When Yosef came out of prison, he became the ruler of Egypt, and he was very rich for 9 years, so why did he not search for his family from the very moment he came out of prison?

This is one of the great questions of Chumash Bereshit, and several answers have been offered. I believe the best approach is that Yosef realized that if he told his father, he would have to tell of his brothers' deed, and that would have destroyed the relations within the family. Yosef knew that he first had to redeem his brothers by proving their loyalty to Binyamin, and that although this prolonged Yaakov's suffering, it was the only reasonable alternative.