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Inspired by the biological behavior of domestic cats, the Cat Swarm Optimization (CSO) is a metaheuristic which has been successfully applied to solve several optimization problems. For binary problems, the Boolean Binary Cat Swarm Optimization (BBCSO) presents consistent performance and differentiates itself from most of the other algorithms by not considering the agents as continuous vectors using transfer and discretization functions. In this paper, we present a simplified version of the BBCSO. This new version, named Simplified Binary CSO (SBCSO) which features a new position update rule for the tracing mode, demonstrates improved performance, and reduced computational cost when compared to previous CSO versions, including the BBCSO. Furthermore, the results of the experiments indicate that SBCSO can outperform other well-known algorithms such as the Improved Binary Fish School Search (IBFSS), the Binary Artificial Bee Colony (BABC), the Binary Genetic Algorithm (BGA), and the Modified Binary Particle Swarm Optimization (MBPSO) in several instances of the One Max, 0/1 Knapsack, Multiple 0/1 Knapsack, SubsetSum problem besides Feature Selection problems for eight datasets.