New evolutionary search for long low autocorrelation binary sequences


Binary sequences with low aperiodic autocorrelation levels, outlined in terms of the peak sidelobe level (PSL) and/or merit issue, have many important engineering applications, such as radars, sonars, unfold spectrum communications, system identification, and cryptography. Searching for low autocorrelation binary sequences (LABS) may be a notorious combinatorial downside, and has been chosen to form a benchmark test for constraint solvers. Thanks to its prohibitively high complexity, an exhaustive search solution is impractical, except for comparatively short lengths. Many suboptimal algorithms have been introduced to extend the LABS explore for lengths of up to a few hundred. In this paper, we address the challenge of discovering even longer LABS by proposing an evolutionary algorithm (EA) with a new combination of several options, borrowed from genetic algorithms, evolutionary strategies (ES), and memetic algorithms. The proposed algorithm can efficiently discover long LABS of lengths up to several thousand. Record-breaking minimum peak sidelobe results of many lengths up to 4096 have been tabulated for benchmarking functions. As well, our algorithm style will be easily custom-made to tackle varied extensions of the LABS problem, say, with a generic sidelobe criterion and/or for probably nonbinary sequences.

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