A Cuckoo Search Algorithm Using Improved Beta Distributing and Its Application in the Process of EDM

• Main Authors: Dili Shen, Wuyi Ming, Xinggui Ren, Zhuobin Xie, Yong Zhang, Xuewen Liu
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Crystals
• Subjects: cuckoo search algorithm; self-adaption; beta distribution; dynamic step-size control factor; EDM
• Online Access: https://www.mdpi.com/2073-4352/11/8/916

Lévy flights random walk is one of key parts in the cuckoo search (CS) algorithm to update individuals. The standard CS algorithm adopts the constant scale factor for this random walk. This paper proposed an improved beta distribution cuckoo search (IBCS) for this factor in the CS algorithm. In terms of local characteristics, the proposed algorithm makes the scale factor of the step size in Lévy flights showing beta distribution in the evolutionary process. In terms of the overall situation, the scale factor shows the exponential decay trend in the process. The proposed algorithm makes full use of the advantages of the two improvement strategies. The test results show that the proposed strategy is better than the standard CS algorithm or others improved by a single improvement strategy, such as improved CS (ICS) and beta distribution CS (BCS). For the six benchmark test functions of 30 dimensions, the average rankings of the CS, ICS, BCS, and IBCS algorithms are 3.67, 2.67, 1.5, and 1.17, respectively. For the six benchmark test functions of 50 dimensions, moreover, the average rankings of the CS, ICS, BCS, and IBCS algorithms are 2.83, 2.5, 1.67, and 1.0, respectively. Confirmed by our case study, the performance of the ABCS algorithm was better than that of standard CS, ICS or BCS algorithms in the process of EDM. For example, under the single-objective optimization convergence of <i>MRR</i>, the iteration number (13 iterations) of the CS algorithm for the input process parameters, such as discharge current, pulse-on time, pulse-off time, and servo voltage, was twice that (6 iterations) of the IBCS algorithm. Similar, the iteration number (17 iterations) of BCS algorithm for these parameters was twice that (8 iterations) of the IBCS algorithm under the single-objective optimization convergence of Ra. Therefore, it strengthens the CS algorithm’s accuracy and convergence speed.