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This paper presents the application of the one new approach using Genetic Algorithm in solving One-Dimensional Cutting Stock Problems in order to minimize two objectives, usually conflicting, i.e., the number of processed objects and setup while simultaneously treating them as a single goal. The model problem, the objective function, the method denominated SingleGA10 and the steps used to solve the problem are also presented. The obtained results of the SingleGA10 are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio10, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that the proposed method, which only uses a genetic algorithm to solve these two objectives inversely related, provides good results.