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Design of mechanical metamaterials is typically realized by repeating microstructured building blocks or unit cells. Microstructures of these unit cells can be identical, whereas individual design of each cell and various combinations of unit cells definitely offer more freedoms and possibilities for combinatorial design of metamaterials. Unfortunately, this combinatorial design problem is prohibitively challenging, if not impossible, due mainly to its huge number of combinatorial cases. This paper poses and addresses the combinatorial optimization of a metabeam, aiming at maximizing its critical buckling load. The problem was conceptualized and solved by combination of ML accelerated surrogate modeling and optimization algorithm, and buckling and post-buckling performance of the optimal design was validated by high-fidelity simulations and experiments. The efforts provide efficient tools for combinatorial design of mechanical metamaterials. We publicly share all the data and codes for implementation. [ABSTRACT FROM AUTHOR]