Search of Binary Sequences with Low Aperiodic Autocorrelation Based on Improved Multi-Objective Genetic Algorithm

Binary sequences with low aperiodic autocorrelation are utilized across various domains, including cryptography, wireless communications, and radar engineering. Currently, the evaluation metrics for measuring binary sequence autocorrelation are peak sidelobe level (PSL) and merit factor (MF). The traditional binary sequence design problem usually adopts a mathematical derivation method based on finite domain theory and so on, but it becomes complicated when combining multiple evaluation metrics of sequence correlation for the study. This paper proposes an improved multi-objective genetic algorithm aimed at searching for binary sequence, which improves the standard algorithm's global search capability and convergence speed by introducing adaptive probability of crossover and mutation, along with utilization of population history information. The algorithm is utilized to search low correlation binary sequences of length 150–300, and the results obtained perform well on both PSL and ISL metrics. The proposed method demonstrates the excellent performance of the multi-objective genetic algorithm in sequence search, which is somewhat better than the binary sequence results obtained by existing single-objective optimization algorithms.