Time series prediction with a hybrid system formed by arti...

Scientia Iranica E (2019) 26(2), 942{958

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringhttp://scientiairanica.sharif.edu

Time series prediction with a hybrid system formed byarti�cial neural network and cognitive developmentoptimization algorithm

U. Kosea;1;� and A. Arslanb

a. Computer Sciences Application and Research Center, Usak University, Usak, Turkey.b. Department of Computer Engineering, Konya Food and Agriculture University, Konya, Turkey.

Received 10 August 2016; received in revised form 5 August 2017; accepted 6 June 2018

KEYWORDSTime series prediction;Time series analysis;Arti�cial neuralnetworks;CognitiveDevelopmentOptimizationAlgorithm (CoDOA);Arti�cial intelligence.

Abstract. Time series prediction is a remarkable research interest that is widely followedby scientists and researchers. Because many �elds include processes of such time seriesanalyses, di�erent kinds of approaches, methods, and techniques are employed often inorder to achieve alternative ways of prediction. It appears that arti�cial-intelligence-basedsolutions have strong potential for providing e�ective and accurate prediction approachesin even most complicated time series structures. For further details and explanation, thisstudy aims to introduce an alternative arti�cial-intelligence-based approach to arti�cialneural networks and cognitive development optimization algorithm, as a recent intelligentoptimization technique introduced by the authors. This study aims to predict di�erentkinds of time series by using the introduced system/approach. In this way, it is possible todiscuss application potential of the hybrid system and report �ndings related to its successof prediction. The authors believe that the study provides a good chance to support theliterature with an alternative solution approach and see the potential of a newly developed,arti�cial-intelligence-based optimization algorithm for di�erent applications.© 2019 Sharif University of Technology. All rights reserved.

1. Introduction

Arti�cial intelligence is an important research �eldapplied to problems of almost all real-life �elds.Nowadays, it has become apparent that the needfor intelligent solution approaches is a vital factor inovercoming real-world problems e�ectively. Because oftheir high potential for success, arti�cial intelligence

1. Present address: Deptartment of Computer Engineering,Faculty of Engineering, Suleyman Demirel University, E9Block, Z-23, West Campus, 32260, Isparta, Turkey.

*. Corresponding author. Tel.: +90532 590 83 26Fax: +90 276 221 21 53E-mail addresses: [email protected] (U. Kose)[email protected] (A. Arslan).

doi: 10.24200/sci.2018.20033

has outstanding popularity, leading to intense designand development of new approaches, methods, or tech-niques. Furthermore, it has also been a traditional wayto apply each newly introduced arti�cial-intelligence-based solution approach to problems of di�erent �elds.

Considering the �elds of mathematics and statis-tics, there are many di�erent types of problems inwhich arti�cial intelligence is often employed. At thispoint, it appears that data series preformed with timefactor is among attractive research interests. Accordingto the literature, the term time series is de�ned as ow of data saved over time: weekly, monthly, oreven yearly [1-4]. It has been realized that timeseries may enable us to understand many aspectsof the subject or event from which time series dataare obtained. Accordingly, time series analysis hasbecome a remarkable application; hence, the growing

U. Kose and A. Arslan/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 942{958 943

popularity of such applications is in `predicting thefuture ow of time series. To predict the future ow oftime series is to analyze previous states of time seriesto �nd more information about the ow in the future.The background of this approach bene�ts from the ideaof the past patterns of time series that will be observedin the future [1].

The approach of time series prediction corre-sponds to events or problems from almost all �elds ofour life. Thus, future conditions related to changes in�nancial values, sales, productions or even behaviorsof natural dynamics can be predicted by means of thetime series prediction. Thus, it is possible for scien-tists, researchers, or experts within a �eld to imaginefuture status and, �nally, reach decisions about newapplications or problem solutions. Eventually, timeseries prediction has become an important applicationas a result of unstoppable, chaotic changes in the reallife and the nature of `uncertainty' because of thissituation.

Based on the literature of time series prediction,traditional approaches or methods have failed to adaptto a complicated and new form of time series [5]. Hence,remarkable e�orts have been made to introduce andemploy alternative solutions to overcome predictionproblems of di�cult and challenging time series. Thus,it was noticed that the usage of arti�cial intelligencecould overcome the related issues and, furthermore,o�er many advantages of `intelligent mechanisms' tosolve real-world problems. This �eld has become apopular application interest when time series predictiongained importance in the context of an encounteredproblem. Today, development of arti�cial-intelligence-based hybrid systems is one of the most attractiveapplications; hence, there are many examples of timeseries prediction applications conducted via hybridsystems structured with more than one method ortechnique.

