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A speciation-based bilevel niching method for multimodal truss design problems

Abstract

Truss design is a well-known structural optimization problem that has important practical applications in various fields. Truss design problems are typically multimodal by nature, meaning that it offers multiple optimal solutions concerning the topology (combinatorial optimization problem) and/or sizes (continuous optimization problem) of the members, but they are evaluated to have similar or equally good objective function values. From a practical standpoint, it is desirable to find as many alternative designs as possible, rather than finding a single design, as often practiced. Several techniques based on classical and metaheuristic optimization methods have been developed for simultaneous optimization of topology and size of a truss. However, all these methods unable to find multiple topologies and their corresponding size solutions in a single run. A few metaheuristics incorporating niching techniques have been developed for finding multiple topologies for the truss design problem, but these studies ignored the fact that for each known topology, multiple design solutions in terms of size can be found. To address this issue, this paper proposes a bi-level truss formulation and subsequently a speciation-based bilevel niching method (BiL-NM) using such a formulation. The BiL-NM consists of a modified SPSO niching method which is robust to find multiple topologies and a canonical PSO for their corresponding size solutions. Extensive empirical studies are carried out to analyze the accuracy, robustness, and efficiency of the BiL-NM. The results confirm that the proposed BiL-NM is superior in all these three aspects over the state-of-the-art methods on several low to high-dimensional truss design problems.

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Notes

  1. 1.

    If the cross-sectional area (\(A_i\)) of a truss member found to be less than the critical cross-sectional area (\(\epsilon \)) i.e., \(A_i<\epsilon \), then this type of truss member is called non-active member.

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Correspondence to Md. Jakirul Islam.

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Islam, M.J., Li, X. & Deb, K. A speciation-based bilevel niching method for multimodal truss design problems. J Comb Optim (2021). https://doi.org/10.1007/s10878-021-00818-x

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Keywords

  • Combinatorial optimization
  • Truss optimization
  • Bilevel optimization
  • Niching method
  • Multimodal optimization