• Marek Lechman Building Research Institute, Filtrowa 1, 00-611, Warsaw, Poland
  • Andrzej Stachurski Warsaw University of Technology, Institute of Control and Computation Engineering, Nowowiejska 15/19, 00-665 Warsaw, Poland



Global optimization, nonlinear equations, least squares method, RC compressed structure members


In this paper, the results of an application of global and local optimization methods to solve a problem of determination of strains in RC compressed structure members are presented. Solutions of appropriate sets of nonlinear equations in the presence of box constraints have to be found. The use of the least squares method leads to finding global solutions of optimization problems with box constraints. Numerical examples illustrate the effects of the loading value and the loading eccentricity on the strains in concrete and reinforcing steel in the a cross-section.
Three different minimization methods were applied to compute them: trust region reflective, genetic algorithm tailored to problems with real double variables and particle swarm method. Numerical results on practical data are presented. In some cases, several solutions were found. Their existence has been detected by the local search with multistart, while the genetic and particle swarm methods failed to recognize their presence.


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