The bbob-mixint Test Suite
The bbob-mixint test suite contains (partly) discretized versions of the 24 single-objective noiseless bbob test functions.
The core idea behind bbob-mixint is to start from the bbob test functions and discretize 80% of the variables and keep 20% continuous (while translating the optima in order to have the optima coincide with the discrete values. 20% of the variables are thereby mapped to binary ones, 20% to 4-ary variables, 20% to 8-ary, and 20% to 16-ary variables, each encoded between 0 and the arity minus one. The original bbob instances are shifted to have their optima on the discrete grid. Implementation-wise, off-grid evaluations (with the variables set to any continuous value) are still possible and return the function value of the closest point of the discrete grid.
More details can be found in the original publication that you may cite as follows:
@inproceedings{bbobmixint2019,
author = {Tea Tu{\v{s}}ar and Dimo Brockhoff and Nikolaus Hansen},
title = {Mixed-integer benchmark problems for single-and bi-objective optimization},
year = {2019},
booktitle={Genetic and Evolutionary Computation Conference (GECCO~2019)},
pages={718--726},
publisher={ACM}
}