Expert Systems with Applications 37 (2010) 3706–3713

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Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Synergy of evolutionary algorithm and socio-political processfor global optimization

Tushar Jain *, M.J. NigamDepartment of Electronics and Computer Engineering, Indian Institute of Technology Roorkee, Uttarakhand 247767, India

a r t i c l e i n f o

Keywords:Genetic algorithmColonial competitive optimizationHybrid optimizationController tuningBall and beam system

0957-4174/$ - see front matter Crown Copyright � 2doi:10.1016/j.eswa.2009.11.055

* Corresponding author.E-mail address: tushaar.iitr@gmail.com (T. Jain).

a b s t r a c t

This paper proposes a hybrid approach by combining the evolutionary optimization based genetic algo-rithm (GA) and socio-political process based colonial competitive algorithm (CCA). The performance ofhybrid algorithm is illustrated using standard test functions in comparison to basic CCA method. Sincethe CCA method is newly developed, very little research work has been undertaken to deal with curseof dimensionality and to improve the convergence speed and accuracy of the basic CCA algorithm. Theproposed CCA–GA algorithm is then used to tune a PID controller for a real time ball and beam system.Simulation results were reported and the hybrid algorithm indeed has established superiority over thebasic algorithms with respect to set of functions considered and it can easily be extended for other globaloptimization problems.

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1. Introduction

The era of evolutionary computation started with genetic algo-rithms in the past three decades. Amounts of applications havebenefited from the utilization of GA (Chaiyaratana & Zalzala,1997). Potter and De Jong (1994) have demonstrated the use ofco-operative co-evaluation GA in multivariable functional optimi-zation. Breeder genetic algorithm (BGA) (Muhlenbein & Schlierk-amp-Voosen, 1993) is first introduced by Muhlenbein et al. Themajor difference lies in the method of selection in comparison tosimple GA. A typical task of GA is to find the best set of values ina predefined set of free parameters associated with either a processmodel or a control vector. The GA uses the basic reproductionoperators such as crossover and mutation to produce the geneticcomposition of a population. Efforts are being made in theenhancement of conventional algorithm (Chen & Yao, 2008; Fran-cisco & Manuel, 2000; Yang & Tinos, 2008; Zhang, Lou, Gao, Liu, &Sun, 2008). GA with neural network and fuzzy control (Siddique &Tokhi, 2002) are used extensively to optimize nonlinear and mul-tivariable systems. In the past, researches were carried out in usinghybrid genetic algorithm approaches for optimization problems.Buczak and Uhrig proposed a novel hierarchal fuzzy-genetic(Buczak & Uhrig, 1996) information fusion technique. Constrainthandling is one of the major concern for solving the optimizationproblems using GA. Chootinan and Chen proposed a gradient infor-mation (Chootinan & Chen, 2006), derived from the constraint set,to systematically repair infeasible solutions.

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Though the GA methods were successful to solve complex opti-mization problems, recent search has identified some deficienciesin GA performance (Eberhart & Shi, 1998). This degradation in effi-ciency is apparent in applications with highly epistatic objectivefunctions (i.e. where the parameters being optimized are highlycorrelated), the genetic operators alone cannot ensure better fit-ness of offspring because chromosomes in the population havesimilar structure and their average fitness are high toward theend of evolutionary process. Research is still on to increase the effi-ciency of GA by hybridization (Lee & Lee, 2005). Yang and Tinos(2007) proposes a hybrid immigrants scheme that combines theconcept of elitism, dualism and random immigrants to address dy-namic optimization problems.

Esmaeil, Farzad, Ramin, and Caro (2008) first proposed thecolonial competitive algorithm (CCA) in 2008. Unlike the currentevolutionary algorithms, such as genetic algorithm (GA) and simu-lated annealing (SA) (Mantawy, Abdel-Magid, & Abido, 1999) thatare computer simulation of natural processes such as natural evo-lution and annealing processes in materials, CCA uses imperialismand imperialistic competition, socio-political evolution process, assource of inspiration. The comparison between CCA and GA wasillustrated by designing a PID controller for distillation column sys-tem (DCS). CCA proved to be superior to GA for a MIMO model.

