A novel prediction model based on particle swarm optimization and adaptive neuro-fuzzy inference system

Abstract

Reasonable structure of human resource is of great significance to development of an organization, so accurate prediction of human resource structure is a very important research problem. Adaptive Neuro-Fuzzy Inference System (abbreviated as ANFIS) is a high-efficiency learning model, and its distributed network structure has very effective result in establishing nonlinear model and constructing time series prediction model. However, classical ANFIS has some disadvantages, such as difficult determination of structure and large randomness of training parameter setting. This paper provides a hybrid prediction model of human resource structure by using the algorithm based on fusion of PSO with random weight, RPSO, and ANFIS, named RPSO-ANFIS. The novel algorithm uses RPSO to train relevant parameters of ANFIS and determine network structure of ANFIS. Empirical results shows that, compared with GA-ANFIS and PSO-ANFIS, RPSO-ANFIS has advantages of rapid learning speed, high prediction accuracy and smaller relative mean error, which indicated RPSO-ANFIS has good practical application value in predicting the structure of human resource.

Keywords

Adaptive neuro-fuzzy inference system PSO the structure of human resources random weight fuzzy logic

1 Introduction

Talents in any organization are of complicated structure and hierarchy [1 –4]. In a society, a region or an industry and even in an enterprise, talents of different specialties and educational backgrounds constitute a multi-hierarchy complicated system—talents swarm. Task of human resource structure prediction is not only exploring talent structure status within a certain period but also conducting scientific and reasonable prediction of specialty matching and hierarchical structure of needed all kinds of talents in order to form the optimal human resource structure, exert maximum economic benefits of talent cultivation and utility, provide better human resource guarantee for organizational development and promote sound development of the organization. Hence, human resource structure prediction within an organization is of great practical significance and practical values. However, human resource structure is usually of discontinuity and complexity. It’s always difficult for common prediction method (such as neural network, etc) to reach good prediction effects.

Adaptive Neuro-Fuzzy Inference Systems (abbreviated as ANFIS) can solve problems such as high nonlinearity [5], complexity and discontinuity, etc. [6 –9], and it also has characteristics of high convergence rate, good stability, repeatable training process, high prediction precision, etc., and it’s especially suitable for handling problems related to time series prediction. Hence, ANFIS has provided a referable scheme for solving the problem of human resource structure prediction [10 –12]. However, it’s found in practical application that ANFIS has some deficiencies which have greatly limited further promotion and application of this method and mainly manifested at establishment of its model structure has great difficulties, and randomness of its training parameter setting is large [13, 14].

In recent years, there are some novel computational intelligence algorithms, such as SVM [15 –21], minimax probability machine [22], Fireworks Algorithm [23], swarm intelligence [24], and etc. Particle Swarm Optimization (PSO) is a random optimization algorithm based on swarm intelligence which was proposed by Kennedy and Eberhart in 1995, and this algorithm solves optimal solution of specific problem by simulating migrating and gathering behaviors of bird flock during foraging process. In this algorithm, individual behavior is influenced jointly by swarm behaviors and its own historical behaviors. At present, PSO algorithm has been widely applied to fields such as functional optimization, neural network training and fuzzy system control with its good optimization performance [25].

This paper adopted mixed learning method of PSO and least square method to determine parameters of ANFIS structure. This mixed-type method mainly used PSO to train antecedent parameters of ANFIS network model and least square method to train its consequent parameters.

Structure of this paper was arranged like this: Section 2 introduced human resource structure prediction model based on PSO and ANFIS, Section 3 adopted human resource data in recent years of one organization to conduct prediction analysis and compared PSO-ANFIS algorithm with standard ANFIS algorithm; Section 4 gave the conclusion.

2 Methods

2.1 ANFIS

ANFIS is an adative network based fuzzy inference system proposed by Jang on basis of Takagi-Sugeno model (or T-S model, Sugeno model0. Study shows that when membership function which adopts trapezoid or non-triangle is input, the number of fuzzy rules and input fuzzy sets needed by T-S system is small, thus this model is suitable for system modeling based on data collection. ANFIS has realized combination of fuzzy logic inference and neural network, so this structural form has both advantages of the two: the former can easily express human knowledge and the latter has advantages of distributed information storage and learning ability. ANFIS is a significant development of intelligence science and provides new effective method for processing of engineering information.

Common rule sets with two fuzzy if-then rules in ANFIS model:

Rule 1: if x is A1 and y is B1, then $f_{1} = p_{1} x + q_{1} y + r_{1}$

Rule 2: if x is 2 and y is B2, then $f_{2} = p_{2} x + q_{2} y + r_{2}$

Typical ANFIS structure is as shown in Fig. 1, in order to realize learning process of T-S fuzzy model, it’s generally transformed into a self-adaption network, namely ANFIS. This self-adaption network is a multilayer feedforward network, and square nodes in it need to conduct parameter learning. Nodes at the same layer have the same function.

