4 research outputs found
The Right Mutation Strength for Multi-Valued Decision Variables
The most common representation in evolutionary computation are bit strings.
This is ideal to model binary decision variables, but less useful for variables
taking more values. With very little theoretical work existing on how to use
evolutionary algorithms for such optimization problems, we study the run time
of simple evolutionary algorithms on some OneMax-like functions defined over
. More precisely, we regard a variety of
problem classes requesting the component-wise minimization of the distance to
an unknown target vector . For such problems we see a crucial
difference in how we extend the standard-bit mutation operator to these
multi-valued domains. While it is natural to select each position of the
solution vector to be changed independently with probability , there are
various ways to then change such a position. If we change each selected
position to a random value different from the original one, we obtain an
expected run time of . If we change each selected position
by either or (random choice), the optimization time reduces to
. If we use a random mutation strength with probability inversely proportional to and change
the selected position by either or (random choice), then the
optimization time becomes , bringing down
the dependence on from linear to polylogarithmic. One of our results
depends on a new variant of the lower bounding multiplicative drift theorem.Comment: an extended abstract of this work is to appear at GECCO 201