Correlations Between the Scaling Factor and Fitness Values in Differential Evolution

Designing fitness-based adaptive scaling factor (
$F$
) is an effective method to enhance the performance of differential evolution (DE) algorithms. This paper investigates the correlations between
$F$
and fitness values of target vectors, base vectors and difference vectors. The correlations are described by the notations of monotonicity and nonlinearity. Monotonicity is used to examine whether the optimization performance of DE and the fitness values of certain vectors have positive or negative correlation. Nonlinearity denotes the operation in which nonlinear mappings are used to redistribute the values of
$F$
in [0, 1] so as to boost the optimization performance. These two aspects of correlations are empirically tested on the Numerical Optimization Competition benchmark functions in IEEE Congress on Evolutionary Computation. Simulation results reveal different qualitative and quantitative correlations between
$F$
and fitness values of different vectors. Then, a new
$F$
that combines these relations is designed. Its strength is numerically verified by testing different CEC Benchmark functions.