CC-CSA: A culture&chaos-inspired clonal selection algorithm for abnormal detection

Abstract

The clonal selection algorithm(CSA) is a core method in artificial immune system, which is famous for its intelligent evolution in artificial intelligence application. However, There are some shortcomings in the algorithm, such as local optima and low convergence speed, which make its practical effects not ideal. Culture algorithm(CA) is driven by knowledge, which can significantly improve the evolutionary efficiency. Chaos mechanism can make the algorithm have better problem space coverage ability. Therefore, a culture&chaos-inspired CSA(CC-CSA) is proposed in this paper to deal with the problems mentioned before. CC-CSA adopts the double-layer evolutionary framework of CA to extract knowledge and guide the crossover and chaotic mutation operation to complete the evolution process. The implicit knowledge is used to adaptively control the chaotic mutation scale, guide the individuals to jump out of the local optima, and realize the accurate search in the latter evolution cycle to gradually approach the optimal solution. It can be seen from the mathematical model analysis that CC-CSA can converge to the global optimal solution. Compared with the experimental results of the original CSA and its representative, up-to-date improved methods, CC-CSA has the fastest convergence speed and the best detection performances. It is also proved that CC-CSA can solve the problems of local optima and slow convergence speed by using the knowledge guidance of CA’s double-layer framework and good coverage ability of chaos mechanism to the problem space.

Keywords

Artificial immune system clonal selection algorithm culture algorithm chaos mechanism abnormal detection

1 Introduction

The evolutionary algorithms based on immune mechanism have been widely used in intelligent optimization, data mining, machine learning, fault diagnosis, anomaly detection and many other fields because of these powerful intelligent processing abilities for complex problems [1, 2]. The clonal selection algorithm (CSA) is one of the most representative evolutionary algorithms [3]. Its core knowledge-base is the detector set. CSA acts on the training process of the immune detectors, and obtains the final optimization results after cross-mutation and other related processes.

However, the traditional CSA tends to fall into a local optima and has a low convergence speed. These problems should be solved to meet the application requirements. There have been many publications to improve CSA for these problems. Hong proposed an elitist CSA to enhance convergence speed [4]. Yin proposed an improved CSA for selecting and cloning the best individuals [5]. Xu proposed a DR-CSA based on degeneration recognizing (DR) to reduce convergence time by eliminating the identified degenerated individuals before evaluation operation [6]. Zhang introduced a recombination operator inspired by the biological combinatorial recombination to CSA [7]. The recombination operator could generate the promising candidates to solve the problems of premature convergence and unsatisfied accuracy. Yin proposed an improved CSA combined feature selection [8]. Ulker introduced the tournament selection to CSA to improve its detection performances [9]. Although the above improved algorithms use different strategies or scales to avoid local optima and accelerate the convergence, the actual effects are not ideal in some respects. And what we found, the knowledge is not fully utilized to improve the convergence ability. In addition, the fixed mutation operator is a key factor, which leads to the too fast or low convergence and the difficulty in accurately locating the optima.

The cultural algorithm (CA) is inspired by the evolution process of human society and has a double-layer evolution framework. It consists of the population space for individual evolution and the belief space for knowledge renewal. Evolutionary information can be extracted and managed effectively by belief space, and guides the evolution of the population space. This mechanism can effectively improve the evolution efficiency. So far, CA has been combined with related intelligent optimization algorithms and achieved better evolution results in many application fields. Teran used CA to optimize the coordination mechanisms [10]. Pan used CA for cell allocation of CMOS molecular circuit [11]. Omran applied CA to nonlinear control systems [12]. Liu applied CA to the spatial forest resource planning problem [13].

To deal with the CSA problems of local optima and low convergence, introducing the efficient evolution framework of CA and the distribution advantage of chaos mechanism, this paper proposes a culture&chaos -inspired CSA (CC-CSA): Using the two-layer evolutionary framework of CA, selects superior individuals from the population space and puts them into the belief space to extracts knowledge; and then, using knowledge and chaotic mutation operator based on Logistic chaotic sequence, guides individuals crossover and mutation in the population space to ensure that the population evolution is getting closer to the optimal solution continuously by more accurate global and local search, and avoid the CSA falling into the local optima, and improve its convergence speed.

The rest of this article is as follows: Section 2 and 3 introduce and analyze the CSA and CA respectively. Section 4 proposes the CC-CSA, details the algorithm process and carries on the convergence mathematical analysis. And then, the experiments are carried out in Section 5. Finally, the section 6 is the conclusion and prospect.

2 Clonal selection algorithm(CSA)

CSA is one of the core algorithms in artificial immune system, which is derived from the clonal selection mechanism of biological immune system(BIS) [3]. In BIS, a pathogen is broken down into many antigen fragments. And the immune cells secrete antibodies to combine with antigens, simultaneously, perform activation and proliferation processes to obtain the corresponding plasma cells to clear the invading antigens based on neutralization and dissolution. BIS has certain memory characteristics, which can utilize blood circulation to lay the foundation for the next period to effectively remove the infection caused by similar or identical antigens. These characteristics of BIS are all simulated by CSA, which enables the continuous evolution of immune cells (called detectors) through cloning, crossover, and mutation operations, etc.

At present, CSA and its improved methods have been well applied in many fields. Rafiei proposed a hybrid approach for probabilistic electricity price forecasting based on CSA and wavelet preprocessing [14]. Shang proposed a high-efficiency immune CSA for capacitated arc routing instances within a limited number of function evaluations [15]. Dornelles presented a method for synthesis of broadband matching networks based on CSA to improve the efficiency [16]. To tune parameters of controller, Dong introduced a parallel adaptive CSA (PACSA) to a nonlinear model for an electro-hydraulic servo actuator and quarter suspension system [17].

