Finding low autocorrelation binary sequences with memetic algorithms

Abstract

This paper deals with the construction of binary sequences with low autocorrelation, a very hard problem with many practical applications. The paper analyzes several metaheuristic approaches to tackle this kind of sequences. More specifically, the paper provides an analysis of different local search strategies, used as standalone techniques and embedded within memetic algorithms. One of our proposals, namely a memetic algorithm endowed with a Tabu Search local searcher, performs at the state-of-the-art, as it consistently finds optimal sequences in considerably less time than previous approaches reported in the literature. Moreover, this algorithm is also able to provide new best-known solutions for large instances of the problem. In addition, a variant of this algorithm that explores only a promising subset of the whole search space (known as skew-symmetric sequences) is also analyzed. Experimental results show that this new algorithm provides new best-known solutions for very large instances of the problem.

Low-autocorrelation binary sequences: On improved merit factors and runtime predictions to achieve them

“…While branch and bound solvers, for both even and odd sequences [18] and for skew-symmetric sequences only [20] have been pursued, they do not scale as well as the stochastic solvers. Stochastic solvers cannot prove optimality, they can only be compared on the basis of the best-value solutions, and to a limited extent, also on the average runtime needed to find such solutions under a sufficiently large number of repeated trials [21,22,23,24,25,26,27,28,29,30]. The experimental results obtained with our stochastic solver lssOrel are compared to the instrumented versions of solvers in [30].…”

Fluttering Pattern Generation Using Modified Legendre Sequence for Coded Exposure Imaging

“…We used the code by the author 2 to generate the sequences for the method [19] as well as to deblur the images. The number of random Method TIME (seconds) Raskar et al [19] (N s =10 6 ) 268.06 Raskar et al [19] (N s =10 8 ) 26779.90 Proposed 0.21 Table 1: Average computational times for generating binary sequences. The computational time of the method [19] depends on the number of samples, while the proposed method requires much shorter time for all sequence lengths.…”

“…Instead, they rely on a randomized linear search that only considers min[log(|F(U )|)] in Eq. (6). To deal with this issue, we find a solution that would take both terms into account and return the maximum coded factor F C .…”

“…Finding binary sequences with low autocorrelation is a deeply studied problem in the field of information theory and physics because it relates to many applications in telecommunications (e.g., synchronization, pulse compression and, especially, radar), physics (e.g., Ising spin glasses) and chemistry [6]. Among many methods for generating the binary sequence, the Legendre sequence has shown some advantages over other methods, especially in terms of the computational time and the autocorrelation measure [9].…”

Improvement of Long Binary Sequence Merit Factors using Modified Legendre Algorithms

“…Stochastic methods were introduced to solve this problem [10] [12]. In the beginning, even these methods failed to produce proper outputs.…”