The purpose of this study is to employ an alter-native, arti�cial-intelligence-based approach to time se-ries prediction. The study equipped with arti�cial neu-ral networks and cognitive development optimizationalgorithm, which is a recently introduced optimizationtechnique, focuses on a hybrid system. As a supportivefactor for the training process of the arti�cial neuralnetwork model, cognitive development optimizationalgorithm is a single-objective optimization algorithmdrawing inspiration from ideas regarding cognitive de-velopment by Piaget [6-9]. This study aimed to predictdi�erent kinds of time series by using the introducedsystem/approach. In this way, it was possible todiscuss application potential of the hybrid system andreport �ndings related to its success on prediction. Inaddition, the authors believed that this study couldbe a good chance to support the literature with analternative solution approach and see the potential of a

newly developed, arti�cial-intelligence-based optimiza-tion algorithm with di�erent applications.

Motivation and the main contributions here canbe expressed brie y as follows:

� The study deals with a remarkable research interestas `time series prediction';

� The study tries to employ an alternative approachto the literature of time series prediction;

� The study employs a novel prediction approach byusing cognitive development optimization algorithmfor the �rst time for training model(s) of arti�cialneural network to perform time series prediction;

� The study aims to deal with predicting advancedtime series through showing its chaotic characteris-tics;

� The study generally proves that hybrid arti�cialintelligence techniques are e�ective enough in pre-dicting time series, even though they are chaotic.In this way, more practical and e�ective aspects ofarti�cial intelligence techniques can be understoodaccording to traditional approaches.

This study is structured as follows. The secondsection concerns the background for application ofarti�cial-intelligence-based techniques in time seriesprediction. Afterwards, the third section explainsmaterials and methods used within the study. In thisway, readers are provided with enough informationabout arti�cial neural networks, cognitive developmentoptimization algorithm, and the designed predictionsystem/approach. The third section is followed bysome information on the applications aimed at pre-dicting some time series (the fourth section). Next,the �fth section reports the results obtained with the(chosen) ANN-CoDOA system. Then, a comparison-based evaluation process with the system and someother alternative ones are done and explained in thesixth section. The seventh section is devoted to a briefdiscussion. Finally, the paper ends with conclusionsand suggestions for some future studies.

2. Background

When we focus on the associated literature, it ispossible to see many alternative studies on time seriesprediction. Because there has been a remarkableinterest in such scienti�c studies, newly introduced ap-proaches, methods, and techniques have been employedin time series prediction studies in order to evaluatethe success of these `new comers'. It is also importantthat arti�cial intelligence appears as a strong factorto perform successful studies on time series prediction.Because this study also focuses on the employment ofan arti�cial intelligence technique, it is better to take a

944 U. Kose and A. Arslan/Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 942{958

brief look into the recent literature on the intersectionof arti�cial intelligence and time series prediction. Asextending the previous background review done by theauthors in [10], some remarkable research studies fromthe literature are as follows:

� Gan et al. and Wong et al. performed someprediction-based research studies using Arti�cialNeural Networks (ANN) technique [11,12];

� In a research, Gentili et al. employed fuzzy logic,feed forward neural network, and a nonlinear localpredictor to perform prediction operations on aperiodic hydrodynamic oscillatory time series [13];

� Chen and Han performed a study on predictingmultivariate chaotic time series. They used a RadialBasis Function (RBF) for prediction processes [14];

� In their study, Wu et al. developed a predictionapproach to chaotic time series [15]. Brie y, theypredicted time series of Mackey-Glass, gas furnace(Box-Jenkins), and EEG. At this point, the pre-diction processes were done by iterated extendedKalman �lter supported by single multiplicativeneuron model;

� Yadav et al. published a study in 2007 [16] concern-ing Single Multiplicative Neuron (SMN) for timeseries prediction purposes. On the other hand,Zhao and Yang performed a study similar to [14];however, they used PSO-SMN to predict time seriesof Mackey-Glass, gas furnace (Box-Jenkins), andEEG [17];

� Yao and Liu ran a Fuzzy Logic (FL) predictionprocess to overcome prediction problem(s) aboutatmospheric visibility in Shanghai [18];

� Particle Swarm Optimization (PSO) was used byUnler to perform optimization-based time seriesprediction operations [19]. Similarly, Zhao and Yangused particle swarm optimization for predictionpurposes [20];

� The literature contains many di�erent studies basedon the employment of Ant Colony Optimization(ACO) to predict systems with chaotic ows [5,21-24];

� Yeh introduced a model that provides a parameter-free simpli�ed swarm optimization for training Arti-�cial Neural Network (ANN) [25]. In this study, themodel was run over di�erent time series (includingEEG time series);

� In their study, Nourani and Andalib employeda Wavelet Least Square Support Vector Machinesystem (WLSSVM) to predict hydrological timeseries [26]. Aiming to predict Suspended SedimentLoad (SSL) on a monthly basis for the Aji-ChayRiver, the authors performed a comparison-based

approach by including some other approaches, suchas ad-hoc Least Square Support Vector Machine(LSSVM) and even models of Arti�cial NeuralNetwork (ANN), to obtain prediction results;

� Regarding the sub-�eld of machine learning, Bon-tempi et al. produced a book chapter to providereviews of recent approaches for predicting the timeseries via speci�c machine learning techniques [27].By providing a research study aimed at predictinggeneral time series, this study is di�erent from thealternatives aiming to handle chaotic time seriesonly. It is an important background study with itstimeline of wide scope;

