Gaussian mutational chaotic fruit fly-built optimization and feature selection

https://doi.org/10.1016/j.eswa.2019.112976Get rights and content

Highlights

  • Gaussian mutation operator was introduced into FOA to avoid the premature convergence.

  • Chaotic local search method was adopted for enhancing the local search ability of FOA.

  • Extensive benchmark problems were used to verify the method.

Abstract

To cope with the potential shortcomings of classical fruit fly optimization algorithm (FOA), a new version of FOA with Gaussian mutation operator and the chaotic local search strategy (MCFOA) is proposed in this research. First, the Gaussian mutation operator is introduced into the basic FOA to avoid premature convergence and improve the exploitative tendencies in the algorithm (MFOA). Then, chaotic local search method is adopted for enhancing the local searching ability of the swarm of agents (CFOA). To substantiate the efficiency of three proposed methods, a comprehensive comparison has been completed using 23 benchmark functions with different characteristics. The best version of FOA among them is the MCFOA, which is extensively compared with the notable swarm-intelligence algorithms like bat algorithm (BA), particle swarm optimization algorithm (PSO), and several advanced FOA-based methods such as chaotic FOA (CIFOA), improved FOA (IFOA), multi-swarm FOA (swarm_MFOA) and differential evolution based FOA (DFOA). Numerical results show that two embedded strategies will effectively boost the performance of FOA for optimization tasks. In addition, MCFOA is also applied to feature selection problems. The results also prove that MCFOA can obtain the optimal classification accuracy.

Introduction

FOA (Pan, 2012) is a recently established algorithm among the swarm intelligence community. As a well-known meta-heuristic algorithm, FOA has been extensively studied in previous works due to its satisfactory performance. FOA is relatively stable and efficient compared to traditional methods; it also available publicly in a variety of programming languages. Therefore, FOA has been applied to many engineering practical problems (Darvish & Ebrahimzadeh, 2018; Han, Pan, Zhou & Liu, 2018; Kanarachos, Dizqah, Chrysakis & Fitzpatrick, 2018; Liu et al., 2017; Mousavi, Tavana, Alikar & Zandieh, 2017; Pan, Zhu, Ma, Zhong & Yuan, 2017; Rahman & Zhang, 2019; Wang & Zheng, 2018; Zheng & Wang, 2018). For instance, Wang, Yin, Zhou, Shen and Wang (2018) proposed a novel algorithm to reduce computer consumption, which was based on a geometric reasoning approach and FOA. The results of the experiments indicated that the proposed algorithm can perform well in declining of the expenditure and the time of casting production cycle. In order to solve the accurate electricity consumption forecasting task, Wang, Lv and Zeng (2018) employed the FOA to select input variables for a novel sparse Adaboost framework. The test results demonstrated that the algorithm mentioned above was able to forecast the industrial electricity consumption.

For some complicated problems, drawbacks of slow convergence rate and limited exploratory abilities will entrap the basic FOA into local extremes. Hence, researchers have proposed some alternative searching strategies for FOA. For instance, Zhang et al. (2017) proposed an optimal deployment methodology for 3D Underwater sensor network, which was based on an enhanced FOA. Furthermore, it was found that the optimal deployment methodology can significantly improve the network's convergence speed compared with the widely studied particle swarm optimizer (PSO) and a developed self-adaptive PSO. In the same year, Yang, Liu and Liu (2017) developed an enhanced technique by combining FOA and the simulated annealing (SA) algorithm. The simulation outcomes showed that the convergence curve of the discussed methodology was better than that of the classical FOA.

A new support vector machine (SVM) model, which feature subset and optima parameters were identified simultaneously by an improved chaotic FOA was developed by Ye, Lou and Sun (2017). The outcomes confirmed that the enhanced model could produce more effective results than other peers. In order to make FOA perform better, an enhanced FOA combining the normal cloud learning (BCMFOA) was developed (Wu, Zuo, Zhang & Liu, 2017). The results demonstrated that the BCMFOA could significantly boost the convergence rate of the basic FOA. In 2018, Zhang, Lu, Jia and Li (2018) have developed a new version of FOA to deal with the path planning task of unmanned aerial vehicles (UAVs). Babalık, İşcan, Babaoğlu and Gündüz (2018) used the FOA with two sign parameters to solve continuous optimization tasks. They concluded that the proposed approach can obviously stimulate the performance of FOA. To make the wind farm cluster more efficient, a modified FOA combined with probabilistic sensitivity indices was developed by Zhang, Shi, Huang, Qiu and Yang (2018) to optimize and coordinate the damping controller parameters of the static VAR compensator. Wu, Liu, Tian, Zhang and Xiao (2018) proposed a better algorithm called IAFOA based on basic FOA. The performance of the developed IAFOA was tested using 29 benchmark tasks. Han, Liu, Wang and Wang (2018) put forward a new FOA with the mechanisms of the co-evolution and the trend search to solve the problems of clustering parameter and continuous function optimization. The results exposed that the proposed FOA-based algorithm had a higher convergence speed and precision than other advanced meta-heuristic algorithms. The mechanisms of logistic chaos mapping were introduced into an improved FOA to solve the problems of constrained engineering design and benchmark function optimization (Du, Ke, Liao & Shen, 2018). The simulation results indicated that the developed model can be better than various deterministic methods such as meta-heuristic methods and basic FOA. Li, Sun, Li and Piao (2018) developed an improved approach, which was adding the cat mapping to improve the distribution of the individuals in original FOA. The results of the experiments indicated that the optimization performance of the mentioned model was superior to that of the other peers.

