling technique · Structural optimization · Metaheuristic algorithm · Harmony search · Computational efficiency
1 Introduction Structural optimization often are constrained problems with high-dimensional, non-convex, and non-differentiable characteristics [1–3]. Metaheuristic algorithms thus have extensively applied in solving structural optimization problems in recent years due to their global search ability, derivativefree, and ease of implementation in comparison to traditional gradient-based optimization algorithms. For instance, Liew * Shiqiang Qin [email protected] 1
School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430074, China
2
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China
3
School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
et al. [4] developed an adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures under multiple frequency constraints. Tejani et al. [5–9] utilized an improved symbiotic organisms search in both single o
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