� The literature also comes with some studies inwhich the authors employ some hybrid systemsstructured via optimization algorithms and SVMto overcome time series prediction problem. Forexample, Hu and Zhang employed Support VectorMachines (SVM) and Chaotic Simulated AnnealingAlgorithm (CSAA) to predict time series [28]. Onthe other hand, Liu and Yao employed a hybridsystem, including PSO and least square SVM, toperform prediction processes [29]. Readers arereferred to [30-36] for more details about SVM onprediction problems;

� Ren et al. studied predicting short-term tra�c owvia an arti�cial-intelligence-based approach. In thiscontext, they used a prediction approach includ-ing BP Neural Network-Niche Genetic Algorithm(NGA) [37]. In another study on predicting tra�c- ow, Ding et al. predicted `lane-change trajectoryby drivers' in urban tra�c ow [38]. In the contextof predicting urban tra�c ow, Yin et al. devel-oped an alternative approach and introduced theFuzzy-Neural Model (FNM) for predict tra�c owobserved in urban street network [39];

� Dunne and Ghosh applied an alternative approachto predict tra�c ow (hourly) by considering rainfalle�ects [40]. In detail, they employed a neuro-wavelet model including Stationary Wavelet Trans-form (SWT);

� As a three-technique hybrid system formation,Pulido et al. employed Ensemble Neural Networks(ENN)-fuzzy logic (as Type-1-Type-2) and ParticleSwarm Optimization (PSO) to perform predictionsover Mexican stock exchange [41];

� Huang et al. used Chaos over BP Arti�cial NeuralNetworks (CBPANNs) system supported by GeneticAlgorithm to perform time series predictions [42].Brie y, they employed their system to predict windpower. In another study on predicting powerand speed of wind, Jiang et al. used a hybridsystem based on Support Vector Regression (SVR)model and Cross Correlation (CC) analysis. They


supported their system with the algorithms ofCuckoo Search (CS) and Brainstorm Optimization(BSO) [43] and applied the research to wind turbinesrunning on a wind farm (China);

� Doucoure et al. used multi-resolution analysis alongwith arti�cial wavelet neural network model to pre-dict wind speed [44]. Brie y, the authors developeda prediction system that could be used in the contextof renewable energy sources. In general, the mainpurpose of the study was to apply intelligent, alter-native management approach to a micro grid systemby achieving renewable energy within isolated andgrid-connected power systems [44];

� Chandra used a recurrent neural networks systemtrained by means of the technique of CooperativeCoevolution (CC) to predict chaotic time series [45];

� In their study, Chai and Lim used arti�cial neuralnetworks and weighted fuzzy membership func-tions (NEWFM) to perform business cycle predic-tions [46]. In detail, the authors used some chaotictime series [adjusted leading composite index timeseries with coordinate embedding (time-delay)] forthe NEWFM and predicted the ow of business inthis way [46];

� Seo et al. employed arti�cial neural networksand adaptive neuro-fuzzy inference system to per-form prediction operations on water levels trackeddaily [47]. The theory of wavelet decompositiontheory was also used within this research study;

� Marzban et al. conducted a research for predictingsome chaotic time series [48]. In detail, they ben-e�ted from di�erently structured Dynamic NeuralNetworks (DNN) to predict chaotic systems such asMackey-Glass and Henon Map;

� Okkan employed a Wavelet Neural Network-based(WNN) approach to perform reservoir in- ow pre-dictions monthly (as the data obtained from thebasin of Kemer Dam in Turkey) [49]. In detail,the system used here includes Discrete WaveletTransform (DWT)-Feed Forward Neural Networks(FFNN), which is supported by the Levenberg-Marquardt optimization algorithm;

� Zhou et al. developed a dendritic neuron model(with dendritic functions and phase space recon-struction) to predict �nancial time series of Shang-hai Stock Exchange Composite Index, DeutscherAktienindex, DJI Average, and N225 [50];

� In a research study, Wang et al. used Di�erentialEvolution (DE) supported by Teaching-LearningBased Optimization (TLBO) to predict chaotic timeseries [51];

� Regarding the prediction of time series with chaotic ow, Heydari et al. employed a Takagi Sugeno Kang

(TSK) second-order fuzzy system supported by AN-FIS (Arti�cial Neural Fuzzy Inference System) [52];

� Wang et al. studied time series prediction bymeans of a back propagation-based neural networkmodel trained by Adaptive Di�erential Evaluation(ADE) [53]. The authors obtained positive, im-proved results within their study;

� Catalao et al. used a hybrid system in their studyto predict short-term electricity prices [54]. Indetail, they employed Particle Swarm Optimization(PSO), Wavelet Transform (WT), and ANFIS fortheir research purposes;

