Abstract:

The shortcomings of the artificial bee colony algorithm (ABC) and its improved algorithm are analyzed. This paper proposes the improved Markov ABC (IMABC) dividing the ABC algorithm into two stages by verifying the Markov property of the artificial bee colony algorithm in the time dimension. In the first stage, this paper runs the ABC algorithm to obtain the initial solution space. In the second stage, this paper uses the Markov chain to reconstruct the solution space generated in the first stage and further predicts the new solution. The IMABC algorithm reduces the randomness of the artificial bee colony algorithm. At the same time, it avoids the premature algorithm caused by relying on a certain optimal value. The pseudo code of IMABC algorithm is given and its convergence complexity and optimization ability are also analyzed. The IMABC algorithm, GABC algorithm and ABC algorithm are run on 9 typical test functions to compare the convergence accuracy, convergence efficiency and running time of the algorithms. The conclusion shows that the IMABC algorithm is superior to the GABC algorithm and ABC algorithm. The influences of the segmentation parameters and solution space dimensions on the function optimization process are verified by comparison.

Key words: Markov chain, artificial bee colony algorithm (ABC), improved Markov ABC (IMABC) algorithm

摘要：

分析人工蜂群算法（ABC）及其改进算法的不足，通过验证人工蜂群算法解空间在时间维度上的马尔可夫性，提出将ABC算法分为两个阶段的improved Markov ABC（IMABC）算法。第一阶段运行ABC算法得出初始解空间，第二阶段利用马尔可夫链对第一阶段产生的解空间进行重构，并进一步预测新解。IMABC算法减少了人工蜂群算法的随机性，同时避免了因依赖某一最优值导致的算法早熟。给出了IMABC算法的伪代码，并对其收敛复杂度和寻优能力进行了分析。将IMABC算法、GABC算法和ABC算法在9个典型测试函数上运行，分别比较算法的收敛精度、收敛效率和运行时间，得出IMABC算法优于GABC算法和ABC算法的结论，并通过比较验证了分割参数和解空间维度对函数寻优过程的影响。

关键词: 马尔可夫链, 人工蜂群算法（ABC）, improved Markov ABC（IMABC）算法