The Success History-based Adaptive Differential Evolution algorithm with Linear Population Size Reduction (L-SHADE) is a highly competitive continuous optimizer. In this paper, we extend L-SHADE towards handling mixed variable optimization problems, where some of the variables may be categorical, ordinal, integer or continuous. For handling the discrete variables, we consider three different options. The first is to adapt the mechanism for handling categorical variables introduced in an earlier proposed ant colony optimization algorithm, called ACOMV to use it with L-SHADE (L-SHADEMV). The second is to apply a simpler scheme that relies on the mechanisms how ant colony optimization algorithms traditionally tackle discrete problems (L-SHADEACO). The third is to introduce a mechanism that exploits the ideas of DE within the generation of new values for the categorical variables, by introducing specific rules to be applied in the mutation (L-SHADERULE). We use an automatic algorithm configuration tool for optimizing the algorithms' parameters to allow an unbiased comparison of the three schemes. The performance of the proposed algorithms was evaluated on artificial mixed-variable optimization problems and compared with L-SHADE that incorporates a simple rounding scheme to handle categorical variables, which is used as a baseline method. The experimental results show that all three categorical handling methods outperform the baseline and L-SHADEACO is the best performing scheme in terms of accuracy and robustness.
