The one dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which arises in many industries. As the setup costs of cutting patterns become more dominant in recent cutting industry, we consider a variant of 1D-CSP, in which the total number of applications of cutting patterns is minimized under the constraint that the number of different cutting patterns is specified in advance. We propose a local search algorithm that uses the neighborhood obtained by perturbating one cutting pattern in the current set of patterns, where the perturbations are done by utilizing the dual solution of the auxiliary linear programming problem (LP). In this process, in order to solve a large number of LPs, we start the criss-cross variation of the simplex algorithm from the optimal simplex tableau of the previous solution, instead of starting it from scratch. According to our computational experiment, it is observed that the proposed algorithm obtains a wide variety of good solutions which are comparable to the existing heuristic approaches.