Optimization

# Optimization

Keywords

• all geometry
• single function
• multi parameter
• constrained optimization
• function or path
• mass, stiffness
• position of mass
• peak, RMS, average

The optimization module of SAM Professional offers constrained single-function multi-parameter optimization based on a mix of evolutionary algorithms and Simplex techniques. Constraints are dealt with by treating each
violation of a constraint as a penalty that is added to the original cost function. The software offers the
option to define own results from the standard set of results via an advanced formula parser. This option
is also used to define and add penalties.

Taking the initial design/topology as a starting point one can for example further improve the quality in
which the trajectory of a coupler point equals the target trajectory by changing the geometry of the
mechanism within pre-defined ranges. Or one can minimize the peak or RMS value of the driving torque
of a mechanism by adding a compensating mass and let SAM determine the optimal value of the mass
and its position within the allowable range. Just as in the case of the trajectory optimization one can
also specify a reference function and minimize the difference between the actual and the reference
function. When designing for example fitness equipment one is generally seeking a predefined force as
function of displacement.

The goal for optimization can be the minimization or maximization of a variety of properties (peak, RMS, average, ...) or the difference between the actual and the target behaviour of a mechanism, such as:

• Trajectory of a node (with of without prescribed timing)
• Any motion or force quantity (as function of time or another quantity)

SAM seeks the optimum by modifying the following properties within user-defined ranges:

• geometry of mechanism
• element properties, such mass, spring constant, transmission ratio, ...

The optimization process in SAM is based on a two step approach, consisting of:

• Exploration of the design space
• Optimization of a specific solution

First, the entire parameter space is explored globally using a combination of a pure Monte-Carlo technique and a so-called Evolutionary Algorithm, which is a optimization technique derived from Genetic Optimization. The top list of such a global exploration are shown in the Explore list box, which displays the value of the optimization function and the corresponding parameters. The individual with the best property is listed at the top.

Next, the designer can select one of the results from the Explore window and start a local optimization. This local search can be either based on a Simplex technique or on a Evolutionary Algorithm with a smaller parameter range centered around the selected solution.

The combination of a global exploration strategy and a local optimization strategy - with the designer in the loop for selecting the mechanism that is further optimized - is believed to give the best trade-off between speed and coverage of the design space. Alternatively, options can also be set in such a way, that a fully automated optimization is performed.