NEW YORK — Shares of Herbalife surged more than 11 percent Friday after disclosing that it’s in advanced talks to settle a federal investigation into claims that the company essentially operates as a pyramid scheme.

It’s a claim that has dogged the company for years and set off what has become an epic battle with activist investor Bill Ackman, who has been waging a campaign against Herbalife since late 2012.

Herbalife, which sells supplements and weight-loss products, said in a regulatory filing that the possible settlement ‘‘would likely include a monetary payment and injunctive and other relief.’’

ASSOCIATED PRESS