In this article we have come up with a hybrid optimizationtechnique, which synergistically couples the GA and CCA. The pro-posed algorithm is validated using test functions and for PID con-troller tuning. The rest of the paper is organized as follows:Section 2 provides a brief literature overview of the genetic algo-rithm followed by the proposed hybrid approach based on CCAand GA. The algorithm is then validated using standard test

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T. Jain, M.J. Nigam / Expert Systems with Applications 37 (2010) 3706–3713 3707

functions and implemented on practical ball–beam system in Sec-tion 3 followed by conclusions and future work.

Table 1Benchmark functions used.

Function Mathematical representation

Sphere f1ðxÞ ¼Pn

i¼1x2i

Rosenbrock f2ðxÞ ¼Pn�1

i¼1 ½100ðxiþ1 � x2i Þ

2 þ ðxi � 1Þ2�Rastrigin f3ðxÞ ¼

Pni¼1½x2

i � 10 cosð2pxiÞ þ 10�Griewank f4ðxÞ ¼ 1

4000

Pni¼1x2

i �Qn

i¼1 cos xiffiip� �

þ 1

2. GA–CCA hybrid system

2.1. Genetic algorithms

In GA, a candidate solution for a specific problem is called anindividual or a chromosome and consists of a linear list of genes.Each individual represents a point in the search space, and hencea possible solution to the problem. A population consists of finitenumber of individuals. Each individual is decided by an evaluatingmechanism to obtain its fitness value. Based on this fitness valueand undergoing genetic operators, a new population is generatediteratively with each successive population referred to as a gener-ation. Sexual reproduction allows some exchange and re-orderingof chromosomes, producing offspring that contain a combinationof information from each parent. This is the recombination opera-tion, which is often referred to as crossover because of the waystrands of chromosomes crossover during the exchange. Diversityin the population is achieved by mutation. Genetic algorithmsare ubiquitous nowadays, having been successfully applied tonumerous problems from different domains, including optimiza-tion, automatic programming, machine learning, operations re-search, bioinformatics, and social systems.

2.2. Colonial competitive algorithm

In CCA, a candidate solution for a specific problem is called acountry in which some having the least cost are selected as impe-rialist states and rest form the colonies of these imperialists. Thedivision of all the colonies of initial countries is based upon the fit-ness value. The imperialist states together with their colonies formsome empires. The colonies in each of the empire start moving to-wards their imperialist countries, based upon a simple model ofassimilation policy. The total power of an empire is defined bythe power of imperialist country and percentage of mean powerof its colonies. Then the imperialistic competition begins amongall the empires. Any empire that is not able to succeed in this com-petition cannot increase its power shall be eliminated. Based uponthis competition, the power gradually increases for some empiresand decreases for others. This results in the collapse of weak em-pires. The movement of colonies toward their relevant imperialiststates along with competition among empires and also the collapsemechanism cause all the countries to converge to a state in whichtheir exist just one empire in the world and all the other countriesare colonies of that empire. In this new world, colonies have thesame position and power as the imperialist.

2.3. The hybrid algorithm

This paper focuses on hybrid system using GA and CCA. Theinfluence of crossover and mutation in GA has been studied andit is found that using CCA and GA, number of iterations increaseswith higher dimensions and leads to sub optimal solutions. How-ever, a hybrid system of CCA and GA speeds up the running timeusing less iteration and leads to optimal solution. We used the fol-lowing operation of GA.

Fig. 1. Fitness profile using CCA and CCA–GA algorithm for sphere function. (a)Fitness profile using CCA. (b) Fitness profile using CCA–GA algorithm.

2.3.1. Ranking and selectionIn a minimization problem of function J(h), a ‘ranking’ operation

(Back, 1996) is performed where individuals are sorted in decreas-ing J(h) value first, and then, J(h) is replaced by its position. Eachindividual has a new cost function value J

0(h).

Selection is made by the operator known as Stochastic UniversalSampling (SUS) (Baker, 1987). If Nind is the number of individuals,then the survival probability of an individual P(hi), is guaranteedto be:

Pð~hiÞ ¼J0ð~hiÞPNind

j¼1 J0ð~hjÞð2:3:1Þ

2.3.2. Crossover operationAn extended intermediate recombination (Mühlenbein &

Schlierkamp-Voosen, 1993) is used for the hybrid algorithm as:

zi ¼ xi þ aiðyi � xiÞ; i ¼ 1; . . . ;n ð2:3:2Þ

3708 T. Jain, M.J. Nigam / Expert Systems with Applications 37 (2010) 3706–3713

where x = (x1, . . . , xn), y = (y1, . . . , yn) are the parents andz = (z1, . . . , zn) is the successor, ai is a random number generator.The operation, achieved with a crossover probability, Pc, can be per-formed on each individual separately.

