Chicken swarm optimization with an enhanced exploration–exploitation tradeoff and its application

The chicken swarm optimization (CSO) is a novel swarm intelligence algorithm, which mimics the hierarchal order and foraging behavior in the chicken swarm. However, like other population-based algorithms, CSO also suffers from slow convergence and easily falls into local optima, which partly results from the unbalance between exploration and exploitation. To tackle this problem, this paper proposes a chicken swarm optimization with an enhanced exploration–exploitation tradeoff (CSO-EET). To be specific, the search process in CSO-EET is divided into two stages (i.e., exploration and exploitation) according to the swarm diversity. In the exploratory search process, a random solution is employed to find promising solutions. In the exploitative search process, the best solution is used to accelerate convergence. Guided by the swarm diversity, CSO-EET alternates between exploration and exploitation. To evaluate the optimization performance of CSO-EET in both theoretical and practical problems, it is compared with other improved CSO variants and several state-of-the-art algorithms on two groups of widely used benchmark functions (including 102 test functions) and two real-world problems (i.e., circle packing problem and survival risk prediction of esophageal cancer). The experimental results show that CSO-EET is better than or at least comparable to all competitors in most cases.


Introduction
Swarm intelligence (SI) algorithms are powerful optimization approaches inspired by the collective behaviors of social insects and animals. SI algorithms are usually characterized by solving optimization problems without central control, overall information, and prior knowledge. Compared with the traditional mathematical approaches, SI algorithms have the advantages of simple structure, convenient implementation, and robust performance. In recent decades, various SI algorithms have been developed, such as ant colony optimization (ACO) (Colorni et al. 1991), particle swarm optimization (PSO) (Kennedy, and Eberhart 1995), artificial bee colony (ABC) (Karaboga 2005), artificial fish swarm optimization (AFSO) (Li et al. 2002), firefly algorithm (FA) (Yang 2009), grey wolf optimizer (GWO) (Mirjalili et al. 2014), chicken swarm optimization (CSO) (Meng et al. 2014), and so on (Slowik 2020).
Among the above SI algorithms, CSO is a relatively novel approach developed by Meng et al. (2014). It simulates the hierarchal order and foraging behavior in the chicken swarm, which consists of roosters, hens, and chicks. In CSO, three kinds of chickens adopt three different search strategies. Specifically, roosters search for food independently, hens follow roosters to forage food, and chicks trail behind hens in search of food. Benefited by three different search equations, CSO could be considered as the integration of ABC, PSO, and DE (Bharanidharan, and Rajaguru 2020). Therefore, CSO has attracted great attention and been applied to many optimization problems in science and engineering, such as multi-objective optimization (Zouache et al. 2019), constrained optimization (Wang et al. 2019), parameters identification (Li et al. 2021), charging station placement (Deb et al. 2020a, b, c), task scheduling (Torabi and Esfahani 2018), trajectory optimization (Wu et al. 2018), and many others (Deb et al. 2020a, b, c).
Like other population-based algorithms, CSO also suffers from slow convergence and easily falls into local optima. To address this issue, numerous variants of CSO have been proposed. On the one hand, modification to the search equations is a popular way to enhance the performance of CSO. For example, Wang and Yin (2018) introduced a feedback mechanism from hens to roosters to modify the search equation of roosters. Wang et al. (2021) made use of the global best information to improve the search equation of roosters. Wang et al. (2017) added a nonlinear inertia weight to the search equation of roosters. Chen et al. (2015) adopted the search equation of chicks to modify that of hens. Wu et al. (2016) improved the search equation of chicks by employing the rooster's information and a learning factor. Qu et al. (2017) replaced the Gaussian distribution in the search equation of roosters with adaptive t distribution, and introduced elite oppositionbased learning into the search equation of hens. Liang et al. (2020) used a levy flight strategy and a nonlinear weight reduction strategy to improve the search equation of hens and chicks, respectively. Zhang et al. (2021) constructed three new search equations for roosters, hens, and chicks by considering both elite and ordinary individuals. Li et al. (2019) improved search equations of roosters, hens, and chicks with several search factors, such as attract factor, convergence factor, learning factor, and swing factor. On the other hand, hybridization with other algorithms is another common way to improve the performance of CSO. For instance, some hybrid algorithms were proposed by combing CSO with ant lion optimization (Deb and Gao 2021), cuckoo search (Liang et al. 2017), teaching-learning-based optimization (Deb et al. 2020a, b, c), tabu search (Niazy et al. 2020), bacterial foraging optimization (Abbas et al. 2018), differential evolution (Kumar and Veni 2018), and bat algorithm (Liang et al. 2016). The works discussed above are not exhaustive, and more information can be found in Deb et al. (2020a, b, c).
For the population-based algorithms, exploration and exploitation are two necessary search processes (Č repinšek et al. 2013). Exploration refers to investigating the unseen regions to seek hopeful solutions, and exploitation refers to searching the space around the already-found hopeful solutions to enhance their quality (Singh and Deep 2019). During the search procedure, exploration and exploitation contradict each other. Generally speaking, excessive exploration results in random search, and excessive exploitation leads to premature convergence. A crucial aspect for the performance of population-based algorithms is maintaining a proper balance between exploration and exploitation. Effective control over this balance can enhance the algorithm's efficacy, as noted by various studies (Arani et al. 2013;Rezaei et al. 2020;Lin and Gen 2009;Segredo et al. 2020). In this regard, this paper presents a CSO with an enhanced exploration-exploitation tradeoff. The primary contributions of this paper are summarized as follows.
(1) CSO is analyzed from the perspective of exploration and exploitation, i.e., CSO has some exploitation ability but lacks exploration ability.
(2) The exploration ability of CSO is improved by adding the information of a random solution to the search equations of roosters, hens, and chicks. (3) The exploitation ability of CSO is enhanced by introducing the information of the best solution to the search equations of roosters, hens, and chicks. (4) The balance between exploration and exploitation is achieved by guiding the search through distance-tocenter-based swarm diversity.
The rest of this paper is structured as follows. Section 2 introduces the original CSO. Section 3 provides a detailed description of the proposed CSO, which incorporates an improved tradeoff between exploration and exploitation. Sections 4 and 5 describe and discuss the experimental results on two groups of benchmark functions and two realworld problems, respectively. Section 6 summarizes this work.

