There is NoRel (or No Relaxation) heuristic in the Gurobi solver which helps to find very good feasible solutions for Mixed Integer Programs. I couldn't find explanation of its idea. Perhaps anybody knows the details? Or it is a commercial secret and there is no paper describing it? I found out some information here: https://support.gurobi.com/hc/en-us/community/posts/9341291193745-NoRel-heuristics-is-this-adding-valid-inequalities-, but it is not sufficient.
You can also read this one, might help you.