Why would the engine misfire when headlights are turned on Cadillac?

I dont own Cadillac but 1 reason possible is weak/poor alternator. I have the same problem but now solved by changing the alternator(AC electrical generator).The headlight aswell as the fuel pump consumes power generated by the alternator as the battery alone cannnot provide sufficient power.As the fuel pump does not get enough power , it cannot properly function to transmit enough fuel needed by the engine.This causes the engine to misfire.Another cause could be bad battery connection.Make sure they are clean and free of carbon.