CSA includes three stages: (1)selection and clonal proliferation; (2)crossover and mutation; (3)update. The first stage mainly realizes the expansion of population space, and the cloning scale is directly proportional to the affinity; In the second stage, the diversity of the population is increased by crossover and mutation, so that the diverse population can have better antibodies than the current population; Through the selection of excellent individuals in the third stage to update and rebuild the next generation, the population space can be compressed to make the population evolve toward a better direction. The basic procedures of CSA are shown in Fig. 1 and its processes are described in detail as follows:

a candidate detector set is initialized and generated, which consists of memory detectors and previous detectors.

n detectors with the higher affinities are selected to be cloned to build the temporary population. The greater affinity to the antigen, the larger scale of the corresponding cloning individuals.

According to the corresponding affinities, the appropriate crossover and mutation strategies are fixed. And then, crossover and high-frequency mutation are processed on the temporary population to obtain the mature population.

Some individuals with higher affinities(num: m) are selected from mature population, and used as memory detectors to replace some individuals with lower affinities in detector set.

Judge whether the algorithm meets the end condition, if so, algorithm ends; Otherwise, go to Step 1.

Fig. 1

Basic procedures of CSA.

CSA is a robust optimization method. But when the search space is large, it often takes long time to find the optimal solution, and often falls into the local optima. To solve these problems, many scholars have proposed many improvement methods. Sayed presented a binary clonal flower pollination algorithm (BCFA) by combining CSA and flower pollination algorithm [18]. Zareizadeh replaced the large search space with the theta-search based on the phase angles [19]. Avatefipour proposed three sub-modifications to expand the search capability of CSA and avoid premature convergence [20]. There are many similar improvements, but the actual optimization effects are not entirely satisfactory in some aspect: or the convergence is accelerated, but it is more likely to fall into local optima; or it avoids local optima, but it converges more slowly.

3 Cultural algorithm(CA)

CA was proposed by Robert G. Reynolds in 1994. The core idea is using implicit experiential knowledge to accelerate the evolution process [21]. This characteristic makes CA useful for optimizing iteration processes of many intelligent algorithms. To solve the problem of premature convergence of sine cosine algorithm (SCA), Zou proposed an improved SCA based on CA framework [22]. Wang introduced CA in particle swarm optimization algorithm (PSO) to improve the searching ability [23]. Guo presented a novel multi-objective cultural PSO by introducing CA to solve the problem of premature [24]. Khan combined CA and differential evolution to decrease the computation complexity [25]. Gao introduced CA into quantum-inspired flower pollination algorithm (QFPA) to improve the ability of searching the optimal solution [26].

The CA framework is shown in Fig. 2. It mainly includes three components: population space, belief space and communication channel.

Fig. 2

Cultural algorithm framework.

(1) Population space is the sample set, and its operations mainly include three functions: Generate(), Select() and Objective(), which are similar to the process in CSA.

(2) Belief space mainly includes standard knowledge: K 1 and topological knowledge:.

1) K 1 is mainly used to record the corresponding feasible problem’s solution space: S_{K
₁}: $K_{1} = 〈 L (t), U (t) 〉,$ (1) $L (t) = {l_{1} (t), l_{2} (t), \dots, l_{n} (t)},$ (2) $U (t) = {u_{1} (t), u_{2} (t), \dots, u_{n} (t)},$ (3) where t is the number of iteration, l_i (t) and u_i (t) respectively represent lower and upper limits of the ith dimension, i = 1,2,3,...,n. Then CA uses Influence() to conduct a global search.

2) K 2 is mainly used to record the fitness distribution of excellent individuals during population evolution:

〈 K _2,1, K _2,2, … K _2,q, … 〉, q = 1, 2, 3, …,

and $K_{2, q} (t) = 〈 L_{K_{2, q}} (t), U_{K_{2, q}} (t), x_{K_{2, q}}^{best} (t) 〉$

indicates the lower limit, upper limit and the best individual in the sub-region: S_{K
_2,q} after partition, satisfying:

L _{K_2,q} (t) ⩾ L(t), U _{K_2,q} (t) ⩽ U(t).

(3) Communication channel can be divided into three functions: Accept(), Influence(), and Update() [32].

Accept() is mainly used to build the sample library recruited by individuals with high affinity in each generation to extract their knowledge.

Influence() is mainly used to determine each knowledge’s influence proportion and role on the population. The chaotic mutation operator in CC-CSA proposed in this paper is guided by knowledge. The influence proportion of chaotic mutation of population can be set dynamically according to the success rate of knowledge influence in the previous generation population.

Assuming that the number of offspring individuals effected by knowledge K_i is m_{K
_i}, the influence proportion is: $P_{K_{i}} = {\begin{matrix} \frac{1}{N_{K}}, & t = 0 \\ α + β \frac{m_{K_{i}} (t - 1)}{m_{v}}, & t > 0 \end{matrix}$ (4) and $N_{K} α + β = 1,$ (5) where N_K is the number of knowledge type. m_v is the number of mutated individuals in the population.

Update() extracts and updates the population knowledge based on the existing knowledge of the belief space and the new individuals.

From the basic processes and main modules of CA, it can be seen that its population processing is very similar to CSA. With the help of the dynamic update of knowledge and the influence on the population evolution, the convergence can be accelerated. Meanwhile, Chaos mechanism has good random ergodicity, which can make the algorithm have better problem space coverage ability to avoid the local optima. Therefore, this paper improves CSA based on cultural algorithm and chaos mechanism.