The original CSO
CSO is first proposed by Meng et al. (2014), which mimics the hierarchal order and foraging behavior in the chicken swarm. In CSO, the chicken swarm is divided into roosters, hens, and chicks. In the process of optimizing problems, CSO operates under the following assumptions: (1) The size of the chicken swarm is N, and the dimension of the search space is D. Each individual in the chicken swarm is described by its position in the search space. For example, x t i;j denotes the position of the ith individual in the jth dimensional space in the tth iteration.
(2) Each individual can be viewed as a potential solution to the optimization problem. According to the fitness values of individuals, the best N R ones and the worst are N C ones are regarded as roosters and chicks respectively, and the remaining N H (N H = N -N R--N C ) ones are treated as hens.
(3) The chicken swarm is separated into N R subgroups, and each one contains a rooster, some hens, and several chicks. The subgroups are formed by hens randomly choosing roosters as their mates and chicks randomly selecting hens as their mothers.
(4) The hierarchal order of rooster-hen-chick, the spouse relationship between roosters and hens, as well as the mother-child relationship between hens and chicks will keep unchanged and get updates after every G time iterations. (5) In each subgroup, roosters play a leading role in searching for food, hens follow roosters to forage food, and chicks follow hens to seek food. That is, three kinds of chickens make use of three different search equations.
If the ith individual is a rooster, it employs the following search equation: where randn 0; r 2 ð Þ is a random number following Gaussian distribution with mean 0 and standard deviation r 2 , k is a randomly chosen rooster's index such that i 6 ¼ k, e is a small constant to avoid zero-division-error, and f is the fitness value of the corresponding x.
If the ith individual is a hen and the index of its mate rooster is r1, it adopts the following search equation: where rand is a random number within the range of [0,1], r2 is a randomly chosen index of rooster or hen such that r1 6 ¼ r2.
If the ith individual is a chick and the index of its mother hen is m, it uses the following search equation: where FL is a random number within the range of [0,2].

