Topology optimization has been widely used in industrial designs. One problem related to topology optimization is that the uncertain elements may result when gradient-based search methods are used. Although using binary coding genetic algorithms (GA) can avoid the problem, the problems of structural connectivity and computational cost are the obstacles to be solved. Two novel approaches are proposed in this research to solve these GA-related problems. To ensure the integrity of the topology generated, a weak ground structure is built in the entire design space to play the role of connecting the disconnected material distributed by GA. To reduce the computational cost, a method of reducing the design space by using the result obtained by gradient-based search methods is proposed. A design example shows that applying these two proposed approaches can effectively overcome the problems associated with GA to solve topology optimization problems.