An alternative adaptive differential evolutionary Algorithm assisted by Expected Improvement criterion and cut-HDMR expansion and its application in time-based sheet forming design

• An alternative adaptive DE algorithm is suggested.
• Two new mutation strategies are proposed.
• EI criterion is employed to identify scale factor adaptively.
• Cut-HDMR is used to determine crossover constant due to coupling characteristic.
• The suggested method is successfully applied to time-based sheet forming optimization.

Differential Evolution (DE) is one of the most powerful stochastic real parameter optimizers. An alternative adaptive DE algorithm called Expected Improvement (EI)-High Dimensional Model Representation (HDMR)-DE is suggested. The EI criterion and the Kriging-HDMR are used to adjust scale factor F and crossover constant Cr, respectively. Considering the expensive computational cost of evaluation, the Kriging is integrated to evaluate the objective function when an accuracy criterion is met. To compare the performance, the suggested method, it has been compared with four popular adaptive DE algorithms over 25 standard numerical benchmarks derived from the IEEE Congress on Evolutionary Computation 2005 competition. To verify the feasibility of the suggested algorithm, a real-world application, time-dependent variable Blank Hold Force (BHF) optimization problem is also carried out by the EI-HDMR-DE. The results show that the EI-HDMR-DE improves the performance of adaptive DE and has potential capability to solve some complicated real-world applications.