2.3.3. Mutation operationThe mutation operation is performed for each individual with a

mutation probability Pm. Then, a random value is added for eachindividual – generated with a normal distribution and a standarddeviation set to 20% of the search space range. If necessary, the mu-tated individual is kept in the search space by truncation.

The GA conducts search using a population of chromosomeswhich correspond to colonies in their respective empire in CCA.Some colonies are eliminated in each empire which is replacedby colonies having position randomly distributed over the searchspace. This can cause the loss of potential colonies which mighthave a good chance to become imperialist and thus can form itsempire. However, instead of revolving the colonies in CCA, the hy-brid algorithm optimizes using genetic operators. Therefore theloss of potential colony is turned into making it as a potential pow-erful country in an empire. The basic CCA optimization is discussedin detail (Esmaeil et al., 2008). In this paper more emphasis is givenin the improvement of convergence rate of the objective function

Fig. 2. Fitness profile using CCA and CCA–GA algorithm for Rosenbrock function. (a)Fitness profile using CCA. (b) Fitness profile using CCA–GA algorithm.

and hence reduction in number of iteration. The proposed hybridalgorithm to search optimal values of parameters is described asfollows:

Step 1. Initialize parameters p, Nc, Nimp, Nd, Coeffassimilation, Mr

Fig. 3. FitnesFitness profi

where P is the dimension of search space; Nc is numberof initial countries; Nimp is number of initial imperialist;Nd is number of decades or iterations; Coeffassimilation isassimilation coefficients and Mr is the mutation rate

Step 2. Generate the initial countries and on the basis of fitnessvalue, initialize the empires with imperialists cost func-tion, Jimp.

Step 3. Decade loop: Nd = Nd + 1.Step 4. For i = 1, 2 . . . , Nimp, do following:

Substep a. Move all the colonies for ith empire towardsimperialist (assimilation policy) using:

x~Uð0;Coeffassimilation � dÞ

where d is the distance between colony and imperialist.Substep b. Revolution using genetic operators: selection,crossover and mutation.Substep c. Evaluate and sort the new cost function of col-onies as, Ji

col.

s profile using CCA and CCA–GA algorithm for Rastrigin function. (a)le using CCA. (b) Fitness profile using CCA–GA algorithm.

Fig. 4. FitneFitness profi

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Substep d. If Jicol < Ji

imp, then exchange the position andcost value of colonies and imperialist, thus makingimperialist more powerful.Substep e. Calculate the total cost of the ith empire using

Jitotal ¼ Ji

imp þ f�meanðJicolÞ

. Step 5. Unite the empires having same fitness value.

Step 6. Imperialistic competition occurs as follows:

Possession probability; pip ¼

Ji0totalPNimp

j¼1 Jiimp

������

������

where, J0itotal ¼maxðJitotalÞ � Ji

totalTo divide the coloniesamong empires based on the possession probability ofthem, vector P is formed as:

P ¼ ½p1p; p

2p; p

3p; . . . ;p

Nimpp �

Then a vector with the same size as P whose elementsare uniformly distributed random numbers is created:R ¼ ½r1; r2; r3; . . . ; rNimp

�; r1; r2; r3; . . . ; rNimp: Uð0;1Þ

D ¼ P� R

ss profile using CCA and CCA–GA algorithm for Griewank function. (a)le using CCA. (b) Fitness profile using CCA–GA algorithm.

Fig. 5. Fitness profile demonstrating faster convergence of objective function usingCCA and CCA–GA algorithm for Rastrigin function. (a) Fitness profile using CCA withthree unknowns. (b) Fitness profile using CCAGA algorithm with 500 unknowns.

Referring to vector D the colony is handled to an empirewhose relevant index in D is maximum.

Step 7. Eliminate the powerless empire.

3. Experimental setup

3.1. Benchmark function used

The performance of the proposed hybrid algorithm has beenevaluated on a test bed of four well-known benchmark functions.The basic CCA and proposed hybrid algorithm has been appliedon these functions to determine the efficiency of algorithms. Thecurse of dimensionality is also been illustrated for both algorithms.We omit the detailed description of the associated fitness functionin order to save space. From application point of view, a popularnonlinear ball and beam system is considered. PID controller isused to provide the stability with change in desired position ofthe ball.

