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On moral grounds, adopted children must honor their adoptive parents in the same way as biological children. The Sages speak at length about the rewards of people who take in abandoned children. They tell us that in the World to Come, God has treasure houses to reward the righteous, including a special treasure house to reward those who bring up such children.
Adopted children are exempt from honoring their biological parents. When the parents gave their children up for adoption, they also waived their rights to honor. (In general, Jewish law says that if parents choose to relinquish the honor due them, they may do so.) So, the children have no obligation to search for them or to honor them. Nevertheless, it is often a good idea for them to do so. First, if their parents gave them up when things were very difficult, they might regret having done so, and long for a connection with their children. Second, if the adopted children do not identify their parents, they could end up marrying a prohibited relative, such as a sibling. Third, even though there is no obligation to honor the biological parents, it is still the fulfillment of the mitzva.
However, if the adoptive parents would find it extremely painful for their children to undertake a search for their biological parents, it is preferable the children do not search. After all, adopted children are obligated to honor their adoptive parents and not their biological ones. Similarly, if finding their birth parents might lead the children to experience a psychological crisis, it is better they do not search. Adopted children who are uncertain about what to do should consult with someone who is wise, experienced, and God-fearing, and who knows them well.