As mentioned above, although many scholars have done valuable research on improving the conventional FOA, their proposed improved FOA has some specific limits on certain aspects. In the field of feature selection, the traditional FOA converges bit by bit and is prone to fall into the local optimum solution. Its exploratory and exploitative trends have a limited capacity and in time of transition from first to second phase, there is a delay, which make the performance out of balance. Therefore, the performance of selecting key features is restricted, and it is challenging to recognize relatively essential features. To alleviate this problem, in this study, we propose to combine the MCFOA with Gaussian mutation and chaotic local search to have a better balance not only for function optimization but also for binary problems such as feature selection. We carefully designed the enhanced version to mitigate the performance bias of the initial method using a fit combination of operations. Considering the evolutionary impacts of these operations, the resulted searching process maybe biased to local optima again as a conflicting evolutionary effect. The innovation of MCFOA method lies in the stable fusion of the two mechanisms so that there is not only no mutual restriction between the phases but also mutual promotion and complementarity. Among them, Gaussian mutation is utilized to enhance the diversity of the population and improve the convergence efficiency of the algorithm in the early stages, and deepen the ability of method to avoid local optimum. From other side, the chaotic exploitative core makes the algorithm more intensive at the last stages. This amendment improves the accuracy of the solution in the later steps of search. At the same time, the optimization mechanism applied in this article is also different from the-state-of-art methods. Zhang, Cui, Wu, Pan and He (2016) divided the swarm into several sub-groups and calculated the average fitness value of each sub-group as a parameter of Gauss distribution. In this paper, the standard normal distribution of each individual is carried out, and the fitness value of each individual does not need to be employed in the process of position variation. Mitić, Vuković, Petrović and Miljković (2015) used chaotic method based on Chebyshev map in the algorithm. However, this paper uses Logistic map, which is more suitable for feature selection cases. The experimental results also reveal that the proposed MCFOA has better performance than other algorithms in feature selection.

Also, the performance of the developed MCFOA was assessed and compared with various traditional algorithms and several advanced FOA-based methods on 23 classical benchmark tasks. As shown in the experimental results, MCFOA can perform much better with two embedded mechanisms.

The remainder of this paper is structured as follows. A brief description of FOA is described in Section 2. The enhanced MCFOA is introduced in Section 3. The results of the experiments and discussions are introduced in Section 4. Finally, conclusions and future works are expressed in Section 5.

Section snippets

An overview of FOA

Initially, Pan (2012) introduced the FOA, which imitated fruit flies' prey behavior for realzing the optimal solutions to optimization problems. Fruit flies have certain advantages in olfactory and visual senses over other species. During the process of food-seeking, fruit flies look for possible food sources by collecting different odors in the air. Then, the swarm gradually approaches the location of the optimal odor concentration. Then, they can orientate the exact location of the food

Proposed MCFOA strategy

In this paper, we harmonize the core exploratory and exploitative drifts of FOA by implementing Gaussian mutation operator, and the chaotic local search mechanism. The Gaussian mutation operator can boost the population variety of FOA, while the chaotic local search mechanism encouraged the algorithm to exploit the locality of potential regions, effectively.

Benchmark function verification

For validating the effectiveness of the MCFOA in this paper, twenty-three typical benchmark functions are introduced for testing, as shown in Table 1, Table 2, Table 3, which are unimodal, multimodal, and fixed-dimension multimodal functions, respectively. In these tables, the corresponding formulas and descriptions of these functions are listed separately. Here, Dim represents the dimension of tasks, fmin represents the optimal solution and Range represents the function boundary of the search

Conclusions and future works

A novel FOA-based method was presented in this work that utilizes the Gaussian mutation mechanism and chaotic local search. In this algorithm, a better harmony among diversification and intensification is achieved and immature convergence is mitigated. From the initial state, the Gaussian mutation mechanism is fully applied to the agents of the population to maintain their diversity and increase the convergence trends of the algorithm. Also, the chaotic local search mechanism is exploited for

CRediT authorship contribution statement

Xiang Zhang: Conceptualization, Methodology, Software, Writing - original draft, Investigation, Writing - review & editing. Yueting Xu: Writing - original draft, Writing - review & editing, Software, Visualization, Investigation. Caiyang Yu: Writing - original draft, Writing - review & editing, Software, Visualization, Investigation. Ali Asghar Heidari: Writing - review & editing, Software, Visualization. Shimin Li: Writing - review & editing, Software, Visualization. Huiling Chen:

Declaration of Competing Interest

The authors declare that there is no conflict of interests regarding the publication of article.

Acknowledgements

This research is supported by Zhejiang Provincial Natural Science Foundation of China (LJ19F020001), the Science and Technology Plan Project of Wenzhou, China (2018ZG012), and National Natural Science Foundation of China (U1809209), Medical and Health Technology Projects of Zhejiang Province (2019RC207) .

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