variable, granted the medial-lateral translational model parameter placing the knee joint
center in the tibia segment is constrained to zero. If both medial-lateral translational
model parameters are used as redundant design variables, the outer-level optimization has
an infinite number of solutions within the constraints of both parameters. Through the
elimination (i.e., constraining to zero) of redundant model parameters, the outer-level
optimization encounters less convergence problems in globally minimizing the objective
function.
Objective Function Formulation
The inner-level optimization objective function should be comprised of marker
coordinate errors rather than marker distance errors. A substantial amount of information
(i.e., % of the number of errors) describing the fitness value is lost with computation of
marker distance errors. In other words, a marker distance error provides only the radius
of a sphere surrounding an experimental marker and it does not afford the location of a
model marker on the surface of the sphere. However, a set of three marker coordinate
errors describes both the magnitude and direction of an error vector between an
experimental marker and a model marker. By using marker coordinate errors, the
inner-level optimization has improved convergence (Table 5-1) and shorter execution
time (Table 5-2).
Optimization Time and Parallel Computing
To reduce the computation time, it is necessary to use an outer-level optimization
algorithm in a parallel environment on a network cluster of processors. The PSO
algorithm was chosen over gradient-based optimizers for its suitability to be parallelized
and its ability to solve global optimization problems. The large computation time is a
result of the random set of initial values used to seed each node of the parallel algorithm.