CSO with an enhanced explorationexploitation tradeoff (CSO-EET)
In this section, a detailed description of the proposed CSO-EET is given. Firstly, the motivation of this paper is presented. Secondly, the core components of CSO-EET, i.e., the judgment of exploration and exploitation, and the achievement of exploration and exploitation, are introduced. Finally, the proposed algorithmic framework is provided.

Motivation
For the population-based optimization algorithms, they need to address exploration and exploitation. Exploration involves investigating the unseen regions to seek potential solutions, helping algorithms escape local optima. Exploitation, on the other hand, involves searching the region around known promising solutions to improve their quality, by utilizing information about the already discovered good solutions. The most notable characteristic of CSO is the hierarchical leadership-based search approach. That is, roosters play a leading role in searching for food, hens follow roosters to forage food, and chicks follow hens to seek food. On the one hand, if roosters get stuck in local optima, hens and chicks will get trapped in local optima too, thus CSO lacks exploration ability. On the other hand, roosters correspond to elite solutions while the global best solution is underutilized, thus CSO has some exploitation ability. Therefore, enhancing exploration and exploitation could improve CSO's performance. Furthermore, controlling the balance between exploration and exploitation has been successfully used to improve other population-based optimization algorithms' performance (Arani et al. 2013;Rezaei et al. 2020;Lin and Gen 2009;Segredo et al. 2020). Based on these considerations, a variant of CSO is proposed by enhancing exploration and exploitation and balancing their relationship. Figure 1 shows the core idea of the proposed CSO-EET.

Judgment of exploration and exploitation
Exploration and exploitation contradict each other during the search process. Diversity is a specific display of the balance between exploration and exploitation (Chen et al. 2009). Generally speaking, when diversity is high, exploitation is needed to decrease diversity; when diversity is low, exploration is required to increase diversity (Wang et al. 2013). This process is graphically described in Fig. 2. Diversity reflects the distribution of a swarm, which could be calculated as follows: where L is the longest diagonal length in the search space, x t j is the jth dimension of the swarm center in the tth iteration, and other variables are as defined in Sect. 2.
Since the threshold values used to assess diversity as high or low may vary depending on the problem (Č repinšek et al. 2013), a simplified measure is defined as follows. When the diversity in the (t -1)th iteration is less than the minimum diversity in the previous (t -2) iterations, the exploration will be performed in the tth iteration. Otherwise, the exploitation will be done in the tth iteration. Moreover, exploration is aimed at finding promising regions, and exploitation is intended to conduct depth search in promising regions. When the best solution is updated, the current search region may be promising. On the contrary, the current search region may be not promising. Finally, the judgment of exploration and exploitation is formulized as follows:

Achievement of exploration and exploitation
In terms of the search scope, exploration can be viewed as global search (Chen et al. 2009), which searches the entire space without favoring any specific region. Complete exploration often leads to random search (Arani et al. 2013), and the search guided by a random solution could provide strong randomness. Therefore, a random solution can be used to enhance the exploration ability (Song et al. 2019). Inspired by this, when CSO performs the explorative search, the information of the random solution is employed to guide the searches of roosters, hens, and chicks, as shown in Eqs. (11), (12), and (13), respectively.
where o, p, and q are randomly selected from {1, 2, In terms of the search scope, exploitation could be interpreted as local search (Chen et al. 2009), which searches in the reduced space around the already-found promising solutions. Complete exploitation usually falls into local optima (Arani et al. 2013), and the search guided by the best solution could speed up the convergence rate. Therefore, the best solution can be used to enhance the exploitation ability (Cao et al. 2019). Inspired by this, when CSO performs the exploitative search, the information of the global best solution is employed to guide the searches of roosters, hens, and chicks, as shown in Eqs. (14), (15), and (16), respectively.
where x t best;j is the jth dimension of the global best solution until the tth iteration.
Furthermore, inertia weight is also an effective means of adjusting the balance between exploration and exploitation. A higher inertia weight tends to increase exploration, while a lower value promotes exploitation (Shi and Eberhart 1999). Inspired by the parameter settings in Shi and Eberhart (1999), a large inertia weight (i.e., 0.9) is introduced into Eqs. (11-13) to further enhance the exploration ability, and a small inertia weight (i.e., 0.4) is introduced

