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# Newton optimization algorithm made 10x faster. From necessity to reality.

A new optimization concept is introduced which involves the gradient-based optimization of any nonlinear structure by using gradients calculated from a linear equivalent, leading thus to significant computational savings compared to the classical Newton-type optimization algorithms which require gradient information from the nonlinear structure itself. The energy dissipated due to elastoplastic hysteretic response of the nonlinear structure and the energy dissipated due to damping action of the equivalent linear structure are used to reduce the nonlinear structure to its linear counterpart.

The objective of the optimization process which is presented in the above journal paper, is to minimize the variation of the energy (viscously damped or hysteretically dissipated) distribution along the height of a MDOF planar shear building, by finding the optimum distribution of the storey stiffness and strength, for a prescribed fundamental (small strain) eigenperiod of the building. A new iterative modified Newton optimization algorithm with line-search control especially designed for structural optimization is used. The optimum stiffness distributions of two representative linear or non-linear MDOF shear buildings are found, so that the distribution of viscously damped and hysteretically dissipated energy, respectively, over the structural height is uniform. The effect of the earthquake excitation, the critical modal damping ratio, and the normalized yield inter-storey drift limit on the optimum stiffness distributions is studied. Structural design based on the proposed approach is more rational and technically feasible compared to other structural optimization strategies (e.g., uniform ductility concept), whereas it is expected to provide increased protection against global collapse and loss of life during strong earthquake events. This study is a clear indication towards energy - oriented seismic design, rather than that based on maximum force and/or displacement response. Finally, it is proven that the new optimization concept can reduce running times by as much as 10 times compared to the classical optimization algorithms, depending on the size of the optimization problem.

Many known optimization algorithms can be modified to incorporate the above concept. Eventually, a new category will appear containing the modified versions, which will be able to capture problems of increased size and complexity while requiring the same computational effort. Beginning with this, the authors will extend many known optimization algorithms with this new concept which will be a window to the future of optimum structural design.

See here or here for more details.

There are two ways to increase speed: increase power or decrease force. The former is a matter of (computational) resources. The latter is a matter of imagination.

- George Papazafeiropoulos's blog
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