� Kose and Arslan (the authors) used an ANFIS-Vortex Optimization Algorithm (VOA) system toachieve time series prediction [10]. In the study,they focused on chaotic time series and predictedtime series of electroencephalogram (EEG) success-fully [10];

� Patra et al. employed an adaptive Local Linear(optimized) Radial-Basis Functional Neural Net-work (LLRBFNN) model to predict �nancial timeseries [55]. The system was successful enough inpredictions and showed better performances thansome other alternative systems reported in thestudy;

� In another recent study on �nancial time seriesprediction, Ravi et al. built a hybrid model in-cluding three di�erent solution elements [56]. Theydesigned some three-stage hybrid models by em-ploying chaos for constructing the phase space inStage 1, Multi-Layer Perceptron (MLP) networkmodel in Stage 2, and particle swarm optimiza-tion with multi-objective mechanism (MOPSO) andelitist Non-Dominated Sorting Genetic Algorithm(NDSGA) in Stage 3;

� M�endez et al. used a di�erent approach to predictboth short-term and long-term time series [57]. Indetail, they built a Modular (structured) NeuralNetwork (MNN) model with two methods of com-petitive clustering and winner-takes-it-all.

By following the rapid look into the associatedliterature, it is now more meaningful to focus on thetime series prediction approach, built with Arti�cialNeural Networks and the intelligent optimization tech-nique of cognitive development optimization algorithmin this study. Fundamentals of the techniques and thehybrid system of these techniques will be explainedrespectively in the next section.

3. Materials and methods

Essential features/functions of the techniques, i.e.,arti�cial neural networks and cognitive development


optimization algorithm, and also details regarding thepredicting approach, as materials and methods of thisstudy, are as follows.

3.1. Arti�cial neural networksSince the �rst introduction of arti�cial intelligence�eld, popularity of some general techniques has rapidlyincreased because they are capable of solving most ofproblems accurately. Arti�cial Neural Network (ANN)is one of these techniques, still applied to di�erent kindsof problems related to di�erent �elds. ANN is a generalmodel of data processing system, which is inspired fromthe human brain structure. Generally, a typical ANNmodel includes some arti�cial neurons, which are somekind of distributed, parallel calculation elements. Bytaking some sets of arti�cial neurons, it is possible toform di�erent ANN models. A typical ANN model candeal with many tasks such as classi�cation, prediction,intelligent optimization, control, pattern recognition,etc. [58-69]. The general structure of a multi-layer ANNis provided in Figure 1 [68].

The �rst structure of arti�cial neuron was intro-duced by McCulloch and Pitts [70]. Besides, therewere a remarkable increase in research studies andintroduction of di�erent ANN models (i.e., Multi-layeror single perceptron, self-organizing map, ADALINE,adaptive neuro-fuzzy inference system, and probabilis-tic network) [56-58,60,62,69,71-73].

Simply, the intelligent mechanism of an ANNworks as follows. It learns from the environment andresponds appropriately to newly encountered situationsby means of the learned experiences or information,which is similar to the mechanism of humans' (and evensome other living organisms) behavior towards learningnew things from experiences and using them for solvingnew problems (or solving already known problemsbetter) [60-62,69,71-73]. Learning an ANN can be doneby three di�erent learning strategies: supervised learn-

Figure 1. Structure of a multi-layer ANN [68].

ing, unsupervised learning, and reinforcement learning.Supervised learning deals with inputs and desiredoutputs to train ANN, while unsupervised learning usesonly inputs, and the reinforcement learning focuses onfeedback value(s) received [60-62,69,71-73].

Common ANN is structured as follows. The net-work includes arti�cial neurons connected to each otherover weights. In general, an arti�cial neuron employsinput(s) with weight(s), a function of summation, andan output. Herein, inputs are multiplied by weightvalues, and the sum of them is used by a transferfunction. The output by the transfer function is thatof the neuron [69,71-73]. Larger models of ANN canbe obtained by using such connections more and morealong arti�cial neurons [69,73].

Nowadays, ANN is still popular in the sense ofarti�cial-intelligence-based applications, as indicatedbefore. At this point, the hybrid system formation iscommon usage of ANN.

3.2. Cognitive development optimizationalgorithm

Cognitive Development Optimization Algorithm(CoDOA) is one of the recent intelligent optimizationalgorithms, introduced by Kose and Arslan withsimple equations and inspiration from ideas by Piagetfor the subject of cognitive development [6,7-9,74].Cognitive development is known as every person'simprovement in terms of knowledge, and Jean Piagetexplained that concept. In detail, Piaget indicatesthat a person's cognitive development is completedthrough di�erent stages of development: socialinteraction, maturation, balancing over new concepts,and improvement of cognitive background [7-9,74].CoDOA is currently used in many studies and runwidely in interdisciplinary applications.

Typically, the CoDOA employs the running pro-cess of the following stages [6,74]:

� Stage of initialization;� Stage of socialization;� Stage of maturation;� Stage of rationalizing;� Stage of balancing.