Fig.1

The Structure of ANFIS.

Here output of the jth node at layer i is O_i,j.

The first layer, which is the membership function layer of input variables, is responsible for fuzzification of input signals.

Node i has output function: O_1,i = μ_{A
_i} (x), O_1,i = μ_{B
_i} (y), (i = 1, 2).

Whereby x and y are inputs of Node i, A_i and B_i are fuzzy sets, O_1,i is membership function value of A_i and B_i and represents the degree of x and y belonging to A_i and B_i. Shapes of membership degree functions μ_{A
_i} and μ_{B
_i} are totally determined by some parameters, and these parameters are called antecedent parameters such as clock-type function: $μ_{A_{i}} (x) = \frac{1}{(1 + {| \frac{x - c_{i}}{a_{i}} |}^{2 b_{i}})}$ whereby {a_i, b_i, c_i} are called antecedent parameters.

The second layer, which is the rule strength release layer, is responsible for multiplying input signals.

Output of each node represents credibility of this rule. $O_{2, i} = ω_{i} = μ_{A_{i}} (x) * μ_{B_{i}} (y)$

The third layer is the normalization layer of all rule strengths. The ith node calculates normalization credibility of the ith rule. $O_{3, i} = {\bar{ω}}_{i} = ω_{i} / (ω_{1} + ω_{2})$

The fourth layer can calculate output of fuzzy rules, each node i at this later is self-adaption node. Output of the ith node is: $O_{4, i} = {\bar{ω}}_{i} f_{i} = {\bar{ω}}_{i} (p_{i} x + q_{i} y + r_{i}), (i = 1, 2)$

Whereby ${\bar{ω}}_{i}$ is the output at the third layer, and p_ix + q_iy + r_i are parameter sets of this mode which are also called consequent parameters.

The fifth layer, which has one fixed node, can calculate total output of all input signals. $O_{5, i} = \sum {\bar{ω}}_{i} f_{i} = \sum ω_{i} f_{i} / \sum ω_{i} = {\bar{ω}}_{1} f_{1} + {\bar{ω}}_{2} f_{2}$

When antecedent parameters are given, output of ANFIS can be expressed as linear combination of consequent parameters through the following transformation: $\begin{matrix} O_{5, i} & = & \sum {\bar{ω}}_{i} f_{i} = \sum ω_{i} f_{i} / \\ \sum ω_{i} = {\bar{ω}}_{1} f_{1} + {\bar{ω}}_{2} f_{2} \\ = & {\bar{ω}}_{1} (p_{1} x + q_{1} y + r_{1}) \\ + {\bar{ω}}_{2} (p_{2} x + q_{2} y + r_{2}) = ({\bar{ω}}_{1} x) p_{1} \\ + ({\bar{ω}}_{1} y) q_{1} + ({\bar{ω}}_{1}) r_{1} + ({\bar{ω}}_{2} x) p_{2} \\ + ({\bar{ω}}_{2} y) q_{2} + ({\bar{ω}}_{2}) r_{2} = R \cdot θ \end{matrix}$

Elements of column vector θ consist consequent parameter set {p₁, q₁, r₁, p₂, q₂, r₂}; least square method can be used to obtain optimal estimation $\hat{θ}$ under minimum meaning of the value of ∥R · θ - f ∥ ², namely $\hat{θ} = (A^{T} A)^{- 1} A^{T} f$ . According to identification result $\hat{θ}$ of consequent parameters and $\hat{f} = A$ $\hat{θ}$ , estimated output $\hat{f}$ of ANFIS can be calculated; finally root-mean square error (RMSE): $RMSE = \sqrt{\sum_{k = 1}^{t} ({\hat{f}}_{k} - f_{k})^{2} / t}$ under current antecedent and consequent parameters is calculated.

ANFIS generally adjust antecedent and consequent parameters of the system with mixing algorithm of BP algorithm and least square method. In the mixing algorithm, forward-direction phase calculates to the fourth layer, least square method is then used to identify consequent parameters. Error signals in reverse-direction phase conducts reverse transmission, and BP algorithm is used to update antecedent parameters. During forward-direction learning process of network, input values of N groups of training data are adopted to solve values of p_i, q_i and r_i and the output value O_5,i. According to rules of least square method, O_5,i values calculate calculated values and originally expected error value of training data, and this error value will be reversely returned and corrects premise parameters according to maximum gradient method. During the process of changing these parameters, modification of membership function graphs is continuously realized, expecting to realize the goal of reaching minimum output error during set cyclic process.

