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Solving multi-objective truss structural optimization problems considering natural frequencies of vibration and automatic member grouping

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Abstract

Minimizing the mass of a structure and maximizing its first natural frequency of vibration are conflicting objectives of real interest in structural design. To avoid problems with resonance, which can lead to their collapse, structures can be designed by making the first natural frequency of vibration high. Furthermore, it is crucial to stay away from excitation frequencies. Here we formulate and solve multi-objective structural optimization problems of trusses with these conflicting objectives. This type of problem is uncommon in the literature, since the natural frequencies of vibration are generally set as constraints rather than as objective functions. The generalized differential evolution 3 (GDE3), the nondominated sorting genetic algorithm II (NSGA-II), decision space-based niching (DN-NSGA-II), the competitive mechanism-based multi-objective particle swarm optimizer (CMOPSO), and the MOPSO with multiple search strategies (MMOPSO) are the algorithms used in this paper. Additionally, cardinality constraints are used to manage the difficulty of discovering the best member grouping, which is very effective in addressing the problems analyzed in this paper. The experiments refer to the 10-, 25-, 72-, and 200-bar trusses. Each involves two analyses, taking into account the performance indicators and the use of a multi tournament decision (MTD) method to extract the desired solutions. Furthermore, the design variables of each extracted solution, including its optimized topology, are provided.

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Funding

The authors wish to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Grants No. 308105/2021-4 and 312682/2018-2, FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais), Grants No. TEC APQ 00103-12, TEC APQ 00337-18, TEC PPM 00174-18, and TEC APQ 00408-21, and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for their support.

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Authors and Affiliations

  1. Graduate Program of Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Érica C. R. Carvalho

  2. Civil Engineering Program, COPPE/Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    José Pedro G. Carvalho

  3. Department of Computer Science, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Heder S. Bernardino

  4. Department of Applied and Computational Mechanics, School of Engineering, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Afonso C. C. Lemonge & Patrícia H. Hallak

  5. Department of Mathematics, Federal Center for Technological Education of Minas Gerais, Belo Horizonte, Brazil

    Dênis E. C. Vargas

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  1. Érica C. R. Carvalho
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Carvalho, É.C.R., Carvalho, J.P.G., Bernardino, H.S. et al. Solving multi-objective truss structural optimization problems considering natural frequencies of vibration and automatic member grouping. Evol. Intel. 17, 653–678 (2024). https://doi.org/10.1007/s12065-022-00804-0

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