The metaheuristic approaches inspired by the nature are becoming powerful optimizing algorithms for solving NP-complete problems. This paper presents five nature-inspired metaheuristic optimization algorithms to find near-optimal Golomb ruler (OGR) sequences in a reasonable time. In order to improve the search space and further improve the convergence speed and optimization precision of the metaheuristic algorithms, the improved algorithms based on mutation strategy and Lévy-flight search distribution are proposed. These two strategies help the metaheuristic algorithms to jump out of the local optimum, improve the global search ability so as to maintain the good population diversity. The OGRs found their potential application in channel-allocation method to suppress the four-wave mixing crosstalk in optical wavelength division multiplexing systems. The results conclude that the proposed algorithms are superior to the existing conventional computing algorithms i.e. extended quadratic congruence and search algorithm and nature-inspired optimization algorithms i.e. genetic algorithms, biogeography based optimization and simple big bang–big crunch to find near-OGRs in terms of ruler length, total optical channel bandwidth and computation time. The idea of computational complexity for the proposed algorithms is represented through the Big O notation. In order to validate the proposed algorithms, the non-parametric statistical Wilcoxon analysis is being considered.

中文翻译：

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为 WDM 系统寻找近 OGR 的五种元启发式自然启发算法的性能比较

受自然启发的元启发式方法正在成为解决 NP 完全问题的强大优化算法。本文提出了五种受自然启发的元启发式优化算法，以在合理的时间内找到接近最优的哥伦布标尺 (OGR) 序列。为了改善搜索空间，进一步提高元启发式算法的收敛速度和优化精度，提出了基于变异策略和Lévy-flight搜索分布的改进算法。这两种策略有助于元启发式算法跳出局部最优，提高全局搜索能力，从而保持良好的种群多样性。OGR 发现它们在信道分配方法中的潜在应用，以抑制光波分复用系统中的四波混合串扰。结果表明，所提出的算法优于现有的传统计算算法，即扩展二次同余和搜索算法以及自然启发的优化算法，即遗传算法、基于生物地理学的优化和简单的 big bang-big crunch 以在以下方面找到近 OGR。标尺长度、总光通道带宽和计算时间。所提出算法的计算复杂性的想法通过大 O 符号表示。为了验证所提出的算法，正在考虑非参数统计 Wilcoxon 分析。遗传算法、基于生物地理学的优化和简单的 big bang-big crunch 在标尺长度、总光通道带宽和计算时间方面找到近 OGR。所提出算法的计算复杂性的想法通过大 O 符号表示。为了验证所提出的算法，正在考虑非参数统计 Wilcoxon 分析。遗传算法、基于生物地理学的优化和简单的 big bang-big crunch 在标尺长度、总光通道带宽和计算时间方面找到近 OGR。所提出算法的计算复杂性的想法通过大 O 符号表示。为了验证所提出的算法，正在考虑非参数统计 Wilcoxon 分析。