Algorithmic framework
According to the above explanations, the flowchart and pseudo-code of the proposed CSO-EET are presented in Figs. 3 and 4.

Test functions and performance metrics
In order to comprehensively investigate the performance of CSO-EET, two groups of widely used benchmark functions are utilized. The first group is the conventional benchmark functions taken from Wang et al. (2020), which span a wide variety of function characteristics, such as unimodal shift and rotation functions (F 71 -F 80 ). Note that, all these functions are minimization problems, and the number of maximum function evaluations (MaxFEs for short) is adopted as the stopping criterion. As suggested by Wang et al. (2020), the conventional benchmark functions are tested on dimensions D = 30 and 100, and the MaxFEs is set to 3000 9 D. As recommended by Mohamed et al. (2020), the CEC 2021 benchmark functions are test on Fig. 4 The pseudo-code of CSO-EET dimensions D = 10 and 20 with MaxFEs = 200,000 and 1,000,000 respectively. Three frequently used evaluation metrics are also employed in the experiments, which are introduced below.
(1) The mean and standard deviation (mean/std for short) of the best fitness values are used to assess the solution quality. For a minimization problem, small values of mean/ std correspond to high-quality solutions.
(2) The nonparametric tests, including the Wilcoxon signed rank test and the Friedman test, are conducted based on SPASS to make a comprehensive evaluation. The former is utilized to detect the significant statistical differences between two algorithms, and the latter is used to show the overall optimization performance of an algorithm among all algorithms. (3) The convergence curve is plotted to show the convergence speed intuitively. The simulation experiment environment is Windows 10 operating system, and the programming language is MATLAB R2017b. The hardware device parameters are Intel Core i5-7400, 3.00 GHz, 8 GB RAM. Note that, owing to space limitations, some experimental results denoted as 'S. Table' and 'S.

