The competition features all 48 clubs from League One and League Two, alongside the Under-21 sides of 16 Premier League clubs.
The 64 teams are split into 16 groups of four, with each group containing three EFL clubs and one Premier League academy. Alongside Swindon, Palace will face Plymouth Argyle and Newport County in this season’s group stage.
As a Premier League academy, all three of Palace’s group fixtures are played away from home.
Following the trip to Swindon, the Young Eagles will visit Plymouth Argyle at Home Park on Tuesday, 22nd September (19:00 BST), before travelling to Newport County’s Rodney Parade on Tuesday, 3rd November (19:00 BST).
Three points are awarded for a win, with one point each awarded if a game finishes level after 90 minutes. A penalty shoot-out then determines who claims a bonus second point.
The top two sides in each group progress to the round of 32, with group winners seeded and guaranteed home advantage against a group runner-up in the first knockout round.
From there, the competition becomes a straight knockout, with regionalised draws separating the northern and southern sections through to the semi-finals.
The final will be held at Wembley Stadium on Sunday, 11th April.