Orlando's brother Oliver is forced to go to the Forest of Arden in search of his brother Orlando because Duke Frederick believes Orlando can tell him where to find his daughter Celia. The secondary source of the rumor that Orlando may be in the company of Rosalind, Celia and Touchstone is a minor character called SECOND LORD. He got the rumor from a character named Hesperia, the primary source of the rumor, who does not appear in the play. She is called "the princess' gentlewoman. The following passage from Act 2, Scene 2 gives all the pertinent information.
My lord, the roynish clown, at whom so oft
Your grace was wont to laugh, is also missing.
Hesperia, the princess' gentlewoman,
Confesses that she secretly o'erheard
Your daughter and her cousin much commend
The parts and graces of the wrestler
That did but lately foil the sinewy Charles;
And she believes, wherever they are gone,
That youth is surely in their company.
Orlando, of course is the wrestler who defeats the professional wrestler, "the sinewy Charles," in Act 1, Scene 2. The Second Lord does not say that Touchstone is with Celia and Rosalind but seems to be suggesting that that is the case. Hesperia is not correct in believing that Orlando is with Celia and Rosalind. Orlando has not yet met Rosalind, and when he does meet her he will think she is a young male named Ganymede. However, this information from Hesperia via the Second Lord is sufficient to have Duke Frederick send Oliver off in search of Orlando in Act 3, Scene 1. He tells Oliver:
Find out thy brother, wheresoe'er he is;
Seek him with candle; bring him dead or living,
Within the twelvemonth, or turn thou no more
To seek a living in our territory.
The Duke's only motive is to find his daughter Celia, but he thinks his best chance of finding her is through finding Orlando and forcing him to lead his officers to Celia, who is undoubtedly with Rosalind. It seems probable that the best place to search will be in the Forest of Arden, since Rosalind's father, called Duke Senior, is known to be living there with his followers. Rosalind has to leave because Duke Frederick banished her. She would naturally go to seek her father, and Celia would go with Rosalind because it has been established that the two girls are inseparable.
In Act 1, Scene 1, Oliver and Charles have a conversation during which Oliver asks about Rosalind's father, whom he calls "the old duke." Charles tells him:
They say he is already in the Forest of Arden, and a many merry men with him; and there they live like the old Robin Hood of England. They say many young gentlemen flock to him every day, and fleet the time carelessly as they did in the golden world.
Oliver goes to the Forest of Arden in search of his brother Orlando because, like Duke Frederick, he thinks Orlando is with Rosalind and he thinks Rosalind, accompanied by Celia, would have gone to find her father Duke Senior. Also, the Forest of Arden appears to be a place where young gentlemen are flocking to join Duke Senior every day. These young gentlemen would probably be younger sons, like Orlando, who did not inherit land because of the law of primogeniture.