Constrained Particle Swarm Optimization of Mechanical Systems

1. Abstract Using Particle Swarm Optimization (PSO) for solving nonlinear, multimodal and non-differentiable optimization problems has gained increasing attention in recent years. Based on the social behavior and interaction of swarms like bird flocks, the method of Particle Swarm Optimization was introduced in 1995. While the behavior of the PSO algorithm is partially similar to other well known stochastic optimization methods such as Evolutionary Strategies or Simulated Annealing, it convinces by its simple structure characterized by only a few lines of computer code. However, engineering optimization tasks often require optimization methods capable of handling problem immanent equality and inequality constraints. This work utilizes the simple structure of the basic PSO technique and combines this method with an extended non-stationary penalty function approach, called Augmented Lagrange Multiplier Method, where ill-conditioning is a far less harmful problem and the correct solution can be obtained even for finite penalty factors. We describe the basic PSO algorithm, its relation to Evolutionary Strategies and the resulting method for constrained problems including results from benchmark tests. The applicability of the Augmented Lagrange Particle Swarm Optimization is shown by a demanding mechanical engineering example, where we optimize the stiffness of an industrial hexapod robot with parallel kinematics. 2.