4 Culture&Chaos-inspired Clonal Selection Algorithm (CC-CSA)

4.1 Algorithm idea and implementation

CC-CSA adopts a double-layer evolutionary framework of CA, which consists of the lower population space and the upper belief space. The population space processes individual evaluations and evolution operations of “selection-crossover-mutation”, and provides the evaluated individuals and their fitnesses stored in the library of the belief space. The belief space selects superior individuals by evaluating affinities from the population space through the Accept(), and extracts and updates implicit knowledge by the Update(), and then conducts evolutionary operations by Influence() to the population space. In general, CC-CSA uses CA to accelerate convergence and chaos mechanism to avoid local optima problem.

The key functions of CC-CSA are set as follows:

Accept() taking a fixed proportion: k_a, extracts the samples in affinity’s descending order.

Influence() is guided based on knowledge and acts on the crossover and chaotic mutation operator:

\begin{matrix} x_{ij} (t + 1) = \\ {\begin{matrix} l_{j} (t) - (u_{j} (t) - l_{j} (t) a_{ij}^{H} (t)), & x_{i} (t) \notin S_{K_{1}} (t) \\ x_{ij} (t) + a_{ij}^{H} (t) \frac{w_{i}}{n} exp (\frac{- α t}{T}) (u_{j} (t) - l_{j} (t)), & x_{i} (t) \in S_{K} (t) \end{matrix} \end{matrix}

(6) where w_i is the rank of individual i in the population.

a_{ij}^{H}

is high-dimensional chaotic sequence value calculated by Logistic chaotic sequence:

α _{l + 1} = μ α_l (1 - α_l), l = 0, 1....

Where μ (t) ∈ [3, 4] is the chaotic factor, α₀ ∈ [0, 1] is a random seed. The larger μ, the better the universality of Logistic chaotic sequence. According to the Literature [33], Based on the variation of feasible solution region, the calculation method of μ is designed as follows: $μ (t) = 3.5 + 0.5 \cdot \frac{μ_{j} (t) - l_{j} (t)}{μ_{j} (0) - l_{j} (0)} .$

According to the formula(1–3), μ (t) ∈ [3.5, 4].

Update() is reflected in two aspects:

1) The extracting and update of standard knowledge triggers topological knowledge redistribution: $\begin{matrix} K_{2, q} (t) = 〈 L_{K_{1, q}} (t), U_{K_{1, q}} (t), x_{K_{1, q}}^{best} (t) 〉 \\ if S_{K} (t) \neq S_{K_{1}} (t - 1) . \end{matrix}$

2) the refinement of topological knowledge.

Definition 1. Information gain records the fitness gradient on each dimension: $Δ I_{j} = \frac{f (x_{j}^{best} (t)) - f (x_{j}^{best} (t - 1))}{x_{j}^{best} (t) - x_{j}^{best} (t - 1)} .$ (7)

Topological knowledge is stored in a binary tree structure: Root node is S_{K
₁}. When the refinement conditions of formula(7) is met, CC-CSA makes refinements in corresponding knowledge space: $\begin{matrix} S_{split} (t) = S_{K_{2, q,} j}, j = \underset{j = 1, 2, ..., m}{argmax} Δ I_{j}, \\ s.t. x_{j}^{best} (t) \in S_{K_{2, q}}, x_{j}^{best} (t - 1) \in S_{K_{2, q}} . \end{matrix}$

Obviously, refinement only can occur at leaf nodes and the variable with the maximum information gain is selected as the refinement direction. And then, according to the formula(6), the chaotic mutation operator is adaptively adjusted in each sub-region as: $\begin{matrix} x_{ij} (t + 1) = x_{ij} (t) + \\ a_{ij}^{H} (t) \frac{w_{i}}{n} \exp (\frac{- α i}{T}) (u_{K_{2, q}, j}) (t) - l_{K_{2, q}, j} (t)), \\ s.t. f (x_{K_{2, q}}^{best} (t)) > r, r \in (0, 1) . \end{matrix}$

where u_{K_2,q,j} (t) and l_{K_2,q,j} (t) are the j’s upper limit and lower limit of the jth dimension in the sub-region: S_{K
_2,q}, $f (x_{K_{2, q}}^{best} (t))$ is the fitness of optimal solution of S_{K
_2,q}.

Given the above, we can summarize the characteristics of CC-CSA as follows:

The higher fitness of individual is, the smaller w_i and its mutation scale are.

The mutation scale decreases with the continuous evolution iteration.

The smaller feasible solution region is, the smaller mutation scale is.

Therefore, we can conclude that knowledge-guided chaotic mutation in CC-CSA can be adaptively adjusted to ensure the diversity of the population during evolution, which is beneficial to the latter evolutionary search.

The main steps of CC-CSA are as follows:

Step 1. Data preprocessing. population is normalized by: $X^{*} = \frac{X - min (X)}{max (X) - min (X)},$ (8) where max( X ) and min( X ) are made up of the maximum and minimum of X in each dimension.

Step 2. Detector generation. Candidate detectors: D_c (t) were randomly generated, and immune-tolerance training with the self set by affinity was conducted on them. The mismatched individuals were considered as mature detectors and put into the detector set: D(t).

Step 3. Constructing CA framework. population space, belief space and the initial knowledge are initialized by detector set, Accept(), Update() respectively.

