Illinois Genetic Algorithms Laboratory

Goldberg, D.E. (2005)
TR No.: 2005021 | Download PDF | Download PS

Abstract:
In 25 years of work in genetic algorithms (GAs), the
author has tried a variety of analytical
methods to better understand GAs and their
deriviatives. As outlined elsewhere (Goldberg,
2002),
that work initially focused on transform methods,
difference equations, and Markov chains, but
these tools were disappointing because they failed
to deliver results that were generally useful in
GA design. Only after turning to simplified models
of GA facets and a means of model
integration borrowed from fluid mechanics and
dimensional analysis did the GA beast succumb
to sufficient analysis for effective design of scalably
efficient procedures.

More recently, the author and others have taken
this method of little models and applied it
to understanding a number of questions of
organizational theory, including team sizing
(Goldberg,
Yassine, & Yu, 2004) and department sizing in a
hierarchy (Yassine, Goldberg, & Yu, 2005).
The modeling methodology is essentially the same
one that proved successful in taming genetic
algorithms, and it appears to have similar power in
shedding important quantitative light on
organizations in a fairly direct manner.

This approach is adopted here in this short note to
address an organizational decision
often made in many workshops and problem-
solving meetings. In particular, it is a
commonplace
in a large workshop to subdivide the workshop into
breakout groups of roughly equal size to give
more people the opportunity to contribute to the
meeting in the allotted time. Given that the
motivation for the breakout is one of discussion
efficiency, it should be possible to calculate the
size of group that results in the most efficient
breakout meeting.

The organization of the note is as follows. The
note starts by considering the tradeoff
between reporting and discussing inherent in the
workshop setting. It continues by deriving a
model of workshop session time that accounts for
balancing reporting and discussing; it
minimizes the model and puts it into dimensionless
form. The note concludes by considering the
probability of meeting success depending upon the
number and size of breakout groups, noting
that the probability of success is uniform under the
assumption of independent discussion success.