The listed stages are algorithmic ones designedthrough inspiration from the stages run within cog-nitive development period. In the CoDOA, designedstages (so, steps) are repeated in a loop until thestopping criteria are met [6,74].

CoDOA with its algorithmic steps is as follows (inthe most recent form) [6,74-75]:

� Step 1 (stage of initialization): De�ne thealgorithm parameters (N for particle number, exfor experience of a particle, ir for interactivity rate,


max ir for max. ir (min ir is 0.0), r for the rational-ity rate, and ml for maturity limit. Adjust necessaryvalues/parameters for the objective problem.

� Step 2: Randomly locate the particles over solutionspace. Calculate �tness. Upgrade ir of the particlewith the best �tness so far by a random value:

best p ir (new)

= best p ir (current)

+(ran:�best p ir (current)); (1)

also, add 1 to ex of that particle.

� Step 3: Loop steps.

Step-3.1 (stage of socialization): Subtract 1from ex of the particles with the least mean �tnessamong all particles (if the aim is minimization).Add 1 to ex of the particles with �tness undermean �tness among all particles (if the aim isminimization). Upgrade ir of these particles by arandom value:

pj ir (new) = pj ir (current)

+ (ran:�pj ir (current)): (2)

Step 3.2: Upgrade ir of all particles by a randomvalue:

pi ir (new) = ran:�pi ir (current): (3)

Step 3.3: Refresh positions of the particles(except from the best one so far) by the followingequation:

pi pos: (new) = pi pos: (current)

+ (ran:�(pi ir (current)�(global

best pos:� pi pos: (current)))): (4)

Step 3.4: Calculate �tness. Apply Eq. (1) forthe best particle and add 1 to its ex.Step 3.5. (stage of maturation): Upgrade irof all particles having ex better than ml (less ifthe aim is minimization, and more if the aim ismaximization) by the following equation:


+ (ran:�pj ir (current)): (5)

Apply Eq. (1) for the best particle and add 1 toex of that particle.

Step 3.6 (stage of rationalizing): Upgrade irand positions of the particle with ex less than 0by the following equations:


+ (ran:�(best p� ir (current)=pj

ir (current))); (6)

pi pos: (new) = pi pos: (current)

+ (ran:�(pi ir (current)�(global

best pos: pi pos: (current)))): (7)

By using Eq. (8), upgrade r times ir of theparticles with ex being at least 0:

pj ir (new) = pj ir (current) + (ran:�(best

p ir (current)=pj ir (current))): (8)

Step 3.7 (stage of balancing): Upgrade ir ofall particles by Eq. (9):

pi ir (new) = ran:�pi ir (current): (9)

Step 3.8: Calculate �tness. Apply Eq. (1) forthe best particle and add 1 to its ex.Step 3.9: For big problems, check stability andrun in-system optimization if necessary. Turnback to the start of the loop if the stoppingcriteria have not been met, yet.

� Step 4: Find optimum value(s) mean solution-optimum solution.

CoDOA employs simple equations for making iteasier to design and apply. Hence, it has been usedfor the ANN model in this study in order to havean alternative approach to time series prediction andrealize the potential of the CoDOA in such problemsolutions.

CoDOA is an algorithm/technique that is thesubject of a sub-�eld called swarm intelligence. In-cluded under arti�cial intelligence, swarm intelligencedeals with particle-based systems derived from the ideaof behaviors seen among social swarms (i.e., birds,�shes, bees, ants, and even humans) observed incollectivity [69,76]. In association with this sub-�eld,many di�erent intelligent algorithms/techniques struc-tured especially for optimization problems have beendeveloped in the literature so far. For example, ParticleSwarm Optimization (PSO), Ant Colony Optimization(ACO), Cuckoo Search (CS), and Arti�cial Bee Colony(ABC) are some of today's popular swarm intelligence


Figure 2. Flow chart of CoDOA.

algorithms/techniques. Readers are referred to [77-84] to get detailed information regarding swarm intel-ligence and the known algorithms/techniques.

Considering the algorithmic steps, a concise owchart of the CoDOA appears in Figure 2.

3.3. Time series prediction approach of ANNsupported by CoDOA

Time series prediction approach designed here is basedon two Arti�cial Intelligence techniques: ANN andCoDOA. The system structured over these techniquesis some kind of hybrid one aiming to predict futurestates of time series. ANN-CoDOA system brie yemploys an ANN model trained by the CoDOA. Due toits simplicity, CoDOA has been employed to train theANN model instead of traditional training approaches,i.e., back-propagation algorithm.

The approach considered here appears not veryinnovative; however, CoDOA has been employed forthe �rst time to train ANN to predict time series. Thenovelty/innovation here may deal with the predictionsuccess according to alternative approaches and as a�rst-time alternative in the associated literature. Thefollowed prediction approach is as follows:

� For training, particles of the CoDOA are associated

with weight and bias of the ANN (CoDOA wasemployed to optimize the weight and bias);

� ANN is trained according to the Mean Square Errorcriteria by considering di�erences between obtainedoutput values and desired output values;

� ANN model is Multi-Layer Perceptron (MLP) em-ploying four inputs and one output;

� ANN model brie y tries to predict x(t+ 3) by usingx(t), x(t� 3), x(t� 6), and x(t� 9). It is importantto mention here that there are many di�erent com-binations of lags used for the prediction approach.However, performed past studies have shown thatthese lags have been the most appropriate ones. Ofcourse, further investigations are always open foralternative choice of lags.

