## Abstrakti

The topic of this thesis is discrete sizing optimization of steel frames and trusses used as load bearing structures in buildings. Instead of only stress or displacement limits, steel structures should comply with design codes and meet their requirements. Thus the resulting design optimization problem is complemented with constraints that can be derived from steel design standards and include fire design as well. The code-based constraints together with discrete design variables originating from availability of steel profiles in certain sizes and types result in design problem to which the variety of available solution approaches is limited. In this thesis, the goal is to assess and further develop such approaches to find best performing procedure in terms of computational cost and quality of the obtained solution.

Three types of optimization approaches are considered. Firstly the popular meta-heuristics, secondly the mixed-integer linear programming (MILP) approach and thirdly the two-phase approach. Meta-heuristics are known to be flexible and easy to implement. However, the optimality of the obtained solution cannot be proven and convergence can be considered slow. Mixed-integer scheme is based on strict mathematical formulation and gives guaranteed global optimum of the problem. However, the computational effort needed for the solution becomes high. Moreover, the strict requirement of problem mathematical properties can be restricting when code-based resistance and stability constraints are applied. Approximations may be needed to ensure compliance with the requirements. The third approach uses continuous relaxation in the first phase after which a subset of the original discrete set around the continuous solution is searched with a suitable method. With the two-phase approach promising results are obtained in comparison with both meta-heuristics and MILP approach.

However, based on multiple example calculations the best approach cannot be selected with respect to all criteria. It seems that choice of approach and method should be done according to properties of the optimization problem being considered.

Three types of optimization approaches are considered. Firstly the popular meta-heuristics, secondly the mixed-integer linear programming (MILP) approach and thirdly the two-phase approach. Meta-heuristics are known to be flexible and easy to implement. However, the optimality of the obtained solution cannot be proven and convergence can be considered slow. Mixed-integer scheme is based on strict mathematical formulation and gives guaranteed global optimum of the problem. However, the computational effort needed for the solution becomes high. Moreover, the strict requirement of problem mathematical properties can be restricting when code-based resistance and stability constraints are applied. Approximations may be needed to ensure compliance with the requirements. The third approach uses continuous relaxation in the first phase after which a subset of the original discrete set around the continuous solution is searched with a suitable method. With the two-phase approach promising results are obtained in comparison with both meta-heuristics and MILP approach.

However, based on multiple example calculations the best approach cannot be selected with respect to all criteria. It seems that choice of approach and method should be done according to properties of the optimization problem being considered.

Alkuperäiskieli | Englanti |
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Julkaisupaikka | Tampere |

Kustantaja | Tampere University |

ISBN (elektroninen) | 978-952-03-2083-6 |

ISBN (painettu) | 978-952-03-2082-9 |

Tila | Julkaistu - 2021 |

OKM-julkaisutyyppi | G5 Artikkeliväitöskirja |

### Julkaisusarja

Nimi | Tampere University Dissertations - Tampereen yliopiston väitöskirjat |
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Vuosikerta | 464 |

ISSN (painettu) | 2489-9860 |

ISSN (elektroninen) | 2490-0028 |