Comparison with other CSO variants
In this subsection, the following six CSO variants are employed to compare with CSO-EET.
For a fair comparison, the parameters of competitors are set the same as in the original papers. Table 1 gives the detailed parameter settings of all algorithms. All algorithms are conducted 30 independent trials for each function. The results are reported in terms of mean/std, and the Wilcoxon signed rank test at a 0.05 significance level is conducted to detect the significant statistical difference between CSO-EET and its competitors from two aspects. First, the difference on each function is tested, and the results are reported in terms '' ? '', '' = '', and ''-'', which represent that the performance of CSO-EET is better than, similar to, and worse than that of the compared algorithm on the corresponding function, respectively. Second, the difference on all functions is tested and the results are provided in terms ''R ? '', ''R -'', and ''p-value''. Here, R ? is the sum of ranks for the functions on which CSO-EET outperforms the compared algorithm, and Ris the sum of ranks for the opposite. p value [ 0.05 indicates that the difference between CSO-EET and the compared algorithm is not significant, and p value B 0.05 means the difference is significant. To further evaluate the overall performance, the Friedman test is conducted, and the results are reported in terms of ''mean ranking'', which denotes the average rank results on all functions. A smaller ranking value means a better overall optimization performance.
S. Tables 1 and 2 present the comparison results of CSO-EET and other CSO variants on the conventional benchmark functions with D = 30 and D = 100, respectively. As can be seen, for the functions with D = 30, CSO-EET obtains the best results on 18 out of 22 functions in terms of mean/std, and 16 out of 22 functions with D = 100. The results of the Wilcoxon signed rank test between CSO-EET and the compared algorithms are summarized in Table 2. Regarding the functions with D = 30, CSO-EET is superior to CSO, ICSO, EOCSO, NW-MCSO, ICSOTLBO, ALOCSO on 15, 13, 16, 14, 13, 12 functions respectively, while CSO-EET is inferior to these algorithms on 0, 2, 1, 1, 6, 2 functions, respectively.  On the contrary, CSO-EET is only bested by these algorithms on 0, 1, 0, 0, 6, 0 functions, respectively. Taken as a whole, CSO-EET performs statistically significantly better than CSO, ICSO, EOCSO, NW-MCSO, ALOCSO, and similar to ICSOTLBO according to the p-values. Moreover, CSO-EET obtains higher R ? values than Rin all cases. Figure 5 presents the mean ranking of all CSO variants using the Friedman test, which shows that CSO-EET obtains the first rank. In order to show the convergence speed intuitively, the convergence curves of all CSO variants on eight selected functions that cover all types of the benchmark functions are plotted in S. Figures 1 and 2. As can be seen, the performance of CSO-EET on convergence is excellent. S. Tables 3 and 4 give the comparison results of CSO-EET and other CSO variants on the CEC 2021 benchmark functions with D = 10 and D = 20, respectively. As can be seen, according to solution quality, CSO-EET obtains the best results on 58 out of 80 functions with D = 10 and 61 out of 80 functions with D = 20. The results derived by the Wilcoxon signed rank test between CSO-EET and other CSO variants are summarized in Table 3. Concerning the functions with D = 10, CSO-EET performs better than CSO, ICSO, EOCSO, NW-MCSO, ICSOTLBO, ALOCSO on 80, 67, 39, 39, 39, 40 functions respectively, while CSO-EET performs worse than these algorithms on 0, 3, 22, 22, 22, 21 functions, respectively. Regarding the functions with D = 20, CSO-EET outperforms CSO, ICSO, EOCSO, NW-MCSO, ICSOTLBO, ALOCSO on 80, 61, 40, 40, 41, 40 functions respectively, while CSO-EET is bested by these algorithms on 0, 2, 19, 19, 19, 19 functions, respectively. On the whole, according to the p-values, CSO-EET is significantly better than all others CSO variants except EOCSO. Moreover, CSO-EET obtains higher R ? values than Rin all cases. The mean ranking of all CSO variants obtained by the Friedman test are depicted in Fig. 6, which shows that CSO-EET achieves the best mean ranking. That is, CSOEET achieves the best overall performance among seven CSO variants. The convergence curves of all CSO variants on eight selected functions that cover all types of the benchmark functions are plotted in S. Figures 3 and 4. As can be seen, CSO-EET has the fastest convergence speed in most cases, the meaning of which is twofold. On the one hand, CSO-EET obtains better solutions than competitors under the same function evaluations. On the other hand, CSO-EET needs smaller function evaluations than competitors to achieve a solution with a certain accuracy.