Step 4. Cloning. The parent population P(t) (some memory detectors selected and D(t)) is cloned to get the child population D_ch (t).

Step 5. Crossover and chaotic mutation. According to the knowledge in the belief space, the D_ch (t) is processed with crossover and chaotic mutation to build the offspring population: D_off (t) through Influence().

Step 6. Evaluating and update. fitnesses of all individuals in D(t) and D_off (t) are calculated, and the superior individuals are selected to build the next generation population.

Step 7. Updating knowledge. According to the fixed-proportion in Accept(), the superior individuals from the generation D(t + 1) are selected and sent to the belief space to extract the knowledge and update the knowledge library by Update().

Step 8. Judging by the ending conditions. If the result of Objective() satisfies the ending conditions, finish the process; else t = t+1 and turn to Step 1. the Objective() of CC-CSA is set as the maximum number of evolution.

4.2 Pseudo code

Input:

Train ( S _nosf, S _sf):

training data set, consists of S _nosf (nonself set) and S _sf (self set)

D _c:

candidate detector set

D :

mature detector set

D _m:

memory detector set, constantly updated during the detection phase

P _t:

parent population

D _ch:

child population

D _off:

offspring population

f[]:

fitness array

n_p:

the population size

the current iteration times

the maximum of iteration times

P _v:

mutation probability

P _c:

crossover probability

Output:

the final population P _t after training

Functions:

Initialization ():

data preprocessing and parameter setting

Belief ():

construct and update CA framework

Knowledge ():

extract and update knowledge

Generate ():

Randomly generate candidate detectors

Tolerance ( D _c):

Put D _c into S _sf for immune tolerance training, and get the D (| D |=n_p);

Selection ( D _m):

Randomly select some memory detectors from D _m

Evaluate ( P _t):

Calculate the fitness of P _t

Clone ( P _t):

Clonal operation with P _t

CMK ( D _ch, f[]):

Crossover and chaotic mutation operation based on Knowledge and fitness with D _ch

BEGIN:

{ D _off=Ø, f[]=Ø; t = 1;// initializing

Initialization ();

D _c = Generate ();

D = Tolerance ( D _c);

P _t = Selection ( D _m)+ D ;

Belief ();

Knowledge ():

while(t++≤T) {

if (| P _t|<n_p) {

new D _c = Generate ();

new D = Tolerance ( D _c);

P _t = P _t +new D ;

}

f[] = Evaluate ( P _t);

D _ch = Clone ( P _t);

D _off = CMK ( D _ch, f[]);

D = Tolerance ( D _off);

P _t = Selection ( D _m)+ D ;

Belief ():

Knowledge ():

}

END.

In detection phase, the data to be tested also needs to be preprocessed. If some detector captures some abnormal data by negative selection algorithm (NSA, similar to immune tolerance training) [34], the algorithm will alarm and update.

According to the above, because the traditional CSA is easy to get a local optimum and has a slow convergence speed, we introduce CA double-layer evolution framework and instruct the crossover and chaotic mutation operator based on knowledge to adaptively control the scale of chaotic mutation to jump out from the local optima and make an accurate search in the latter period of evolution to accelerate the convergence.

4.3 Algorithm convergence analysis

Theorem 1: The population sequence: {X (t) , t ⩾ 0} of CC-CSA is a finite homogeneous Markov chain, where t is the number of evolution iteration.

Proof: As the other evolutionary algorithms, the state transitions of CC-CSA are performed in a finite space, besides the vector’s elements in the population space are different, so the population is finite.

Due to: $X (t + 1) = T (X (t)) = T_{s}^{C} \circ T_{m}^{C} \circ Θ (X (t)) .$

where Θ is the cloning operation, $T_{m}^{C}$ represents mutating operation, $T_{s}^{C}$ represents selecting operation. The three functions are independent of t. That is, X (t + 1) is only related to X (t). So { X (t),t ≥ 0} is a finite homogeneous Markov chain.

Assuming that, X (t) = { x¹, x², … xⁿ } is the population of tth-generation, x_i is the ith individual, f is the fitness function of X (t). And $B^{*} = {x | max (f (x)) = f^{*}} (x \in X (t))$ is the set of optimal solution. f* is the global optimal value. So we can get:

Definition: f_t = max { f (x) :i = 1,2, …n} represents the highest fitness in tth-generation. If the following conditions are met, the algorithm is convergent. $lim_{t \to \infty} p {f_{t} = f^{*}} = 1 .$

Theorem 2: CC-CSA converges with probability of 1.

Proof: Markov chain can be used to describe the state transferring process of CC-CSA. All approximate solutions of each population are regarded as the state set: S = {S¹, S²,..., S^T}. $X_{t}^{i}$ represents that the tth-generation X _t is in the state s_i, s_i= (x¹, x², ..., xⁿ) ∈ S.

Define: $f (s_{i}) = (f (x^{1}), f (x^{2}) \dots, f (x^{n})) .$ If f (s_i) = f (s_j) or the first nonzero component of f (s_i) - f (s_j) is positive, we identify f (s_i) ≥ f (s_j).

Define: $I = {i | s_{i} ⩾ s_{j}, \forall s_{j} \in S} .$ And we can know from above, If i ∈ I, s_i= (x¹, x², ..., xⁿ)is satisfied with: $f (x^{1}) = f (x^{2}) = \dots f (x^{n}) = f * .$ Therefore, s_i ∩ B* ≠ ∅.

