Abstract:

In order to overcome the shortcomings which the search efficiency of the bat algorithm is lowing and it is easy to fall into local optimum in solving multimodal and complex nonlinear problems, an improved bat algorithm is proposed in this paper. The fractional order strategy with short-term memory characteristics is introduced to update bat position so as to increase population diversity and improve the convergence speed of the algorithm. A new solution is generated locally by the Archimedes spiral with Lévy flight strategy, which enhances the local exploitation ability and helps the algorithm jump out of the local optimum. The new nonlinear dynamic mechanism for adjusting loudness and pulse emission rate is to balance the exploration and exploitation abilities of the algorithm. The CEC2014 benchmark functions including unimodal, multimodal, hybrid and composition functions is selected to test the proposed algorithm and other swarm intelligence algorithms. The results show that the search efficiency and solution accuracy of the proposed algorithm are obviously improved compared with contrast algorithms. The superiority of the algorithm is verified by Friedman statistical analysis. Finally, the proposed algorithm is used to solve the design problem of mechanical engineering reducer. The experiment results verify the effectiveness of the proposed algorithm compared with PSO-DE, WCA, and APSO.

Key words: bat algorithm, fractional order, Archimedes spiral, Lévy flight, speed reducer design problem

摘要：

针对蝙蝠算法在求解多峰、复杂非线性问题时，搜索效率降低、易陷入局部最优等不足，提出了一种改进的蝙蝠算法。引入具有短期记忆特性的分数阶策略来更新蝙蝠位置，增加种群多样性，提高了算法收敛速度；用带有Lévy飞行的阿基米德螺旋策略产生局部新解，增强局部开发能力，同时有助于算法跳出局部最优；采用新的非线性动态机制调节响度和脉冲发射率，以平衡算法的探索和开发。选取CEC2014测试集，包括单峰、多峰、混合以及复合函数，对提出的算法和其他群智能算法进行仿真实验，测试结果表明提出的算法搜索效率和求解精度相较于对比算法得到提升，用Friedman统计分析验证了算法的优越性。将提出的算法用于求解机械工程减速器设计问题，与PSO-DE、WCA、APSO进行实验对比，验证该算法的有效性。

关键词: 蝙蝠算法, 分数阶, 阿基米德螺旋, Lé, vy飞行, 减速器设计问题