Are there any global optimization algorithms that support categorical input variables?
Evolutionary algorithms generally need to perform local mutation, however, unlike real or integer variables, it is hard to define similarity of categorical variables
See, please, Cross-Entropy Algorithm - it applicable for any discrete optimization problem.
Chapter Cross-Entropy Method
If you code the categorical input in a numerical method, you can use a numerical optimization techniques and finding a approximation to the problem
We have a recently published article that fully answers your question: including discrete/categorical variables in Bayesian optimization.
Tran, Anh, Minh Tran, and Yan Wang. "Constrained mixed-integer Gaussian mixture Bayesian optimization and its applications in designing fractal and auxetic metamaterials." Structural and Multidisciplinary Optimization 59.6 (2019): 2131-2154.
Feel free to let me know if you have any further question.
We can optimise mixed continuous and categorical variables with Bayesian Optimisation. Please check out our paper Bayesian Optimisation over Multiple Continuous and Categorical Inputs and the code below.
Paper: https://arxiv.org/pdf/1906.08878.pdf
Code: https://github.com/rubinxin/CoCaBO_code
The Article Ant Colony Optimization for Mixed-Variable Optimization Problems
" (Liao et al., 2014) method is able to deal with continuous, ordinal and categorical variables with appropriate mechanisms for each optimization task.(I have no relationship with the authors)
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