In this paper, several design methods of CSD (Canonic Signed Digit) coefficient FIR (Finite Impulse Response) filters are compared to investigate a search process of each method. The design problem is formulated as a combinatorial optimization problem. Because it requires high computation time to obtain the optimal solution, many design methods using metaheuristic approaches have been proposed. In this study, the search process of design methods are verified. As a result, the differences between the design methods are clarified and thus it is expected that some cues for improving the performance can be attained.