2.2 RPSO

In 1995, American social psychologist-James Kennedy and electrical engineer Russell Eberhart jointly proposed particle swarm algorithm, and its basic idea was enlightened by research results of modeling and simulating bird flock behaviors. Their model and simulation algorithm mainly modified model of Frank Heppner to make particles fly to solution space and land at the best solution.

In a D-dimensional searching space, n particles consist a particle swarm, and each particle is a D-dimensional vector, and its spatial position is expressed as x_i = (x_i1, x_i2, …, x_iD), i = 1, 2, … n. Spatial position of particles is a solution in target optimization problem, adaption value can be calculated by substituting this spatial position into adaption function, and advantages and disadvantages of particles can be measured according to size of adaption value; flying speed of the ith particle is also a D-dimensional vector and recorded as v_i = (v_i1, v_i2, …, v_iD); the position which the ith particle with the best adaption value has gone through is called the best historical value of the individual and it’s recorded as p_i = (p_i1, p_i2, …, p_iD); the best position which the whole particle swarm has gone through is called the best global historical position and it’s recorded as p_g = (p_g1, p_g2, …, p_gD), evolutionary equation of particle swarm can be described as: $\begin{matrix} v_{ij} (t + 1) & = & v_{ij} (t) + c_{1} r_{1} (t) (p_{ij} (t) - x_{ij} (t)) \\ + c_{2} r_{2} (t) (p_{gj} (t) - x_{ij} (t)) \end{matrix}$ (2.1) $x_{ij} (t + 1) = x_{ij} (t) + v_{ij} (t + 1)$ (2.2)

Where by: subscript j represents the jth dimension of particle, subscript I represents particle I, t represents the tth generation, c₁ and c₂ are acceleration constants which are usually within (0,2), r₁ ∼ U (0, 1), r₂ ∼ U (0, 1) are two mutually independent random functions. It can be seen from above evolutionary equation that c₁ is step length which regulates particle to fly to the direction of its best position, and c₂ is the step length which regulates particle to fly to global best position.

By analyzing some features of basic particle swarm, it can be known that the first part in Equation (2,1) is previous speed of particle; the second part is “perception” part which represents though of the particle itself; the third part is “social” part which represents social information sharing between particles.

In this paper, RPSO is used to train the structure of ANFIS. In RPSO algorithm, random weight ω is used in the classical PSO. $θ = θ_{min} + (θ_{max} - θ_{min}) * N (0, 1)$ (2.3) $ω = θ + σ * N (0, 1)$ (2.4)

So, formula 2.1 can be modified as follow,

$\begin{matrix} v_{ij} (t + 1) & = & ω * v_{ij} (t) + c_{1} r_{1} (t) (p_{ij} (t) - x_{ij} (t)) \\ + c_{2} r_{2} (t) (p_{gj} (t) - x_{ij} (t)) \end{matrix}$ (2.1)

2.3 Prediction model based of human resource structure on PSO and ANFIS: RPSO-ANFIS

Each learning process based on chaotic particle swarm learning algorithm includes antecedent parameter learning phase and consequent parameter learning phase, and its learning algorithm flow is:

Step 1. Initialize particle swarm in searching space, and give initial values to position vector and speed vector;

Step 2. Take position vector ({a_i, b_i, c_i}) of each particle as antecedent parameters, calculate incentive strength ω_i and normalized incentive strength ${\bar{ω}}_{i}$ of all rules; adopt least square method to identify consequent parameter $\hat{θ} : (p_{i}, q_{i}, r_{i})$ ; finally calculate root-mean-square error (RMSE) generated by ANFIS corresponding to this particle as adaption value of this particle;

Step 3. Compare current adaption value RMSE_j of each particle with its own p_best and update p_best;

Step 4. Compare current adaption value RMSE_j of each particle with best adaption value G_best of its swarm, and update G_best;

Step 5. Update weight using formula (2.3) and (2.4);

Step 6. If maximum iteration is reached, then output results, or skip back to Step 2 and go on the following steps.

Flow chart of this algorithm is as shown inFig. 2.

Fig.2

Flow Chart of PSO-ANFIS Algorithm.

3 Empirical analysis and discussion

3.1 Dataset

This paper adopted dataset as shown in Table 1, and this dataset represented human resource conditions of one large-scale company. This table includes 12 groups of data representing human resource conditions in recent 12 years of this company. The algorithm in this paper took gross output, economic benefits and total number of enterprise staff as input data and proportions of management personnel and technical personnel in total number of staff as output data to respectively establish human resource structure prediction model based on RPSO-ANFIS model.

