Jaco F. Schutte

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 gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently-developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithms global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent 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 multistart 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 provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.

Decomposition and Two-level Optimization of Structures with Discrete Sizing Variables

A generalized decomposition approach is demonstrated for quasiseparable design problems containing discrete variables. Quasiseperable problems involve local design variables and global design variables, shared between subsystems. The primary idea is to assign each subsystem a budget and global system variable values, and require the subsystems to individually maximize their constraint margins. The subsystem constraint margin optimization problems are independent, always feasible, and can be executed concurrently on a parallel machine. An illustrative structural design problem consisting of three beams with discrete cross section selection, reflecting commercially available sections, is presented.

Improved Global Convergence Probability Using Independent Swarms

In global optimization it may sometimes be more efficient to perform multiple independent optimization runs with a limited number of fitness evaluations in place of a single run with an equal number of total fitness evaluations. This is especially true for problems with a number of widely separated local optima in the design space because a single optimization has a larger probability of becoming entrapped in a local optimum than multiple independent runs. This approach can be further exploited by utilizing parallel computation. Some preliminary results of an investigation on the feasibility of multiple independent optimizations are reported. I. Nomenclature Pi = individual optimization global convergence probability Pc = multiple optimization cumulative global convergence probability Cr = convergence ratio N = number of optimization runs Nc = number of globally converged optimization runs nfe = number of fitness evaluations nb = budget of fitness evaluations allocated to solving problem ni = allowed fitness evaluations for each independent optimization nl = number of fitness evaluations required by optimization algorithm to find minima se = standard error

Sampling by Exploration and Replication for Estimating Experimental Strength of Composite Structures

The industry has to resort to experiments for practical design of composite laminates when physical models/simulations are inadequate for desirable accuracy or require excessive computational resou...