Visualizing and Characterizing the Parameter Configuration Landscape of Differential Evolution using Physical Landform Classification

It is well known that appropriately configuring the control parameters for computational intelligence algorithms is a challenging problem. Thus, analysis of the configuration space can provide critical insights towards designing more effective parameter tuning strategies. Recently, the concept of parameter configuration landscapes was proposed by drawing parallels between the parameter configuration space and traditional fitness landscapes, thereby facilitating the use of fitness landscape analysis in the parameter configuration domain. This paper extends the idea of the parameter configuration landscape and proposes the use of geomorphons, a physical landform classification scheme, to visualize and characterize the parameter configuration landscape. Additionally, a measure of ruggedness is proposed to quantity the difficulty associated with tuning the control parameters for an algorithm. The proposed methodology is applied to the parameter configuration landscape of the differential evolution (DE) algorithm on 20 benchmark problems in 10, 30, and 50 dimensions.