Fig. 1

The main framework of BP-QUATRE. The flowchart of BPQUATRE algorithm consists of population initialization, population division, subpopulation evolution, subpopulation merging and approach of updating parameter scale factor F. Gen is the current generation number and MaxGen is the maximum generation number. Better means the subpopulation with better fitness values (i.e., with the lower fitness values for a minimization problem). Worse means the subpopulation with worse fitness values. The better subpopulation evolves by adopting mutation strategy “QUATRE/best/1” to make good exploitation around the individuals with better fitness values and to have good convergence rate. The better subpopulation evolves by adopting mutation strategy “QUATRE/best/1” to make good exploitation around the individuals with better fitness values and to have good convergence rate. The worse subpopulation evolves by using mutation strategy “QUATRE/target-to-best/1” to make a good exploration around the individuals with worse fitness values and to preserve population diversity