Table 1
Statistical table of human resources in 12 Years

Year Gross Economic Total Proportions of Proportions

output benefits number of management of technical

enterprise personnel personnel

staff (%) (%)

1 89 000 3 200 30 108 5.06 60.66

2 96 000 3 380 29 183 4.59 62.68

3 113 000 3 800 29 190 4.66 62.97

4 147 000 4 900 28 130 4.47 64.14

5 165 000 6 400 28 211 4.11 62.18

6 194 000 7 500 26 857 3.85 61.92

7 230 000 9 310 25 668 3.69 61.88

8 297 000 12 000 23 247 3.80 59.96

9 335 000 14 200 22 468 3.44 59.86

10 412 000 19 700 22 084 3.40 59.86

11 501 000 26 100 21 905 3.31 59.74

12 615 000 35 200 20 885 3.29 59.69

Year	Gross	Economic	Total	Proportions of	Proportions
1	89 000	3 200	30 108	5.06	60.66
2	96 000	3 380	29 183	4.59	62.68
3	113 000	3 800	29 190	4.66	62.97
4	147 000	4 900	28 130	4.47	64.14
5	165 000	6 400	28 211	4.11	62.18
6	194 000	7 500	26 857	3.85	61.92
7	230 000	9 310	25 668	3.69	61.88
8	297 000	12 000	23 247	3.80	59.96
9	335 000	14 200	22 468	3.44	59.86
10	412 000	19 700	22 084	3.40	59.86
11	501 000	26 100	21 905	3.31	59.74
12	615 000	35 200	20 885	3.29	59.69

3.2 Calculation results and discussion

Enterprise development relies on its occupation, allocation and usage conditions of human resources (mainly management personnel and technical personnel). Hence, when we predict human resource structure, the main prediction targets are proportions of management personnel and technical personnel. Data in Table 1 is divided into two parts, 10 groups of data are taken as learning and training set of PSO-ANFIS network, and the other 2 are taken as inspection dataset. The operating environment is i5 2.60 GHz CPU, 64-bit Windows7 operating system.

Experiment finds that: training precision reaching 10^–5 satisfies expected requirements; Fig. 2 is training error curve of ANFIS network. It can be obviously obtained that: as the network adopts mixing algorithm namely least square method and RPSO algorithm during training process, initialization and learning convergence rate of the network are fast, and the network continuously corrects errors, and finally tend to be stable. The key of ANFIS network prediction is selection of the number of membership functions. After multiple experiments, the prediction effect is the best when 3 membership functions are selected.

In order to verify performance of this algorithm, this paper compared prediction effects of GA-ANFIS, PSO-ANFIS and RPSO on the same dataset. Convergence curves of the two algorithms in predicting proportions of management personnel and technical personnel are respectively as shown in Figs. 3 and 4. It can be found from Figs. 3 and 4 that no matter predicting proportion of management personnel or predicting that of technical personnel, convergence rate of RPSO-ANFIS algorithm is obviously superior to that of GA-ANFIS and RPSO-ANFIS, which process that in this dataset, RPSO-ANFIS model embodies good convergence performance.

Fig.3

Convergence Curves of GA-ANFIS, PSO-ANFIS and RPSO in Predicting Proportion of Management Personnel.

Fig.4

Convergence Curves of GA-ANFIS, PSO-ANFIS and RPSO in Predicting Proportion of Technical Personnel.

4 Conclusions

This paper presents a prediction model based on RPSO and ANFIS. The model is used to predict human resource structure need of one company. Prediction results show that RPSO-ANFIS model could reasonably handle all kinds of major factors within enterprise and had good convergence performance. It’s seen from numerical experiment that PSO-ANFIS model could highly precisely predict human resource structure of the enterprise and laid a foundation for scientifically formulating human resource plans and even making all kinds of human resource management decision of the enterprise. This model has provided a new approach for human resource structure prediction, and good experimental results also indicate that this new algorithm has the favorable application prospect.

Footnotes

Acknowledgments

This work is partly supported by Guangdong Natural Science Foundation (NO. 2015A030313664), Guangdong science and technology project (NO. 2016A070713004), Guangzhou science and technology project (NO. 2016A070713004 and 2017A040403068) and Special Foundation for applied science and technology development of Guangdong Province (NO. 2015B010131017). The authors have been supported by a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology.

References

Stone

D.L.

, Deadrick

D.L.

, Lukaszewski

K.M.

, et al., The influence of technology on the future of human resource management, Human Resource Management Review25(2) (2015), 216–231.

