水下节点定位时通常采用距离估算法，在节点之间利用点到点的距离来估计或基于角度估计来完成节点定位。然而，这种算法存在较大的定位误差。为了提升定位的精确度，引入了人工蜂群(ABC)优化算法，该算法通过将节点定位结果优化问题转化为对节点目标函数的优化问题，有效地提高了水下节点的定位精度。尽管如此，ABC算法在迭代过程中仍存在收敛速度慢、易陷入局部最优的问题。针对这些问题，提出了一种通过Logist-ic混沌映射与差分进化改进的人工蜂群优化水下定位算法(improved artificial bee colony optimization underwater localization algorithm by Logistic chaos mapping and differential evolution，LDIABC)。首先，在算法种群初始化阶段，引入了Logistic混沌映射，利用该映射函数产生的混沌序列代替随机数生成器，从而使种群在初始化分布时蜜源位置更均匀，并从理论上证明了Logistic混沌序列的互异性，从而避免由于种群分布过于密集导致算法在迭代过程中陷入局部最优;其次，提出了适应度方差这一标准来验证在算法迭代过程中未陷入局部最优，进一步证明其有效性;然后，在引领蜂搜索阶段，基于差分进化的变异策略，提出了权重因子改进引领蜂邻域搜索方式，提高了引领蜂的全局搜索效率，加快了算法的收敛速度。仿真实验表明，LDIABC算法能够有效避免传统ABC算法收敛速度慢和易陷入局部最优的问题。相较于Tent-IABC算法、ELOABC算法、CODEGWO算法以及SAPSO算法，LDIABC算法在收敛速度和节点定位成功率上均有显著提升，并且优化定位精度分别提升了6。36%、13。33%、14。16%和16。88%。这些结果证明LDIABC算法能够有效提升水下节点定位精度，具有良好的优化效果。
Improved Artificial Bee Colony Optimization Underwater Localization Algorithm by Logistic Chaos Mapping and Differential Evolution
Objective Localization algorithms for underwater acoustic sensor networks typically depend on distance estimation methods,such as point-to-point distance estimation or angle estimation,to achieve node localization between nodes.However,techniques like least squares may yield mul-tiple coordinate values,leading to significant inaccuracies in node localization.To address this issue,it is essential to implement an optimization algorithm that can provide the optimal result,thereby enhancing the accuracy of node localization.Methods The artificial bee colony algorithm represents a category of intelligent optimization algorithm that imitates the honey harvesting mech-anism observed in honey bees.It is relatively straightforward to implement and comprises four phases:population initialization,leading bee,fol-lowing bee,and detecting bee.The artificial bee colony algorithm offers a novel approach to improving the accuracy of underwater node localiza-tion.This is achieved by transforming the optimization problem of node localization results into an optimization problem for the node objective function.However,the traditional artificial bee colony algorithm exhibited significant deficiencies,namely a slow convergence speed and a tend-ency to converge on local optima during the iterative process.To address these issues,the improved artificial bee colony optimization underwater localization algorithm by logistic chaos mapping and differential evolution(LDIABC),was proposed.This new algorithmic approach was de-veloped with a particular focus on the population initialization phase and the leading bee search phase.Firstly,in order to address the issue of the traditional artificial bee colony algorithm being susceptible to falling into local optima due to excessive concentration or dispersion in the initializ-ation of the population distribution,it was proposed to introduce logistic chaotic mapping into the population initialization phase of the proposed algorithm.The chaotic sequence generated by the mapping function was employed as a replacement for the random number generator,with the objective of achieving a more uniform distribution of the population during the initial distribution phase.Moreover,the discrepancy between the chaotic sequences generated by logistic chaotic mapping was demonstrated theoretically.Consequently,the proposed algorithm could avoid fall-ing into local optima during the iterative process due to an overly concentrated population distribution,thus enhancing the global search ability of the proposed algorithm.Secondly,a fitness variance criterion was proposed to verify that the proposed algorithm was capable of avoiding the loc-al optima problem during the iterative process.This further demonstrated the effectiveness of introducing the logistic chaotic mapping strategy in-to the population initialization phase.Subsequently,in the leading bee phase,a weight factor was incorporated as a parameter based on the vari-ation strategy of the differential evolution,thereby improving the lead bee neighborhood search mode in the initial and final stages of the leading bee.By modifying the search mode in the initial and final stages of the leading bee,the leading bee was directed toward the optimal solution,thereby enhancing the global search efficiency of the leading bee and accelerating the convergence of the proposed algorithm.The theoretical im-plications of adjusting the weight factor for the leading bee during the initial and final stages of the optimization process were thoroughly ex-amined.Finally,simulation experiments of the proposed algorithm and the comparison algorithm were carried out using the MATLAB software,employing identical simulation settings and datasets to evaluate the performance of the proposed LDIABC algorithm against its counterparts.Results and Discussions It was demonstrated that the LDIABC algorithm significantly improved the convergence speed and avoid falling into the local optima during the iterative process,thereby substantially enhancing the accuracy of node localization.In terms of convergence speed,the al-gorithm achieved convergence with 300 iterations,whereas the competing algorithm requires superior approximately 400 iterations to stabilize.Consequently,the LDIABC algorithm demonstrated superior convergence rates compared to the Tent-IABC,ELOABC,CODEGWO and SAPSO algorithms.Once the algorithms had reached a state of stability,the average localization error of the LDIABC algorithm was also the lowest,which indicated that the LDIABC algorithm effectively solved the issues present in the traditional artificial bee colony algorithm.In terms of the success rate of node localization,the LDIABC algorithm exhibits a higher success rate than the Tent-IABC,ELOABC,CODEGWO and SAPSO algorithms,with a success rate of up to 95%.In comparison,the four aforementioned algorithms demonstrated a success rate of between 80%and 86%.This indicated that the LDIABC algorithm increased the number of nodes with improved localization accuracy.In terms of optimized local-ization accuracy,the LDIABC algorithm demonstrated enhanced performance in comparison to the Tent-IABC,ELOABC,CODEGWO and SAPSO algorithms,with improvements of 6.36%,13.33%,14.16%and 16.88%,respectively.Moreover,in terms of maximum and average error,the LDIABC algorithm exhibited a lower localization error than the other algorithms,indicating an effective optimization effect.Conclusions The LDIABC algorithm has proven effective in improving convergence speed and preventing the process from becoming trapped in local optima during iterations.Consequently,this algorithm significantly enhances the accuracy of underwater node localization,resulting in im-pressvie optimization outcomes.By improving and enhancing the artificial bee colony algorithm and other intelligent optimization algorithms,it is possible to further optimize the results of node localization,thereby increasing the accuracy of node positioning and enhancing the value of the collected data.Furthermore,this development has advanced other intelligent optimization algorithms,allowing for deeper integration and applica-tion in optimizing parameters and model structures within underwater localization systems.
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