Multi-modal distribution crossover method based on two crossing segments bounded by selected parents applied to multi-objective design optimization

This paper discusses airfoil design optimization using a genetic algorithm (GA) with multi-modal distribution crossover (MMDX). The proposed crossover method creates four segments from four parents, of which two segments are bounded by selected parents and two segments are bounded by one parent and another segment. After these segments are defined, four offsprings are generated. This study applied the proposed optimization to a real-world, multi-objective airfoil design problem using class-shape function transformation parameterization, which is an airfoil representation that uses polynomial function, to investigate the effectiveness of this algorithm. The results are compared with the results of the blend crossover (BLX) and unimodal normal distribution crossover (UNDX) algorithms. The objective of these airfoil design problems is to successfully find the optimal design. The outcome of using this algorithm is superior to that of the BLX and UNDX crossover methods because the proposed method can maintain higher diversity than the BLX and UNDX methods. This advantage is desirable for real-world problems.