Improved Artificial Bee Colony Optimization Underwater Localization Algorithm by Logistic Chaos Mapping and Differential Evolution - Jiaxing CHEN; Yang LIU; Xiaoqian LIU; Zhihua LIU (工程科学与技术)
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 multiple 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 mechanism observed in honey bees. It is relatively straightforward to implement and comprises four phases: population initialization, leading bee, following bee, and detecting bee. The artificial bee colony algorithm offers a novel approach to improving the accuracy of underwater node localization. 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 tendency 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 developed 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 initialization 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 falling 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 local optima problem during the iterative process. This further demonstrated the effectiveness of introducing the logistic chaotic mapping strategy into the population initialization phase. Subsequently, in the leading bee phase, a weight factor was incorporated as a parameter based on the variation 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 implications of adjusting the weight factor for the leading bee during the initial and final stages of the optimization process were thoroughly examined. 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 algorithm 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 localization 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 impressvie 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 application in optimizing parameters and model structures within underwater localization systems.