3 Results

3.1 Measuring Fitness Landscape Morphing

To evaluate whether coevolution takes place in the species
model, it must be demonstrated that changes in context (for
fitness evaluation) can morph the fitness landscape enough to
change which mutations are considered positive adaptations.
In other words, the order of fitness rankings between the un-
mutated and mutated versions of the species (also referred to as
the parent and child) must be shown to depend upon the
context.

Measurement Procedure: Measuring changes to the fitness
landscape takes place using the following procedure. During a
migration event, a record is kept of each solution’s original
context (individuals in its island prior to migration) and its new
context (individuals in its island after migration). The fitness
landscape for a solution is then sampled by generating 100
children using the mutation operator defined previously. Each
child is evaluated in the two contexts and we determine (based
on the selection procedure in Figure 3) if the child would
replace the parent species for each context. We next define the
contextual sensitivity as the proportion of children where the
change in context results in different replacement outcomes. In
other words, the contextual sensitivity for a species is measured
as the proportion of reachable points in fitness landscape (i.e.
children) that are strongly sensitive to the change in context.
The average sensitivity over all species is reported as the
sensitivity metric S.

A positive value for S indicates that the contextual sensitivity is
strong enough to morph the fitness landscape in ways that alter
which mutations are positive adaptations. Because such
morphing can influence the evolutionary path that a species
takes, positive S values provide empirical evidence that
coevolution is feasible within the given experimental
conditions. Results for the contextual sensitivity metric S are
given in Table 2 for both single objective and multiple
objective test problems. Here, the contextual sensitivity is
found to be strong (positive) only when evolution occurs in a
multi-objective environment.

Table 2 Average sensitivity metric S for ESIM on SOP and
MOP problems

3.2 Observing Coevolutionary Dynamics

Although a positive S indicates that a change in context is
strong enough to matter, it does not tell us if the change in
context actually influences the evolutionary path (sequence of
adaptive steps across the fitness landscape) that a species
takes. Whether the path that evolution takes is affected in
practice depends on the magnitude of S and the attractor
characteristics for a particular algorithm searching a particular
fitness landscape. Although a rigorous assessment of this
behavior is challenging for several reasons, indirect evidence
of coevolution can be provided in a relatively straightforward
manner.

In preliminary experiments, we found that each species in
ESIM tends to converge over time in objective space; a
common feature of optimization in a static fitness landscape.
Convergence indicates that the accessibility of adaptive steps
within the local fitness landscape for each species is decaying
over time. If migration events result in brief periods of new
adaptive progress, it would indicate that the evolutionary paths
of species were in fact being influenced by morphological
changes to the fitness landscape. In particular, it would
demonstrate that a stable species had become destabilized as a
result of changes in interacting species. Here we use this
knowledge to provide evidence of coevolutionary dynamics
actually occurring in ESIM.

Measurement Procedure: The evolutionary activity of a
species is defined as the movement of a species in objective
space over time and is calculated in the following manner.
First, the history of phenotypes (objective function values) for
each species is recorded in an archive for each generation, as
indicated in Figure 3. For a given number of generations τ over
which movement in objective space is being measured, the
metric for evolutionary activity ΔPh is then defined in (2) as
the average change in all m objective functions from all μ
species in the population. For these experiments, τ=10
generations however results were largely insensitive to this
parameter.

1 ^μm

^δp (^t )=τ^ ∑∑∣ Phij, t—^p'^h ', t-I     (2)

μm_{i j}

The results in Figure 4 display the time series of evolutionary
activity for single objective and multiple objective problems.
For visualization purposes, ΔPh outputs are rescaled so that
each experiment spans over three orders of magnitude and is
shifted vertically so that multiple results can be clearly viewed
on the same graph.

In all experiments, evolutionary activity decays over time
indicating that species are converging towards attractors in
their respective fitness landscapes. However during migration

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