Permanent residents are free to travel outside the United States; temporary travel, depending on its duration, does not affect permanent immigration status.
The purpose and duration of your foreign trips determines whether you have abandoned your status or done anything that shows intention for you to abandon your permanent status.
If you would like to maintain your permanent status, you have to prove intention to return back to the United States. You can do so by proof that you have maintained US employment, maintained family ties, filed US taxes as a resident, or proved you plan on returning to the United States in another legitimate manner.
Other factors that may be considered include whether you maintained a U.S. mailing address, kept U.S. bank accounts and a valid U.S. driver’s license, own property or run a business in the United States, or any other evidence that supports the temporary nature of your absence.