A variant of the united multi-operator evolutionary algorithms using sequential quadratic programming and improved SHADE-cnEpSin

United multi-operator evolutionary algorithms (UMOEAs) combine multi-operator differential evolution (DE), the multi-operator genetic algorithm (MOGA), and the covariance matrix adaption evolution strategy (CMA-ES). UMOEAs-II, an improved version of UMOEAs, uses three differential evolution variants as multi-operator differential evolution (MODE), and CMA-ES. In this study, we further reform UMOEAs-II using an improved SHADE-cnEpSin that employs a novel adaptive strategy of scaling factor F, a crossover rate cr_i,j updating mechanism which can calculate crossover rate for the i^th individual with a particular j^th component, an improved rank-based selective pressure based mutation strategy, and nonlinear population size reduction along with sequential quadratic programming method. The effectiveness of the improved rank-based selective pressure based mutation strategy, nonlinear population size reduction, and sequential quadratic programming are evident from the individual validations. The novel framework, enhanced the exploration and exploitation abilities, is named UMOEAs-III and is evaluated using the CEC2017 benchmark functions. The experiments are tested on 10, 30, 50, and 100 dimensions. The experimental results demonstrate the outstanding performance of UMOEAs-III in both low and high-dimensional tests compared to the state-of-the-art DE-based variants and hybrid algorithms.