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Salp swarm algorithm (SSA) is a unique swarm intelligent algorithm widely used for various practical applications due to its simple framework and good optimization performance. However, like other swarm-based algorithms, SSA yields local optimal solutions and has a slow convergence rate and low solution accuracy when dealing with high-dimensional global optimization problems. Based on quadratic interpolation and a local escape operator (LEO), a salp swarm optimization algorithm (QSSALEO) is proposed to address these issues. Quadratic interpolation around the best search agent aids QSSALEO's exploitation ability and solution accuracy, whereas the local escaping operator employs random operators to escape local optima. These tactics complement one another to help SSA promote convergence performance. Furthermore, the algorithm strives for a balance of exploitation and exploration. The proposed QSSALEO method was tested using the CEC 2017 benchmark with 50 and 100 decision variables, as well as seven CEC2008lsgo test functions with 200, 500, and 1000 decision variables, and its performance was compared to that of other metaheuristic algorithms and advanced algorithms, including seven salp swarm variants. The experimental results reveal that QSSALEO outperforms SSA and other population-based algorithms regarding convergence rate and solution correctness. The QSSALEO was then evaluated as a feature selection algorithm on 19 datasets (including three high-dimensional datasets). Friedman and Wilcoxon rank-sum statistical tests are also used to analyze the results. According to experimental data and statistical tests, the QSSALEO algorithm is very competitive and often superior to the algorithms employed in research. Therefore, the proposed method can also be considered a specialized large-scale global optimization optimizer whose performance surpasses state-of-the-art algorithms such as CMA-ES and SHADE. The algorithm source code is available at https://github.com/MohammedQaraad/An-Innovative-Quadratic-interpolation-Salp-Swarm. [ABSTRACT FROM AUTHOR]