Comparison with other state-of-the-art SIs
In this subsection, the following three ABC variants and three PSO variants are employed to compare with CSO-EET.
• ABC with multiple search strategies ABCX (Hakli and Kiran 2020). • ABC based on neighborhood selection (NSABC) (Wang e al. 2020). • ABC variant based on multi-elite guidance (MGABC) (Zhou et al 2021).   Table 5. Regarding the functions with D = 30, CSO-EET performs better than ABCX, NSABC, MGABC, EPSO, XPSO, SDPSO on 9, 10, 11, 13, 16, 13 functions respectively, while CSO-EET performs worse than these algorithms on 7, 7, 7, 8, 5, 7 functions, respectively. Concerning the functions with D = 100, CSO-EET surpasses ABCX, NSABC, MGABC, EPSO, XPSO, SDPSO on 10, 11, 9, 15, 17, 14 functions respectively, while CSO-EET is bested by these algorithms on 7, 7, 5, 6, 3, 6 functions, respectively. Taken as a whole, the Wilcoxon signed rank test also considers that CSO-EET is not significantly different from all competitors. In addition, CSO-EET obtains higher R ? values than Rin most cases. In terms of the Friedman test, Fig. 7 shows the mean ranking of CSO-EET and ABC/PSO variants. As can be seen, CSO-EET obtains the first and second ranks among all seven algorithms for D = 30 and D = 100 respectively, which shows the high efficiency of CSO-EET. S. Figures 5  and 6. plot the convergence curves of CSO-EET and ABC/ PSO variants on some selected functions with D = 30 and D = 100, respectively. It can be seen that the convergence performance of CSO-EET is excellent. For example, CSO-EET achieves the optimal value on f 18 with D = 100 and shows the fastest convergence speed.
S. Tables 7 and 8 give the comparison results of CSO-EET and ABC/PSO variants on the CEC 2021 benchmark functions with D = 10 and D = 20, respectively. As can be seen, CSO-EET shows better performance in most cases  Chicken swarm optimization with an enhanced exploration-exploitation tradeoff and its application 8021 according to solution quality. The results derived by the Wilcoxon signed rank test between CSO-EET and ABC/ PSO variants are summarized in Table 6. Concerning the functions with D = 10, CSO-EET is superior (inferior) to ABCX on 80 (0) (2) functions. On the whole, the performance of CSO-EET is significantly better than that of all competitors with higher R ? values than Rin all cases. Figure 8 presents the Friedman test results. As can be seen, the mean ranking of CSO-EET is better than that of all competitors, which implies that CSO-EET has better performance. S. Figures 7  and 8 plot the convergence curves of CSO-EET and ABC/ PSO variants on the selected functions with D = 10 and D = 20, respectively. It can be seen that the convergence performance of CSO-EET is better in most cases.

Experiments on real-world optimization problems
In order to evaluate the optimization performance of CSO-EET in practical applications, two real-world problems (i.e., circle packing problem and survival risk prediction of esophageal cancer) are considered in this section.

Circle packing problem
The circle packing problem consists of placing a set of circles into a container without overlap. The objective is to minimize the container size and, in turn, minimize the   The p-values below the 0.05 significance level are shown in bold amount of waste. It is encountered in many industries, such as wood, paper, glass, and textile. In this study, the problem of packing unequal circles into a rectangular container is investigated. Specifically, given an initial rectangle of fixed width W and unlimited length L, as well as a set of n circles c i with radius r i (i = 1,…,n). Let the lower-left coordinates of the rectangle be (0,0), and the coordinates of the center of the circle c i be (x i , y i ). Then, the circle packing problem can be modelled as follows: min L s:t: x i À x j À Á 2 þ y i À y j À Á 2 ! r i þ r j À Á 2 ; j\i; i; j ð Þ 2 n 2 x i À r i ! 0; 8i 2 n y i À r i ! 0; 8i 2 n W À y i À r i ! 0; 8i 2 n L À x i À r i ! 0; 8i 2 n The objective of the model is to minimize the length L, the first constraint states that no circle overlaps with other circles, and other constraints require that no circle extends outside the container. Therefore, the circle packing problem is a constrained optimization problem that has proven to be NP-hard, meaning that finding an optimal solution is computationally very challenging.
The test instances in Kubach et al. (2009) are used in this experiment, the numbers of circles in instances KBG_SPP6, KBG_SPP46,KBG_SPP95,and KBG_SPP103 are 25,50,75,and 100,respectively. For each test instance, all algorithms with the same parameters as in Tables 1 and 4 are conducted by 10 independent runs, and the MaxFEs is set to 10,000 9 D. In terms of the mean and standard deviation, Table 7 shows the computational results of CSO-EET and its competitors, where the best results are marked in bold. As shown in Table 8, CSO-EET obtains the best results for 3 out of 4 instances. For the instance KBG_SPP95, CSO-EET is only beaten by MGABC and achieves the second-best result. The best packing layouts achieved by CSO-EET are shown in Fig. 9.

