Robot: Line follower - Obstacle avoidance - High Speed

How does a robot follow a line and at the same time avoid obstacles?
Johan_Ha suggests on solution. Rotate 90 degrees, drive circle.
But I think that this is problematic. You are hoping that you will encounter a line. And you are hoping that you will follow the line in the proper direction.

Problem: How can I make my robot Faster?

You want it to complete the task faster. Does that mean that you have built the robot and it is able to complete the task now? That would be important for us to know. Because ANY suggestions to make it faster are worthless if you cannot complete the task at all.

What have you accomplished so far?