Search is a universal problem-solving method in Artificial Intelligence. Specifically, Heuristic Search algorithms, such as A*, use a heuristic function to guide the search process. The heuristic function allows algorithms to explore only a part of the search space, resulting in an efficient search process. This paper presents a new heuristic function to solve the Generalized Covering Traveling Salesman Problem (GCTSP). The heuristic function is precalculated. The method to obtain the function is pre-calculating optimal solutions consecutively to small sub-problems of the GCTSP of increasing difficulty, using an incremental Best First Search algorithm, which reuses heuristics values previously precalculated. The resultating heuristic function can be used with different heuristic search algorithms. To the best of our knowledge, this problem has not been solved with Heuristic Search. This paper is the first to present a solution to the GCTSP using Heuristic Search algorithms, such as A∗ and Anytime search algorithms. We evaluated different Heuristic Search algorithms. The experimental evaluation shows results of the same quality, obtained orders-of-magnitude faster than the exact methods traditionally used in Operations Research.