Assuming the transferring probability of random process { X _t } is p_ij : $p_{ij} (t) = p {\frac{X_{t + 1}^{j}}{X_{t}^{i}}} .$ Because the mutation process is guided by knowledge, the reserved individuals is optimal, which are used to the next clone selection. So if t ≥ 0, f ( X _t + 1) > f ( X _t ), and the population will not degrade during the evolution process.

If i ∈ I, j ∉ I, then p_ij = 0. So we can get the optimal solution from the parent population.

If i ∉ I, j ∈ I, in addition, f ( X _t + 1) > f ( X _t ), so p_ij > 0.

Define: p_i(t) is the probability of the population: X _t in the state s_i, and $p (t) = \sum_{i \notin I} p_{i} (t) .$ Through the characteristics of Markov chain, we can know: $\begin{matrix} p (t + 1) = \sum_{s_{i} \notin S} \sum_{j \notin I} p_{i} (t) p_{ij} (t) \\ = \sum_{i \in I} \sum_{j \notin I} p_{i} (t) p_{ij} (t) + \sum_{i \notin I} \sum_{j \notin I} p_{i} (t) p_{ij} (t) . \end{matrix}$ (9) And due to: $\begin{matrix} \sum_{i \notin I} \sum_{j \notin I} p_{i} (t) p_{ij} (t) \\ + \sum_{i \notin I} \sum_{j \in I} p_{i} (t) p_{ij} (t) = \sum_{i \notin I} p_{i} (t) = p_{t}, \end{matrix}$ So we can know: $\sum_{i \notin I} \sum_{j \notin I} p_{i} (t) p_{ij} (t) = p_{t} - \sum_{i \notin I} \sum_{j \in I} p_{i} (t) p_{ij} (t) .$ (10) Taking the formula (10) into the formula (9), we can get: $0 ⩽ p_{t + 1} < \sum_{i \in I}^{n} \sum_{j \notin I}^{n} p_{i} (t) p_{ij} (t) + p_{t} = p_{t} .$ So lim_t→∞ p_t = 0.

Due to: $lim_{t \to \infty} {f_{t} = f *} = 1 - lim_{t \to \infty} \sum_{i \notin I} p_{i} (t) = 1 - lim_{t \to \infty} p_{t} .$ We can know: $lim_{t \to \infty} p {f_{t} = f *} = 1 .$ Therefore, the algorithm converges with the probability of 1.

5 Experiments and analyses

The experiments were carried out under a local area network consisting of 6 PCs., one of which acts as a server to train the detectors, the remaining 5 are used as clients to send test datasets. The operating system is Redhat CentOS 6.5.

In abnormal detection, the detection performances of the algorithms are measured mainly by calculating the detection rate (DR) and false-positive rate(FR): $\begin{matrix} DR = TP / (TP + FN), \\ FR = FP / (FP + TN) . \end{matrix}$ where TP is the amount of abnormal samples identified correctly. FN is the amount of abnormal samples regarded as normal. FP is the amount of normal samples regarded as abnormal. TN is the amount of normal samples identified correctly.

5.1 Data processing and parameter setting

The experiments used the KDD CUP 1999 10-percent dataset which is well-known in relevant research fields, contains 494021 samples with 41 dimensional features. There are 39 abnormal types in the dataset. Before experiments, the data set was reconstructed dimensionally by principal component weighted real-valued negative selection (PCW-RNS) algorithm [34]. And then, the first 14 dimensional principal component features of each sample, sorted in descending order, were selected to construct the experimental data set. The training set contains 22 abnormal types, randomly selected 4000 abnormal samples and 1000 normal samples to generate, train and optimize the detectors by CC-CSA. and the test set contains the remaining 17 abnormal types, randomly selected 4000 abnormal samples and 1000 normal samples to test the detection performances of optimized detectors. Finally, 500 mature detectors were obtained.

The experiment platform is artificial immune network monitoring system(AINM) [35]. the traditional CSA module was replaced by the CC-CSA or other comparison algorithms, so as to adjust the experimental platform. The activation threshold of D_m is 15 in AINM. Due to the large gap between the data used by the original AINM and the adjusted AINM in these experiments, the detector lifetime of the adjusted AINM was shortened in equal proportion. After shortening, the lifetime of the mature detector became 1 minute, and the lifetime of the memory detector became 6 minutes. P _c was set as 0.8 and the P _v was set as 0.1. The experiments only consider two types of knowledge, so N _K = 2; according to the formula(4-5), α∈ [0,0.5], was set as 0.3 in this paper, which can ensure that each type of knowledge affected at least 30% of the mutant individuals in the population.

In the detection phase, the 5 clients sent 10 samples to the server each time, and sent 100 times in total. Each experiment was repeated 10 times, and the mean and standard deviation of detection results were recorded as the experimental results.

5.2 The experimental analysis of affinity matching threshold

Affinity matching threshold is the key parameter of artificial immune algorithms, should be set firstly. The affinity calculation usually uses the Euclidean distance. In the data set after PCW-RNS, the biggest affinity value between antigen and antibody is: ${(\sum_{i = 1}^{14} (1 - 0)^{2})}^{1 / 2},$ so the affinity matching threshold: dis ∈ (0, $\sqrt{14}$ ). The detection results with different dis are shown in Fig. 3.

Fig. 3

Detection results with different affinity matching thresholds in AINM with CSA.

As can be seen, the whole detection results can be divided into three parts: (1) when dis∈ [0.1,1.5], with the increase of dis, both the DR and FR increased gradually. The growth rate of DR was fast, while the growth rate of FR was slow, and the overall effects tended to be good. (2) When dis ∈ [1.5,2], the DR continually increased and tended to be stable, while the FR starts to accelerate. (3) When dis [2,3, 2,3], DR remained stable, but FR increased sharply and the overall effects began to deteriorate.

