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Since the scale factor and the crossover rate significantly influence theperformance of differential evolution (DE), parameter adaptation methods (PAMs)for the two parameters have been well studied in the DE community. AlthoughPAMs can sufficiently improve the effectiveness of DE, PAMs are poorlyunderstood (e.g., the working principle of PAMs). One of the difficulties inunderstanding PAMs comes from the unclarity of the parameter space thatconsists of the scale factor and the crossover rate. This paper addresses thisissue by analyzing adaptive parameter landscapes in PAMs for DE. First, wepropose a concept of an adaptive parameter landscape, which captures a momentin a parameter adaptation process. For each iteration, each individual in thepopulation has its adaptive parameter landscape. Second, we propose a method ofanalyzing adaptive parameter landscapes using a 1-step-lookahead greedyimprovement metric. Third, we examine adaptive parameter landscapes in PAMs byusing the proposed method. Results provide insightful information about PAMs inDE.

Analyzing Adaptive Parameter Landscapes in Parameter Adaptation Methods for Differential Evolution