Figure 3 shows a brief view of the ANN-CoDOAprediction system.

4. Applications of time series prediction

It is an important point to understand the e�ectivenesslevel of the designed system in order to understand ifit can overcome the problem of prediction and becomean alternative in the associated literature. Therefore,


Figure 3. ANN-CoDOA prediction system.

it has been applied to di�erent time series data in orderto test its accuracy in prediction. Here, four di�erentCoDOA settings (in the context of parameters) havebeen used for a single ANN model structure, asexplained in the next paragraphs.

4.1. Considered time seriesThis study obtained time series from the `DataMarket',which is a Web source for enabling users to reachdi�erent kinds of data taken from the real life andvisualized over a platform for general use [85]. Onchoosing time series, greater degree of focus was givento the data of natural dynamics. It is importantthat all the chosen time series be drawn accordingto the saved/provided data points for each of them.Considered time series are brie y as follows [85]:

� ANN-CoDOA system has been used �rstly to pre-dict the dataset of `daily maximum temperaturesmeasured in Australia, Melbourne between 1981 and1990' [85]. From 3650 data rows, a sample of 1106data rows has been chosen for the prediction. Thistime series is called as `Application 1';

� Following the �rst prediction, the system has beenapplied to the dataset of `Application 2' relating to`winter negative temperature sum (in �C) between1781 and 1988' [85]. A total of 208 data rows havebeen chosen for the prediction;

� The third prediction (Application 3) has been doneon a dataset for the `mean annual Nile ow between1871 and 1970' [85]. A total of 208 data rows havebeen chosen for the prediction;

� The fourth prediction operation (Application 4) hasbeen performed by using the dataset for the `MackeyGlass time series corrupted with the noise levels at20 dB' [85]. Mackey Glass time series is actually atime series showing chaotic ows based on Eq. (10)[86]. For this time series, a total of 700 data rowshave been chosen for the prediction.

dxdt

= �x�

1 + xn�� x; ; �; n > 0: (10)

4.2. Settings of ANN and CoDOAAs mentioned before, four di�erent CoDOA settings(in the context of parameters) have been used fora single ANN model structure along with predictionapplications in this study. By performing predictionapplications to each hybrid system designed, the sys-tem with the best results has been chosen to take partin the comparison-based evaluation.

Table 1 provides information about essential set-tings of the ANN model structure used in the predictionapplications. On the other hand, di�erent parametervalues used for getting four di�erent CoDOA settingsare presented in Table 2.

Hybrid systems employing the same ANN andfour di�erent CoDOA settings have been applied to therelated time series. At this point, 65% of data (rows)for each time series have been used for the `training'processes; generally, predictions have been observedover the whole time periods by including all the pointswhether they are associated with the training (65% ofthe data) or not (remaining/35% of the data). Resultsobtained with the applications are reported under thenext section.

5. Application �ndings-results

To make sure which ANN-CoDOA solution is moresuccessful in predicting the used time series, predictionerrors obtained with four di�erent applications havebeen compared. In order to make comparisons, errorsin prediction performances have been calculated withthe Mean Absolute Error (MAE). MAE is presentedbrie y as follows [87].

Table 1. Settings of ANN used in the prediction applications.

Number of inputs (input layer) 4

ANN input(s) x(t), x(t� 3), x(t� 6), and x(t� 9)regarding the time series

Number of outputs (output layer) 1ANN output(s) x(t+ 3) regarding the time seriesNumber of hidden layer(s) 2Number of neurons at each hidden layer 8 neurons in each hidden layerUsed activation function Sigmoidal


Table 2. Four di�erent CoDOA settings.

Parameters Setting 1 Setting 2 Setting 3 Setting 4

Number of particles (N) 50 75 100 150

Iteration (stopping criterion) 1500 3000 6000 7500

Initial interactivity rate (ir) 0.15 0.25 0.50 0.75

Max. interactivity rate (ir) 5.0 5.0 10.0 10.0

Maturity limit (ml) 2 2 3 5

Rationality rate (r) 2 5 2 4

Table 3. MAE obtained with four di�erent ANN-CoDOA systems.

Application(time series)

ANN-CoDOA system including CoDOA with the

Setting 1 Setting 2 Setting 3 Setting 4

Application 1 15.5930 14.2297 11.6652 13.6155

Application 2 17.2641 16.8513 13.8674 13.3127

Application 3 13.2280 12.9501 11.0182 12.4883

Application 4 19.6382 18.9203 18.1366 20.0841

Let yi be the observation i and yi be the predic-tion regarding yi,

MAE = mean of jeij ; (11)

where ei = yi � yi: (12)

Table 3 presents MAE obtained with four di�erentANN-CoDOA systems.