Therefore, dis should be between [1.5, 2]. Comparing the detection results of this range, when dis = 1.8, the detection rate was 87.65%, and the false alarm rate was 3.32%, and the overall effects were the best. Therefore, dis was set as 1.8 in the experiments.

5.3 The experimental analysis of detection stability with CC-CSA

The detection stability is very important and can be measured by the mean and standard deviation of the experimental results under the same conditions. In this experiment, 5 test date sets were randomly selected, and the selection method, parameter setting and experimental process of each test dataset were the same as above. The detection results were summarized in Figs. 4 and 5.

Fig. 4

CC-CSA’s DR results.

Fig. 5

CC-CSA’s FR results.

It can be seen that, FR on data set 2 has the best result, DR on data set 4 has the best result, the mean of DR and FR on data set 5 are the worst, and the standard deviation of DR and FR on data set 3 are the largest and most unstable. the standard deviations of DR and FR on each data set were within reasonable range. Because different data sets contain different characteristics, such differences of experimental results in different data sets are ideal and acceptable.

Meanwhile, by comparing with Fig. 3, the actual detection results are better than that of the original CSA on any data set in general. This shows that the CC-CSA optimized by CA and chaos mechanism is better than the original CSA in terms of detection stability and detection results, so it can be proved that CC-CSA can evolve to a better optimal solution than original CSA.

5.4 The experimental analysis between CC-CSA and CCSA

In order to verify the optimization effects of CA on CC-CSA, this experiment compared the detection performances in different iterative cycles between CC-CSA and chaotic CSA(CCSA, only uses chaotic mutation without CA). Parameter setting and experimental procedure were the same as above. The experimental results were shown in Fig. 6.

Fig. 6

The detection performance comparison between CC-CSA and CCSA.

(1) Convergence: CC-CSA tended to converge within the iteration period of [70, 80] as the results of DR and FR tended to be stable. the evolution process was in a steady convergence state throughout the whole period; However, CCSA tended to converge in the iteration period of [130, 140], and in the iteration period of [80, 110], the iteration trend had a certain volatility. This shows that CA’s double-layer evolution framework based on knowledge and the crossover and adaptive chaos mutation scale can find the optimal solution space more accurately, accelerate the convergence, and guarantee the stability of convergence.

(2) Detection performances: Before convergence, the detection performances of CC-CSA were better than that of CCSA. After convergence, the detection performances of the two algorithms were almost the same. This shows that chaotic good spatial distribution can help CSA to broaden evolutionary search range. But only use a fixed chaotic mutation without knowledge guidance, CCSA was easier to fall into the local optima in the middle iteration period and wasted a large part of time in local optimization, which resulted in an unsatisfactory detection performances. On the contrary, in CC-CSA, the crossover and adaptive chaotic mutation scale based on knowledge guidance can make the CC-CSA search global optima more accurately, jump out from some local optima to avoid iterative evolution in some local search space and make CC-CSA converge to the global optimal solution with steady acceleration.

5.5 The experimental analysis between CC-CSA and some other up-to-date improved CSAs

In order to verify that CC-CSA has better optimization effects on CSA, we compared it with some other representative and up-to-date improved CSAs:

CN-CSA [36]: with chaos mechanism and niche technology, it has better population diversity and convergence.

PSO-CSA [37]: with particle swarm optimization, by minimizing the inter-individuals movements, it can accelerate the convergence speed.

DE-CSA [38]: with differential evolution bilinear second-order blind source separation, it has a better robustness to noise.

decomposition-CSA [39]: with decomposition mechanism which was employed to clone less-crowded individuals for evolution, it can enhance whole evolution effects by quantifying sub-problems.

cluster-CSA [40]: with cluster in a dynamic fitness landscape, it has better search ability for global optimization.

Parameter setting and experimental procedure were the same as above, and the test data used the whole data set. The experimental results were shown in Figs. 7 and 8.

Fig. 7

DR results of the six algorithms.

Fig. 8

FR results of the six algorithms.

Convergence: It can be analyzed from Figs. 7 and 8:

CC-CSA and Cluster-CSA had the best convergence effects, and the processes were similar, both converged at about 80th iteration smoothly and rapidly as the results of DR and FR tended to be stable;

PSO-CSA can quickly entered a better convergence state, but the whole evolution process fluctuated greatly, and there was no absolute convergence ultimately;

The convergence process of the other three algorithms is similar, which had converged at about 120th iteration, but had slight fluctuation before and after convergence.

Detection performances: It can be analyzed from Fig. 7 and 8:

efore convergence, the detection performances of Cluster-CSA were slightly better than that of CC-CSA. After convergence, the CC-CSA’s DR was better than that of Cluster-CSA, but the FR was slightly worse than that of Cluster-CSA. Overall, these two algorithms had the best evolutionary results;

Before the 40th iteration, the detection performances of PSO-CSA were comparable to that of Cluster-CSA and CC-CSA, and better than that of the 3 other algorithms. However, after the 40th iteration, PSO-CSA began to be weaker than Cluster-CSA and CC-CSA. After the 80th iteration, it began to be weaker than the other 3 algorithms, and got the worst detection performances. Moverover, its detection performances fluctuated the most during the whole evolution process;

The other three algorithms were not ideal in the detection performances before convergence, and slightly worse than Cluster-CSA and CC-CSA after convergence, and also had certain fluctuation before and after convergence.

