Particle swarm optimization for non-convex problems of size and shape optimization of trusses

The simultaneous size and shape optimization of truss structures can represent the non-convex problems. In this paper, an improved particle swarm optimization algorithm is developed and applied to find global optimum solutions. The optimisation problem is concerned with minimizing the structural weight subject to the constraints on nodal displacements, stresses and buckling in the bars. The optimisation variables are the nodal coordinates and the cross-sectional areas. Also the lower and upper bounds are imposed on these two types of optimisation variables. The classical PSO algorithm is modified to satisfy that all the particles fly inside the variable boundaries. A method derived from the harmony search algorithm is used to deal with the particles which fly outside the variables boundaries. The multi-stage penalty function method is adopted within PSO to satisfy the constraints of the optimisation problem and obtain the feasible optimal solutions. The classical PSO algorithm has good exploration abilities but weak exploitation of local optima. The inertia weight is employed to control the impact of the previous history of velocities on the current velocity of each particle. Thus this parameter regulates the trade-off between global and local exploration ability of the swarm. A general rule is to set the initial inertia weight to a large value in order to make better global exploration of the search space and then gradually decrease it to get more refined solutions. Thus a dynamic variation of inertia weight is used in the paper by applying a fraction multiplier. Some benchmark problems of size and shape optimisation of truss structures are tested and the obtained results are compared with the known results from the literature.