Optimum Design of Steel Structures with the Particle Swarm Optimization Method Based on EC3

Abstract eng:
A number of optimization algorithms have been used in structural design optimization in the past, ranging from gradient-based mathematical algorithms to probabilistic-based search algorithms, for addressing global non-convex optimization problems. Many probabilistic-based algorithms have been inspired by natural phenomena, such as Evolutionary Programming (EP), Genetic Algorithms (GA), Evolution Strategies (ES), among others. Recently, a family of optimization methods has been developed based on the simulation of social interactions among members of a specific species. One of these methods is the Particle Swarm Optimization (PSO) method [1, 2] that is based on the behavior reflected in flocks of birds, bees and fish that adjust their physical movements to avoid predators and seek for food. In PSO, as in GA, a population of potential solutions is considered and utilized to search within the design space. However, its members do not reproduce but rather communicate with each other their knowledge of solutions in order to reach the optimum. Each “particle”, “flies” through the multi-dimensional design space, with a certain velocity vector for each iteration. In this study, a discrete PSO algorithm is employed for the optimization of 2D and 3D steel frames and the results are compared to the ones obtained with a discrete GA. Both methods are applied in single-objective, discrete, constrained structural engineering optimization problems where the aim is to minimize the weight of the structure under various constraints on displacements and forces (biaxial bending with axial force and shear force) which are based on Eurocode 3. The constraints are checked by performing a Finite Element analysis for every candidate optimum design. A new linear analysis software tool for three-dimensional frames has been developed, featuring some distinct characteristics. The applied loads can be nodal or elemental (uniform, triangular or trapezoidal in any direction within an element), while any release (translational or rotational) can be implemented at an end of any element, in any of the 6 Degrees Of Freedom (DOFs). The output of the analysis program includes the constraint reactions, nodal displacements, forces at the ends of the elements, plus the displacements of the released DOFs of all elements with releases, and any displacement or any force at any given point within an element. The accuracy of the analysis results is verified by a direct comparison to the corresponding results of a reliable commercial finite element software program. For each method, the performance, functionality and effect of different setting parameters are studied. After a fine tuning of the parameters, the results are compared to each other. The comparison is done with regard to the speed of convergence, in terms of number of objective function evaluations, and accuracy of the solution. Various 2D and 3D steel structures are considered as test examples. References [1] Kennedy, J. and R. Eberhart, Swarm Intelligence. 2001, San Francisco, USA: Morgan Kaufmann Publishers. [2] Kennedy, J. and R. Eberhart, Particle swarm optimization, in IEEE International Conference on Neural Networks. 1995: Piscataway, NJ, USA. p. 1942–1948.

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