From the above analyses, it can be seen that the overall evolution process of Cluster-CSA and CC-CSA were the best, PSO-CSA was the worst, and the other three algorithms were in the middle. However, the cluster algorithm needs to set the k (number of sub-cluster) in advance and is sensitive to the initial classification state of the data set. The computational cost of clustering operation is also greater than that of the CA. Therefore, the practical evolution efficiency and effects of CC-CSA are better than the other representative and up-to-date improved algorithms. In all, It can be seen from all the above experimental analyses that chaos mechanism can indeed help CSA to search for the global optimum as much as possible to improve the detection performances and maintain a high detection stability. CA based on knowledge can help CCSA to adaptively adjust the scale of chaotic mutation so as to search the global optimum more accurately and accelerate the evolution convergence under the premise of guaranteeing the high detection performances. The combination of CA and chaos mechanism for CSA evolution is also better than other representative and up-to-date improved CSA algorithms in the overall detection performances. Thus, the feasibility of CC-CSA and its advantages in accelerating convergence and avoiding local optima are illustrated.

6 Conclusion

In order to make the balance between the global and local search and take full advantage of the knowledge in the population evolution and ability of chaos mechanism to cover problem space to solve the local optima and slow convergence of CSA, CC-CSA proposed in this paper uses the CA and its double-layer evolution framework to continually extract the knowledge of samples from the population space to update the knowledge library, which is used to adaptively adjust the population’s chaotic mutation scale, reduce some unnecessary evolution, and make the population evolve more precisely and rapidly towards the global optimal direction, to improve the quality of the detectors and enhance the abnormal detection performances eventually. Experimental results confirm the above conclusion.

Nevertheless, CC-CSA still needs to be tested on more data sets to verify its actual detection performances. Especially, its adaptive adjusting ability under dynamic environments needs to be further analyzed and improved.

Conflict of interest statement

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Footnotes

Acknowledgments

This work was sponsored by the National Natural Science Foundation of China (61172168), Natural Science Foundation of Heilongjiang Province (F2018019).

References

Marinakis

, Marinaki

and Migdalas

, A hybrid clonal selection algorithm for the location routing problem with stochastic demands[J], Annals of Mathematics and Artificial Intelligence 76(1-2) (2016), 121–142.

Chen

C.H.

and Yang

S.Y.

, Efficient DE-based symbiotic cultural algorithm for neuro-fuzzy system design[J], Applied Soft Computing 34 (2015), 18–25.

de Castro

L.N.

and Von Zuben

F.J.

, Learning and optimization using the clonal selection principle[J], IEEE Trans on Evolutionary Computation Special Issue on Artificial Immune Systems 6(3) (2002), 239–251.

Hong

, Wang

J.Z.

, Zhang

, et al., Average convergence rate estimation of clonal selection algorithm[J], Advances In Mechanical Engineering 9(9) (2017), 1–6.

Yin

C.Y.

, Ma

L.Y.

and Feng

, Towards accurate intrusion detection based on improved clonal selection algorithm[J], Multimedia Tools and Applications 76(19) (2017), 19397–19410.

, Ding

Y.S.

, Ren

L.H.

, et al., Degeneration recognizing clonal selection algorithm for multimodal optimization, IEEE Transactions on Cybernetics 48(3) (2018), 848–861.

Zhang

W.W.

, Lin

J.J.

, Jing

H.L.

, et al., A novel hybrid clonal selection algorithm with combinatorial recombination and modified hypermutation operators for global optimization[J], Computational Intelligence and Neuroscience, 2016, Article ID: 6204728.

Yin

C.Y.

, Ma

L.Y.

and Feng

, A feature selection method for improved clonal algorithm towards intrusion detection[J], International Journal of Pattern Recognition and Artificial Intelligence 30(5) (2016), Article ID: 1659013.

Ulker

E.D.

, An improved clonal selection algorithm using a tournament selection operator and its application to microstrip coupler design[J], Turkish Journal of Electrical Engineering and Computer Sciences 25(3) (2017), 1751–1761.

10.

Teran

, Aguilar

and Cerrada

, Integration in industrial automation based on multi-agent systems using cultural algorithms for optimizing the coordination mechanisms[J], Computers In Industry 91 (2017), 11–23.

11.

Pan

Z.L.

, Chen

and Zhang

G.Z.

, Efficient design method for cell allocation in hybrid CMOS/nanodevices using a cultural algorithm with chaotic behavior[J], Frontiers of Physics 11(2) (2016), Article ID: 116201.

12.

Omran

M.G.H.

, A novel cultural algorithm for real-parameter optimization[J], International Journal of Computer Mathematics 93(9) (2016), 1541–1563.

13.

Liu

W.Y.

and Lin

C.C.

, Spatial forest resource planning using a cultural algorithm with problem-specific information[J], Environmental Modelling & Software 71 (2015), 126–137.

14.

Rafiei

, Niknam

and Khooban

M.H.

, Probabilistic electricity price forecasting by improved clonal selection algorithm and wavelet preprocessing[J], Neural Computing & Applications 28(12) (2017), 3889–3901.

15.

Shang

R.H.

, Ma

H.N.

, Wang

, et al., Immune clonal selection algorithm for capacitated arc routing problem[J], Soft Computing 20(6) (2016), 2177–2204.

16.

Dornelles

L.T.

, Sa

L.B.D.

and Mesquita

A.C.D.

, Synthesis of low sensitivity broadband matching networks using clonal selection algorithm[J], Latin America Transactions 14(7) (2016), 3168–3177.

