Real-coded genetic algorithms (RCGA) are expected to solve efficiently real parameter optimization problems of multimodality, parameter dependency, and ill-scale. Multi-parental crossovers such as the simplex crossover (SPX) and the UNDX-m as extensions of the unimodal normal distribution crossove (UNDX) show relatively good performance for RCGA. The minimal generation gap (MGG) is used widely as a generation alternation model for RCGA. However, the MGG is not suited for multi-parental crossovers. Both the SPX and the UNDX-m have their own drawbacks respectively. Therefore, RCGA composed of them cannot be applied to highly dimensional problems, because their hidden faults appear. This paper presents a new and robust faramework for RCGA. First, we propose a generation alternation model called JGG (just generation gap) suited for multi-parental crossovers. The JGG replaces parents with children completely every generation. To solve the asymmetry and bias of children distribution generated by the SPX and the UNDX-m, an enhanced SPX (e-SPX) and an enhanced UNDX (e-UNDX) are proposed. Moreover, we propose a crossover called REX(φ,n+k) as a generlization of the e-UNDX, where φ and n+k denote some probability distribution and the number of parents respectively. A concept of the globally descent direction (GDD) is introduced to handle the situations where the population does not cover any optimum. The GDD can be used under the big valley structure. Then, we propose REXstar as an extention of the REX(φ,n+k) that can generate children to the GDD efficiently. Several experiments show excellent performance and robustness of the REXstar. Finally, the future work is discussed.
