Multi-strategy assisted chaotic coot-inspired optimization algorithm for medical feature selection: A cervical cancer behavior risk study
Graphical abstract
Introduction
Optimization theory aims to discover the best implementation of a problem under all known public options. Because of their universality and application, optimization methods have attracted extensive attention from various industries. Many fields, including science, engineering, agriculture, and architecture [1], are involved in the optimization process. In almost all engineering and business applications, the essence of optimization is to maximize (or minimize) an index. However, there are various difficulties in the actual optimization process, including multi-objective, multi-constrained, uncontrollable, local, and deceptive global solutions [2]. Generally speaking, mathematics-based optimization uses mathematical methods to study optimization problems in planning and design [3]. In this context, two strategies for solving optimization problems burst out. Traditional techniques, including the branch and bound method, and Newton's iterative strategy [4], are widely used to solve generic optimization. However, most of these methods still suffer from certain limitations, such as local solutions and non-convergence, when dealing with non-convex, discrete, and other problems. Another mathematically based optimization class is the recently emerged meta-heuristic algorithm [5]. It is a method to explore the solution space using computational intelligence strategies based on stochastic technology [6]. This class of methods typically uses a set of randomly generated solutions to initialize the optimization space and improve the initial solution within a predetermined number of steps [7].
Intelligent algorithms are very popular among researchers in different fields due to their clarity, flexibility, and capacity to skip local solutions [8]. Some intelligent algorithms, such as genetic algorithms (GA) [9], are inspired by nature, which learns from biological and genetic variation. Biological swarm approaches mimic the collective behavior of different animals and plants to search for the optimal global solution more quickly. Many well-known techniques for swarm intelligence, including particle swarm optimization (PSO) [10] based on the movement of a bird, slime mould algorithm (SMA) [11] based on bacterial foraging mode, and artistic bee colony (ABC) [12] based on bee cluster behavior. Recently, population-based optimization algorithms have gained attention for their excellent proficiency in solving optimization problems, including, but not limited to, teaching-learning-based optimization (TLBO) [13], which simulates the effect of teachers on learners.
Exploration and development are two essential ideas in various meta-heuristic intelligent algorithms [14]. The exploration phase usually involves finding new search regions of infeasible spaces; the development phase analyzes the potential of a solution within a detectable search region. Meta-heuristic algorithms influenced by both ideas have shown their advantages in various practical application fields [15,16]: Hu and Zhu proposed an improved marine predators algorithm for shape optimization of developable surfaces [17]. Xu and Tan offered an improved arithmetic optimization algorithm combining sinusoidal chaotic mapping and Gaussian mutation mechanism for model identification of the proton exchange membrane fuel cells [18]. Jiang and Wu proposed a diversified group teaching optimization algorithm for unmanned aerial vehicle route planning [19]. Kamel, H. Hassan proposed an improved slime mould algorithm to solve the optimal economic emission dispatch problem [20]. Hu and Du applied an improved black widow optimization algorithm to the feature selection problem [21]. Abdel-Basseta and Mohameda proposed a hybrid whale optimization algorithm for multi-level thresholding color image segmentation [22].
Metaheuristic algorithms are usually divided into three classifications: (I) evolutionary optimization algorithms, (II) swarm intelligence algorithms, and (III) optimization algorithms that simulate physical phenomena. In evolutionary technology, the design of algorithms is inspired by the evolution of nature. Among these algorithms, genetic algorithms (GA) [9] and evolutionary programming (EP) [23] algorithms are some famous examples of evolutionary algorithms. Algorithms based on physical phenomena are usually designed by simulating the laws of physics and mathematics. Gravitational search algorithm (GSA) [24], central force optimization (CFO) [25], charged system search algorithm (CSS) [26], black hole (BH) [27], ray optimization (RO) [28] are some examples of physics-based algorithms. The algorithm based on swarm intelligence explores the best global solutions by mimicking the collective and social behavior of ants, whales, dolphins, lions, fruit flies, wolves, and other organisms. Some of the most popular and widely used algorithms are krill herd (KH) [29], black widow optimization algorithm (BWO) [30], emperor penguin optimizer (EPO) [31], jellyfish search optimizer (JS) [32], marine predators algorithm (MPA) [33], harris hawks optimization (HHO) [34], virus colony search (VCS) [35], and orca predation algorithm (OPA) [36]. At present, swarm intelligence-based optimization algorithms are frequently used to solve large-scale optimization problems in real engineering.
In 2021, Naruei and Keynia proposed a brand-new metaheuristic algorithm founded on the coot birds, called the coot optimization algorithm (COOT algorithm, for short) [37]. The COOT algorithm solves various optimization problems by simulating the conduct of coot birds on the river. The COOT algorithm is simple, efficient, and competent in solving complex engineering problems. Since its proposal, it has gained a wide range of applications in various fields of application and has successfully solved some optimization application problems. For example, Koc used the COOT algorithm to optimize fast community detection for social networks [38]. Houssein et al. proposed a modified COOT algorithm to solve the battery parameter identification problem [39]. Memarzadeh et al. used the COOT algorithm to optimize an optimal energy storage system model for wind turbines based on long and short-term memory [40]. Qin et al. used the COOT algorithm to solve the optimal carbon–energy combined flow of the power grid with aluminum plants [41].
Many new swarm intelligence algorithms and various modified versions of multi-strategy algorithms have appeared in recent years. However, we still construct a new version of the COOT algorithm with three primary purposes. The first point is that these algorithms are often affected by the No-Free Lunch (NFL) theory [42]. It is impossible for any optimization algorithm to solve all optimization problems in the NFL theory. As a second point, large-scale applications and studies have also shown that the COOT algorithm still has several deficiencies: 1) slow movement of the Coot bird on the river, 2) easy to fall into local optimum with low diversity, 3) slow convergence, and 4) imperfect balance between exploitation/exploration [41]. The third point is that considering the importance of feature selection for medical data mining and classification tasks, this study tries to identify an efficient method to apply to the medical feature selection problem, i.e., extracting useful information from massive data.