Based on Table 3, the ANN-CoDOA system runaccording to Setting 3 (Table 2) has shown the best per-formance in three of the four prediction applications.In addition, the result of one remaining application(Application 2) is close enough to the best resultobtained. In this context, Figures 4 to 7 show thevisual summaries for the prediction applications donefor Application 1 to Application 4 by the ANN-CoDOAsystem including CoDOA with Setting 3. By meansof the �gures, readers can understand the predictionprocesses better by comparing both original timesseries (at the top with blue color) with the predictedtime series (at the bottom with red color).

The results obtained here show that the ANN-CoDOA system with Settings 3 of CoDOA is suc-cessful enough in predicting the related time seriesaccurately. In addition to the evaluation work, it isalso important to compare successful ANN-CoDOAwith some alternative systems, including the ANN andother techniques/algorithms of swarm intelligence. Inaddition, some recent alternative prediction approachescan be compared with the ANN-CoDOA. Details ofthese evaluation processes are provided under the sixthsection.

6. Comparison-based evaluation

In addition to the evaluation of predictions doneby ANN-CoDOA, a comparison-based evaluation wasperformed to realize the e�ectiveness of the ANN-CoDOA. At this point, the chosen (best) ANN-CoDOAsystem of former prediction results was compared withalternative hybrid systems, in which the same ANNmodel structure (Table 1) with changing optimizationalgorithms as trainers was used. The evaluation wasdone according to the same criteria under Eqs. (11)and (12).

As for the trainers, Particle Swarm Optimiza-tion (PSO) [82,88,89], Cuckoo Search (CS) [90,91],Fire y Algorithm (FA) [92,93], and Bat Algorithm(BA) [94,95] were used for the ANN, and each dif-ferent system was employed over the same time seriesconsidered in this study (the ANN-CoDOA system hasbeen run again during this evaluation in order to checkits harmony with the results previously obtained byapplications/evaluation).

Table 4 reports MAE obtained over the time seriesby di�erent ANN-based systems.

Results provided in Table 4 show that ANN-CoDOA is better than other systems for three of fourapplications. In addition, the result of Application3 is close to the best value obtained by ANN-CSsystem. Thus, we can say with con�dence thatthe ANN-CoDOA approach/system is successful ande�ective enough in predicting time series according toalternative hybrid, ANN-based systems.

Out of the comparison of di�erent ANN-basedsystems, the approach of ANN-CoDOA was compared


Figure 4. Prediction for Application 1: `daily maximum temperatures in Australia (Melbourne) between 1981 and 1990'.

Figure 5. Prediction for Application 2: `winter negative temperature sum (in deg. �C), between 1781 and 1988'.

with some alternative time series prediction approachesover the four applications. In detail, alternativetime series prediction approaches include DynamicBoltzmann Machine (DyBM) [96], Support Vector Ma-chine (SVM) [97], Hidden Markov Model (HMM) [98],

and Bayesian learning on Gaussian process model(BG) [99]. The authors of this study have developedthe related approaches again by considering their essen-tial features and functions introduced in the associatedstudies.


Figure 6. Prediction for Application 3: `mean annual Nile ow between 1871 and 1970'.

Figure 7. Prediction for Application 4: `Mackey glass time series corrupted with the noise levels at 20 dB'.

Table 5 presents the MAE obtained for the timeseries via ANN-CoDOA and some other alternativeapproaches.

According to Table 5, the ANN-CoDOA is goodfor two of the performed four applications when it is

compared with alternative prediction approaches outof ANN-based models. Considering all applications,it is possible to express that ANN-CoDOA generallyperforms well and has MAE values close to the betterones, even though it is not the best system to predict


Table 4. MAE obtained over the time series via �ve di�erent ANN based systems.


ANN-CoDOA ANN-PSO ANN-CS ANN-FA ANN-BA

Application 1 11.5899 22.1116 12.7588 18.5277 19.0280Application 2 14.1811 26.7781 14.5231 16.8091 14.1159Application 3 11.8569 21.6025 11.5894 19.8201 19.3862Application 4 18.0513 32.0989 19.1633 27.3165 22.6091

Table 5. MAE obtained for the time series via ANN-CoDOA and some other alternative approaches.


ANN-CoDOA DyBM [96] SVM [97] HMM [98] BG [99]

Application 1 11.7218 13.0855 12.8777 12.0317 14.5901Application 2 15.2146 20.7098 13.4511 15.1708 17.3047Application 3 11.8719 18.6231 11.9972 12.0350 20.1790Application 4 18.2398 28.5105 19.8071 17.6208 22.6311

the objective time series.

