  Since the scale factor and the crossover rate significantly influence the
performance of differential evolution (DE), parameter adaptation methods (PAMs)
for the two parameters have been well studied in the DE community. Although
PAMs can sufficiently improve the effectiveness of DE, PAMs are poorly
understood (e.g., the working principle of PAMs). One of the difficulties in
understanding PAMs comes from the unclarity of the parameter space that
consists of the scale factor and the crossover rate. This paper addresses this
issue by analyzing adaptive parameter landscapes in PAMs for DE. First, we
propose a concept of an adaptive parameter landscape, which captures a moment
in a parameter adaptation process. For each iteration, each individual in the
population has its adaptive parameter landscape. Second, we propose a method of
analyzing adaptive parameter landscapes using a 1-step-lookahead greedy
improvement metric. Third, we examine adaptive parameter landscapes in PAMs by
using the proposed method. Results provide insightful information about PAMs in
DE.