Therefore, this study develops an alternative version of the chaotic COOT algorithm by alleviating the shortcomings of COOT algorithm with a combination of opposition-based learning and hunting strategy. The chaotic maps and opposition learning strategy mainly address the slow motion and slow convergence speed problems in two main ways: 1) the chaotic map increases the convergence speed by reprogramming the solution at the early stage and reconstructing the distribution of solutions. 2) The opposition learning strategy helps the scheme to reprogram a backward solution, thus increasing the overall solution quality. The hunting strategy guides toward the best direction according to the elected leader, which mainly addresses the early convergence problem and ensures the balance between exploitation/exploration. The improved coot algorithm is divided into two stages: in the first stage, a random coot population is generated through an appropriate chaotic mapping strategy, and then the fitness function is computed for each generated solution. The second stage updates the schemes with classical COOT algorithm. Then, the OBL and hunting strategies are applied to the updated solution to re-evaluate.
The innovations and main contributions of this paper are as follows.
- (1)
The improvement effects of ten different chaos theories in the COOT algorithm are analyzed.
- (2)
Aiming at the shortcomings of premature convergence and slow speed of the algorithm, opposition-based learning and hunting strategies are introduced.
- (3)
A comprehensive experiment is designed and implemented. The performance of the proposed algorithm named COBHCOOT on the CEC2017 function and CEC2019 function is compared with the previous intelligent algorithms, and good consequences are obtained. Meanwhile, the scalability of dimensions was studied in CEC2017, including 30, 50, and 100 dimensions. The operation results show that COBHCOOT has the ability to solve problems of different scales.
- (4)
COBHCOOT is implemented in two real engineering optimization problems and four truss structure optimizations.
- (5)
Experimental comparison of COBHCOOT with eight feature selection methods on eight medical data demonstrated the efficiency of COBHCOOT in searching for effective features.
- (6)
The COBHCOOT is applied to detect cervical cancer behavior risk in a case study.
The content of this paper is arranged as tracks: In Section 2, we introduce the basic COOT optimization algorithm; A COOT algorithm based on three improved strategies is proposed in Section 3, called the COBHCOOT algorithm; In Section 4, the performance of COBHCOOT in various aspects is discussed. In Section 5, the results of six engineering optimization problems are analyzed. Section 6 applies the COBHCOOT to the truss optimization problem. In Section 7, COBHCOOT is applied to medical feature selection and cervical cancer behavioral risk research. Finally, the conclusions and future work are discussed.
Section snippets
The theory of the COOT algorithm
The Coot optimization algorithm is a meta-heuristic based on the coot population proposed in 2021. The algorithm simulates the collective movement (regular movement and irregular motion) of coots on the river, including four-movement modes: (1) random motion to this side and that side, (2) chain motion of the bird, (3) adjusting the situation according to the leader, (4) the leader leads the team to the best area. In addition, the front coots lead the whole population to the destination, so
Multi-strategy boosted chaotic COOT algorithm
Aiming at the problems of the slow speed of convergence and insufficient convergence accuracy of the COOT algorithm, a multi-strategy boosted COOT algorithm named COBHCOOT combined with a chaotic map strategy, opposition-based learning strategy, and hunting strategy is proposed. The main content of this section is to introduce the specific improvement methods of the proposed algorithm and make a simple analysis.
Numerical examples and analysis
To benchmark the performance of the proposed algorithm, the study uses 29 benchmark functions from the standard CEC2017 test suite and ten benchmark functions from the legal CEC2019 test suite to execute the experimental sequence. At the same time, two engineering optimization problems and four truss optimizations are cited as examples to test the practical application. In this study, the number of population n is set to 30, the dimensions of CEC2017 are 30, 50, and 100, respectively, and the
Real application: engineering optimization problems
This section will cover the following contents: The proposed COBHCOOT algorithm is used to solve two practical engineering problems, including cantilever beam (CBDP) and welded beam design problems (WBDP). To prove the practicality of the proposed COBHCOOT, we select 11 other famous algorithms for comparison in each practical engineering problem. Each algorithm has 30 candidate solutions and 1000 iterations. Meanwhile, each algorithm runs 20 times on different problems independently to avoid
Truss topology optimization using COBHCOOT
Truss design has been a rapidly developing field of structural optimization research in recent phases. And as a form of truss design, the primary goal of structural optimization is to locate the most suitable area in the cross-sectional domain of the design element and to satisfy various constraints that limit the dimensions and structural response [32]. The mathematical representation of the truss structural problem is:
Minimize:Subject to
An application of medical feature selection
Feature selection is an optional task in multiple domains, such as data mining, pattern recognition and data processing, especially for its ability to handle high-dimensional datasets [21]. Feature selection outcomes in the selection of the best subset of features with minimum redundancy and maximum recognition power [89].
In this section, we apply COBHCOOT to nine commonly available medical feature selection datasets and one medical disease case: a cervical cancer behavior risk study [90]. By
Conclusions
This paper presents an improved version of the COOT optimization algorithm with three improvements. Firstly, the chaotic maps strategy replaces random initialization and expands the search space to improve convergence speed. Meanwhile, this improved strategy can find a set of optimal chaotic map methods according to different experiments. Secondly, the population movement is reformed by introducing the opposition-based learning strategy, which concentrates on improving the convergence speed of
Availability of data and materials
All data generated or analyzed during this study are included in this published article.
Declaration of competing interest
The authors declare no conflict of interest.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 51875454).
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