shape optimization of truss structures for displacement constraints using a modified particle swarm optimization (mpso) algorithm

This paper presents a modified particle swarm optimization (mpso) algorithm for the shape optimization of truss structures under displacement constraints. the proposed mpso employs a multi-stage strategy, where the final solution of each stage is used to reinitialize the swarm in the next stage, improving convergence accuracy. a normal-based distribution is used for swarm regeneration, promoting effective exploration around the best solution found. design variables are the nodal coordinates of the structures, and the total weight is considered as the objective function. design constraints include limitations on nodal displacements, and some geometric constraints are also considered. the method is evaluated using four benchmark truss examples. results show that mpso reduces structural weight by 7% for the 13-bar truss, 5.7% for the 25-bar truss, and 2.2% for the 52-bar truss, compared to those reported in the literature, while also maintaining or improving displacement control. in the 37-bar planar truss, the algorithm marginally outperforms the existing result by reducing weight by 0.18%. these outcomes confirm that the proposed mpso provides competitive or superior performance compared to reference methods in both efficiency and solution quality.