Creating a strategy game AI without writing a board evaluation function?

I've recreated a favorite obscure two player board game of mine, where the board is divided into cells and pieces move across these cells (like chess, checkers, etc...)

I want to try and create an AI that will be able to play the game - but I want to avoid writing the board evaluation function myself (for a minmax algorithm). Are there any general good ways to achieve that?

From the little research I've done, I found out about genetic algorithms - and they seem like they would fit but I can't fathom how would one create a dna schema that describes a board evaluation function