Differential Evolution With Exponential Crossover: An Experimental Analysis on Numerical Optimization

Since the inception in 1995, Differential Evolution (DE) has gained significant attention from researchers worldwide, and many DE variants proposed in the last decades obtained excellent performance in many scientific and engineering applications. However, the vast majority of these well-performed DE variants employ binomial crossover rather than exponential crossover in generating trial vector candidates though both of the two schemes were proposed simultaneously. That may be also the reason why there still doesn’t exist such a thorough analysis of DE with exponential crossover. Different from the majority of DE researchers believing that DE variants with binomial crossover usually exhibit superior performance than the ones employing exponential crossover and DE variants with exponential crossover are good at tackling optimization problems with linkages among neighboring variables, we found that DE variants with exponential crossover can achieve competitive performance with the ones employing binomial crossover regardless of whether there are linkages among the variables or not after discovering the proper crossover rate
$CR$
and its corresponding parameter control. In order to enrich research of DE on exponential crossover, this paper presents an thorough experimental analysis of DE algorithm with exponential crossover in numerical optimization, presenting the basic concepts of exponential crossover, giving the mathematical analysis why they can actually achieve similar optimization between exponential crossover and binomial crossover, experimental validation under the 100 benchmark functions from CEC2013, CEC2014, CEC2017, CEC2022 test suites as well as the tension/compression spring design problem, and summarizing and classifying various engineering applications that exponential crossover DEs are used to solve. Furthermore, we also look into the future challenges and potential directions for further development of DE with exponential crossover.