Revision 2 Evaluation of a Particle Swarm Algorithm for Biomechanical Optimization

Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradientbased algorithms can be affected by scaling to account for design variables with different length scales or units. This study evaluates a recently developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm’s global search capabilities were investigated using a suite of difficult analytical test problems, while its scaleindependent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms – a global genetic algorithm (GA) and multi-start gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm (freely available with this article) provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units. Revision 2 Schutte et al. 1