Sears, Roebuck & Co. agreed to sell its Western Auto Supply car-parts chain to Advance Auto Parts for $175 million and a 40% stake in the closely held retailer. Advance, based in Roanoke, Va., operates 915 stores in 17 states. It had fiscal 1997 sales of $848.1 million. The purchase will put Advance, which operates in the Southeast, in markets in the Northeast, Midwest and Southwest. Western Auto, based in Hoffman Estates, Ill., operates 630 stores in 19 states and Puerto Rico, and had 1997 sales of $1.3 billion. The combined company will operate most stores under the Advance name. The sale is expected to close by year-end. The sale is part of a move by Sears, the nation's largest department store chain, to cut back on its specialty stores. Sears said last month that it may sell its HomeLife furniture stores. Investors in Advance, including an investment fund organized by Freeman Spogli & Co., will put an additional $70 million in Advance. Shares in Sears, which announced the agreement after the close of trading, rose 81 cents to close at $49.06 on the New York Stock Exchange.