Investigation of three genotypes for mixed variable evolutionary optimization

While the handling of optimization variables directly expressed by numbers (continuous, discrete, or integer) is abundantly investigated in the literature, the use of nominal variables is generally overlooked, despite its practical interest in plenty of scientific and industrial applications. For example, in civil engineering, the designers of a structure made out of beams might have to select the best cross-section shapes among a list of available geometries (square, circular, rectangular, etc.), which can be modeled by nominal data. Therefore, in the context of singleand multi-objective evolutionary optimization for mixed variables, this study investigates three genetic encodings (binary, real, and real-simplex) for the representation of mixed variables involving both continuous and nominal parameters. The comparison of the genotypes combined with the instances of crossover is performed on six analytical benchmark test functions, as well as on the multi-objective design optimization of a six-storey rigid frame, showing that for mixed variables, real (and to a lesser extent: real-simplex) coding provides the best results, especially when combined with a uniform crossover.