17.

Dong

X.B.

, Zhao

D.X.

, Yang

, et al., Fractional-order control of active suspension actuator based on parallel adaptive clonal selection algorithm[J], Journal of Mechanical Science and Technology 30(6) (2016), 2769–2781.

18.

Sayed

S.A.F.

, Nabil

and Badr

, A binary clonal flower pollination algorithm for feature selection[J], Pattern Recognition Letters 77 (2016), 21–27.

19.

Zareizadeh

, Helfroush

M.S.

and Kazemi

, A new multiobjective evolutionary optimization algorithm based on theta-multiobjective clonal selection[J], Journal of Intelligent & Fuzzy Systems 32(3) (2017), 1685–1696.

20.

Avatefipour

and Nafisian

, A novel electric load consumption prediction and feature selection model based on modified clonal selection algorithm[J], Journal of Intelligent & Fuzzy Systems 34(4) (2018), 2261–2272.

21.

Yan

X.S.

, Song

and Wu

Q.H.

, An improved cultural algorithm and its application in image matching[J], Multimedia Tools and Applications 76(13) (2017), 14951–14968.

22.

Zou

, Li

A.Q.

, He

X.C.

and Wang

X.M.

, Optimal operation of cascade hydropower stations based on chaos cultural sine cosine algorithm[C], The 3rd Asia Conference On Power and Electrical Engineering, Kitakyushu, Japan, March 22, 2018 – March 24, 366 (2018), 1–6.

23.

Wang

X.M.

, Hao

W.Q.

and Li

Q.M.

, An adaptive cultural algorithm with improved quantum-behaved particle swarm optimization for sonar image detection[J], Scientific Reports, 2017, 7, Article ID: 17733.

24.

Guo

Y.N.

, Yang

, Wang

, et al., Cultural particle swarm optimization algorithms for uncertain multi-objective problems with interval parameters [J], Natural Computing 16(4) (2017), 527–548.

25.

Khan

S.U.

, Qureshi

I.M.

, Zaman

, et al., Detecting faulty sensors in an array using symmetrical structure and cultural algorithm hybridized with differential evolution[J], Frontiers of Information Technology & Electronic Engineering 18(2) (2017), 235–245.

26.

Gao

H.Y.

, Liang

Y.S.

, Liu

D.D.

, et al., IIR digital filter design based on cultural quantum-inspired flower pollination algorithm[C]. the 17th IEEE International Conference On Communication Technology, Chengdu, China, October 27, 2017 – October 2017 (30), 1693–1697.

27.

Guo

Y.N.

, Cheng

and Gong

D.W.

, Interval multi-objective quantum-inspired cultural algorithms[J], Neural Computing & Applications 30(3) (2018), 709–722.

28.

Ali

M.Z.

, Awad

N.H.

, Reynolds

R.G.

, et al., A balanced fuzzy cultural algorithm with a modified levy flight search for real parameter optimization[J], Information Sciences 447 (2018), 12–35.

29.

Ali

M.Z.

, Awad

N.H.

and Suganthan

P.N.

, et al., A modified cultural algorithm with a balanced performance for the differential evolution frameworks[J], Knowledge-based Systems 111 (2016), 73–86.

30.

Ali

M.Z.

, Suganthan

P.N.

, Reynolds

R.G.

, et al., Leveraged neighborhood restructuring in cultural algorithms for solving real-world numerical optimization problems[J], IEEE Transactions on Evolutionary Computation 20(2) (2016), 218–231.

31.

Ali

M.Z.

, Awad

N.H.

, Suganthan

P.N.

, et al., A novel hybrid Cultural Algorithms framework with trajectory-based search for global numerical optimization[J], Information Sciences 334 (2016), 219–249.

32.

Z.J.

and Liu

M.D.

, Research on cultural algorithm [J], Computer technology and development 18(5) (2008), 126–130.

33.

Guo

Y.N.

, Wang

and Cheng

, A class of adaptive chaotic culture algorithm[J], Control and Decision 24(4) (2009), 514–519.

34.

Wang

D.W.

and Zhang

F.B.

, Research on performance of detector in immune based intrusion detection system [D], Harbin University of Science and Technology, 2010.

35.

, An immune based model for network monitoring[J], Chinese Journal of Computers 29(9) (2006), 1515–1522.

36.

Hong

, Ji

Z.C.

and Gong

C.L.

, An improved clonal selection algorithm and its strong convergence nearly anywhere, Control and decision 25(5) (2010), 725–729.

37.

Caprihan

, Slomp Gursaran

and Agarwal

, A quantum particle swarm optimization approach for the design of virtual manufacturing cells[C]. Proceedings of 2009 IEEE International Conference on Industrial Engineering & Engineering Management, Hong Kong, China, 2019, 125–129.

38.

Jarboui

, Deville

, Hosseini

, et al., A second-order blind source separation method for bilinear mixtures[J], Multidimensional Systems and Signal Processing 29(3) (2018), 1153–1172.

39.

L.J.

, Lin

Q.Z.

, Liu

S.B.

, Gong

D.W.

, Carlos

, Coello

and Zhong

, A novel multi-objective immune algorithm with a decomposition-based clonal selection[J], Applied Soft Computing Journal, 2019, 81, Article Number: UNSP105490:1–14.

40.

Zhang

W.W.

, Zhang

W.Z.

, Gary

G.Y.

and Jing

H.L.

, A cluster-based clonal selection algorithm for optimization in dynamic environment[J], Swarm and Evolutionary Computation, 2019, Article Number:100454, 1–13.