7. Derived ideas from the study

Considering the works done here, it is possible to men-tion some remarkable points brie y that are importantfor the characteristics of this study and its e�ects onthe associated literature(s):

� Predicting time series is a remarkable issue, espe-cially in Informatics era that requires rapidity informing information/data, manipulating it, sharingit, and obtaining alternative information/data (i.e.,future states, explanations for problems/solutions),which is greatly usable. Hence, the research studydone here is an important alternative to similarstudies done in the associated literature(s);

� Results obtained here show importance of arti�cialintelligence and its role in solving real-world prob-lems. It is also important that arti�cial intelligenceis a science building the future because of itsinterdisciplinary scope;

� Dealing with chaotic time series is an importantresearch way in time series prediction. This studybrie y shows the e�ectiveness of the introducedANN-CoDOA system/approach (and the role ofarti�cial intelligence and the related techniques) inpredicting chaotic time series successfully enough;

� According to the comparison done, the ANN systemsupported by CoDOA appears with better resultsthan some other alternative systems. Therefore,results obtained here can be accepted as a goodcontribution to the alternative research studies doneso far about time series prediction;

� Because the literature is a dynamic environment,which will always have better candidates, there is

an open opportunity for author(s) to continue futurestudies;

� Predicting natural dynamics is an important pointfor dealing with real-world problems. Researchstudy done here has been a good solution in thismanner;

� Swarm intelligence is an important sub-�eld ofarti�cial intelligence and employs the potential forthe future. Use of CoDOA here and its e�ectiverole in shaping the solution are remarkable pointsfor supporting the ideas about swarm intelligence;

� The author(s) think that the future of arti�cialintelligence is always based on designing appropriatehybrid systems by using the most recent approaches,methods, and techniques. This study is a re-markable example of developing a hybrid arti�cialintelligence system to solve real-world problems;

� By improving the scope of this research and addingsome modular components to the structure of thesystem, which is able to derive some feedbackfor people/users (according to meaning of futurestates of time series), thus forming general arti�cialintelligence systems, such as Expert Systems [100-102]. Furthermore, the designed hybrid system heremay be a small part of bigger, adaptive controlsystems, which continuously support some real-timeprocesses.

8. Conclusions and future studies

A hybrid time series prediction approach of Arti�cialNeural Network (ANN) and Cognitive DevelopmentOptimization Algorithm (CoDOA) techniques wereintroduced. As a new single-objective optimizationalgorithm, CoDOA is an algorithmic inspiration from


the ideas by Piaget expressed for cognitive develop-ment. The technique of CoDOA was used within ANNmodel to perform the learning process. Eventually, theusage of both these techniques enabled the authors toobtain an additional solution approach to time seriesprediction.

ANN-CoDOA system was applied to some timeseries data for testing its success and e�ectivenessin time series prediction. At this point, the ob-tained results showed that the ANN-CoDOA systemwas able enough to predict time series e�ectivelyenough. Additionally, the ANN-CoDOA system wasbetter than some other alternative prediction systemsbuilt with ANN and di�erent swarm intelligence tech-niques/algorithms. Research study done here has alsomany outputs as brie y expressed under the sectiondevoted to general discussion.

The authors were encouraged by the obtainedpositive results to continue future developments of theapproach and the hybrid system. In the context offuture studies, it was planned to apply the systemto more di�cult, alternative time series data in orderto investigate its success in time series prediction.Another planned future study is related to evaluatingthe prediction performance of the approach/systemby changing parameters of both ANN and CoDOAtechniques and considering alternative lags chosen fromtime series as inputs to the ANN and not investigatedbefore. Finally, there will be also some studies onusing CoDOA and alternative arti�cial intelligencetechniques (as di�erent from ANN) to investigateperformances of di�erent hybrid systems in predictingtimes series.

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Biographies

Utku Kose is a Lecturer at Usak University, Turkeyand also the Director of the Computer Sciences Appli-cation and Research Center at the same university. Hereceived the BS degree in 2008 in Computer Educationof Gazi University, Turkey as a faculty valedictorian;next, he received the MS degree in 2010 from AfyonKocatepe University, Turkey. Now, he continuesDS/PhD at Selcuk University, Turkey in the �eld ofComputer Engineering. Between 2009 to 2011, he


worked as a Research Assistant and between 2011 to2012 worked as a Lecturer and Vocational School-ViceDirector in Afyon Kocatepe University. Currently,his research interest includes arti�cial intelligence, thechaos theory, distance education, e-learning, computereducation, and computer science.

Ahmet Arsalan is a Professor at the Department ofComputer Engineering at Selcuk University, Turkey.He received the BS degree in 1984 and MS degree in1987, both in Electrical Engineering from University of

Firat, Turkey. He also completed DS/PhD at BilkentUniversity, Turkey in the �eld of Computer Engineer-ing. Between 1992 to 1999, he was an AssistantProfessor and until 2005 was an Associated Professorat the Firat University. He served as the Head of theDepartment of Computer Engineering (2004-2012), theDirector of Computer Research and Application Center(2002-2012), and the Dean of Faculty of Technology(2011-2013) at Selcuk University, Turkey. His researchinterest includes data mining, machine learning, com-puter learning, and computer-assisted designing.

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