Stone

D.L.

and Deadrick

D.L.

, Challenges and opportunities affecting the future of human resource management, Human Resource Management Review25(2) (2015), 139–145.

Greene

P.G.

, Brush

C.G.

and Brown

T.E.

, Resources in small firms: An exploratory study, Journal of Small Business Strategy8(2) (2015), 25–40.

Navimipour

N.J.

, Rahmani

A.M.

, Navin

A.H.

, et al., Expert cloud: A cloud-based framework to share the knowledge and skills of human resources, Computers in Human Behavior46 (2015), 57–74.

Pérez-García

V.M.

, et al., Applied mathematics and nonlinear sciences in the war on cancer, Applied Mathematics and Nonlinear Sciences1 (2016), 423–436.

Wang

J.S.

and Lee

C.S.G.

, Self-adaptive neuro-fuzzy inference systems for classification applications, IEEE Transactions on Fuzzy Systems10(6) (2002), 790–802.

Güler

and Übeyli

E.D.

, Adaptive neuro-fuzzy inference system for classification of EEG signals using wavelet coefficients, Journal of Neuroscience Methods148(2) (2005), 113–121.

Kim

and Kasabov

, HyFIS: Adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems, Neural Networks12(9) (1999), 1301–1319.

Çaydaş

, Hasçalik

and Ekici

, An adaptive neuro-fuzzy inference system (ANFIS) model for wire-EDM, Expert Systems with Applications36(3) (2009), 6135–6139.

10.

Tripura

and Babu

, Intelligent speed control of DC motor using ANFIS, Journal of Intelligent & Fuzzy Systems26(1) (2014), 223–227.

11.

Wang

, Zhang

, Lu

, et al., Developing a car-following model with consideration of driver’s behavior based on an Adaptive Neuro-Fuzzy Inference System, Journal of Intelligent & Fuzzy Systems30(1) (2015), 461–466.

12.

Meysam Seyyedbarzegrar

and Mirzaie

, ANFIS based model for power loss estimation of metal oxide surge arrester, Journal of Intelligent & Fuzzy Systems29(5) (2015), 1779–1786.

13.

Aghdam

I.N.

, Varzandeh

M.H.M.

and Pradhan

, Landslide susceptibility mapping using an ensemble statistical index (Wi) and adaptive neuro-fuzzy inference system (ANFIS) model at Alborz Mountains (Iran), Environmental Earth Sciences75(7) (2016), 1–20.

14.

Yaïci

and Entchev

, Adaptive Neuro-Fuzzy Inference System modelling for performance prediction of solar thermal energy system, Renewable Energy86 (2016), 302–315.

15.

Xia

, Wang

, Sun

and Wang

, Steganalysis of least significant bit matching using multi-order differences, Security and Communication Networks7(8) (2014), 1283–1291.

16.

, Sheng

V.S.

, Wang

, Ho

, Osman

and Li

, Incremental learning for ν-Support Vector Regression, Neural Networks67 (2015), 140–150.

17.

Xia

, Wang

, Sun

, Liu

and Xiong

, Steganalysis of LSB matching using differences between nonadjacent pixels, Multimedia Tools and Applications75(4) (2016), 1947–1962.

18.

Yuan

, Sun

and Rui

L.V.

, Fingerprint liveness detection based on multi-scale LPQ and PCA, China Communications13(7) (2016), 60–65.

19.

, Sheng

V.S.

, Tay

K.Y.

, Romano

and Li

, Incremental support vector learning for ordinal regression, IEEE Transactions on Neural Networks and Learning Systems26(7) (2015), 1403–1416.

20.

, Sheng

V.S.

, Wang

, Ho

, Osman

and Li

, Incremental learning for ν-support vector regression, Neural Networks67 (2015), 140–150.

21.

, Sheng

V.S.

and Li

, Bi-parameter space partition for cost-sensitive SVM, Proceedings of the 24th International Conference on Artificial Intelligence, 2015, pp. 3532–3539.

22.

, Sun

and Sheng

V.S.

, Structural minimax probability machine, IEEE Transactions on Neural Networks and Learning Systems (2016). DOI: 10.1109/TNNLS.2016.2544779

23.

Bing

, Ning

and YeHong

, LAV path planning by enhanced fireworks algorithm on prior knowledge, Applied Mathematics and Nonlinear Sciences1(1) (2016), 65–78.

24.

Liu

and Fu

, An effective clustering algorithm with ant colony, Journal of Computers5(4) (2010), 598–605.

25.

Liu

, Optimization design on fractional order PID controller based on adaptive particle swarm optimization algorithm, Nonlinear Dynamics84(1) (2016), 379–386.