Augmented Lagrangian Particle Swarm Optimization in Mechanism Design

Abstract

The problem of optimizing nonlinear multibody systems is in general nonlinear and nonconvex. This is especially true for the dimensional synthesis process of rigid body mechanisms, where often only local solutions might be found with gradient-based optimization methods. An attractive alternative for solving such multimodal optimization problems is the Particle Swarm Optimization (PSO) algorithm. This stochastic solution technique allows a derivative-free search for a global solution without the need for any initial design. In this work, we present an extension to the basic PSO algorithm in order to solve the problem of dimensional synthesis with nonlinear equality and inequality constraints. It utilizes the Augmented Lagrange Multiplier Method in combination with an advanced non-stationary penalty function approach that does not rely on excessively large penalty factors for sufficiently accurate solutions. Although the PSO method is even able to solve nonsmooth and discrete problems, this augmented algorithm can additionally calculate accurate Lagrange multiplier estimates for differentiable formulations, which are helpful in the analysis process of the optimization results. We demonstrate this method and show its very promising applicability to the constrained dimensional synthesis process of rigid body mechanisms.