Survival risk prediction
In this section, the esophageal cancer survival risk prediction is employed. First, an esophageal cancer survival risk prediction model is established based on Elman neural network (ElmNN). Then, CSO-EET is employed to optimize the initial weigh values and threshold values of ElmNN.  The best results are shown in bold Chicken swarm optimization with an enhanced exploration-exploitation tradeoff and its application 8023

Prediction model based on ElmNN
As a typical dynamic recursive neural network, Elman neural network (ElmNN) is composed of four layers, namely the input, hidden, context, and output layers, as shown in Fig. 10. ElmNN adds the context layer to the hidden layer as a delay operator for memorization purposes, which enhances the network's ability to handle dynamic information. Therefore, ElmNN has been widely used in cancer classification and prediction (Alkhasawneh 2019;Sultana et al. 2021 Finally, the structure of the prediction model is defined as 10-5-1. The model has 55 weights and 6 thresholds that need to be optimized. The objective function is defined as the accuracy of survival risk prediction and is calculated as follows: where w and v represent weights and thresholds, respectively; TP denotes the number of samples that are in fact low risk and predicted to be low risk; FP denotes the number of samples that are in fact high risk but predicted to be low risk; FN denotes the number of samples that are in fact low risk but predicted to be high risk; TN denotes the number of samples that are in fact high risk and predicted to be high risk. The best results are shown in bold (c) KBG95 (d) KBG103 Fig. 9 The best packing layouts achieved by CSO-EET

Experimental results
In the experiment, the sample data is normalized and randomly divided into two parts: 80% as a training set and the remaining as a test set. We use CSO-EET and its competitors to optimize the initial weight and threshold values of the prediction model. For all algorithms, population sizes are set to 50, and other parameters are set the same as Sects. 4.2 and 4.3. Each algorithm is run independently 10 times with a stopping criterion that function evaluations reach 1000 9 49. In the network training process, the learning rate, the minimum training error, and the maximum training times are set to 0.01, 0.01, and 1000, respectively. In addition to accuracy, sensitivity and specificity are another two commonly used performance indicators in medical applications. Sensitivity is calculated as TP/ (TP ? FN), which represents the ability to classify lowrisk patients from low-risk samples accurately. Specificity is calculated as TN/(TN ? FP), which represents the ability to identify high-risk patients from high-risk samples accurately. Table 8 presents the mean/std of the results achieved by each algorithm in terms of accuracy, sensitivity, and specificity over 10 independent trials. As shown  in Table 8, the prediction results of CSO-EET are all over 90%, which are better than that of its competitors. Figures 11,12,13 further plot the prediction results in terms of accuracy, sensitivity, and specificity, respectively.

Conclusion
In this work, the basic chicken swarm optimization (CSO) is analyzed from the viewpoint of exploration and exploitation. It could be concluded that CSO has some exploitation ability and lacks exploration ability. Thus, a novel chicken swarm optimization with an enhanced exploration-exploitation tradeoff (CSO-EET) is proposed. On the one hand, CSO-EET designs a diversity-based index to determine the search states of exploration and exploitation. On the other hand, CSO-EET employs a random solution and the best solution to enhance exploration and exploitation abilities, respectively. CSO-EET is tested on twenty-two benchmark functions and a real-world esophageal cancer survival risk prediction, and compared with six CSO variants, three ABC variants, and three PSO variants. The experimental results demonstrate that, in most cases, CSO-EET outperforms or is at least comparable to all other competitors. For future work, it can be carried out from two aspects. One is the extension of CSO-EET to solve more real-world optimization problems. The other is the achievement of exploration-exploitation tradeoff through different ways. For instance, Cui et al. (2017) suggested that increasing the population size could enhance exploration ability, while decreasing the population size could improve exploitation ability.