For both CCA as well as CCA–GA algorithms, we use same pop-ulation size of 200 countries. To make the comparison fair, thealgorithms were initialized using the same random seed. Wechoose the number of decades as a measure of the computational

Fig. 6. Parameter sensitivities for Rastrigin function: (a) dimension of problem, (b) no. of initial countries, (c) no. of imperialist countries, (d) coefficient of assimilation.

Fig. 7. Functional components of mechanical plant.

Fig. 8. Structure of the control algorithm.

Specify target positionof the ball

Inside thepermissible

range?

XRead current actualposition from feedback

Xdes

NoYes

+

-

Xreal

Xdes

Compute the control accordingtoCCA-GA algorithm

(Xdes-Xreal )

Amplify and modulatethe control signal

Ucom

The system moves the ball tothe specified target position

Fig. 9. Flowchart of the control program.

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time. We take p = 30, Nc = 200, Nimp = 8, Nd = 2000, Coeffassimilation =2, u = 0.02, f = 0.02, Mr = 0.9 (see Table 1).

The curse of dimensionality can be seen in all figures, from Figs.1–4. For higher order dimension say 30, the optimization usingCCA does not reach optimal solution (Fig. 3) while optimizationusing CCA–GA reaches (Fig. 3). On increasing the dimension of

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problem to 500 from 30 in CCA–GA, the function reaches the opti-mal solution (Fig. 5b) but needs more computation time. UsingCCA, the optimality is achieved with fewer dimensions (say 3) asshown in Fig. 5a. However, CCA requires more iteration even forthree dimensions in comparison to CCA–GA.

The sensitivity of parameter is also analyzed to select thebest possible initialization parameters for global optimization.Fitness profile of Rastrigin function with respect to number ofparameters, numbers of initial countries, number of initial impe-rialist countries, and assimilation coefficient are illustrated inFig. 6.

3.2. Tuning of PID control for ball–beam system using CCA–GAapproach

The ball–beam system is a frequently encountered example ofnonlinear dynamical system. While the ideal system is indeed non-

Fig. 10. Block diagram of ball–beam

Fig. 11. (a) Step response with desired position 10 cm using CCA–GA algorithm. (b) Stewith desired position 30 cm.

linear, its practical implementation has additional nonlinearities,including: deadband, backlash introduced by the DC motor andgearbox, discrete position sensing and uneven rolling surface.The system is a product from Googol Technology. The practical sys-tem is shown in Fig. 7.

The motion of the motor’s shaft is governed by IPM100 intelli-gent drive. This is a high precision, fully digital servo drive withembedded intelligence and 100 W power amplifier suitable forbrushless/brush motors. Based on feedback information from sen-sors, it computes and then applies appropriate PWM modulatedvoltage to the motor windings in such a way that a sufficient tor-que moves the motor shaft according the programmed controlalgorithm. This embedded intelligence provides a true real-timecontrol performance independent of any delays caused by PC’snon-real time Operating System.

The closed loop control algorithm employed for the applicationis given in Fig. 8.

system with a PID controller.

p response with desired position 20 cm using CCA–GA algorithm. (c) Step response

Table 2Performance comparison using different methods.

Methods kp ki kd Mo (%) ess ts tr

CCA 9.6960 8.3156 48.3786 1.0030 0.023 0.1086 0.0644CCA–GA 14.5911 0.5126 47.3933 0.8721 0 0.1080 0.0637

3712 T. Jain, M.J. Nigam / Expert Systems with Applications 37 (2010) 3706–3713

The DC motor provides actuation of the beam via a gear. The PIDcontrol algorithm inside IPM100 intelligent drive is employed in aninner control loop as a motor position controller. The PID gains aretuned in such a way that the motor exhibits a fast response with-out overshoot. The flowchart of the control algorithm is depicted inFig. 9.

Ball and beam represents a Single Input Single Output (SISO)system where X(s) and h(s) are the Laplace representation of theoutput (position of the ball on the beam) and input (beam angle)of ball and beam. The open loop transfer function of the systemmechanics can be approximated by double integrator. The closedloop model is shown in Fig. 10.

Where mass of ball, m = 0.111, ball moment of inertia,J = 2 * m * R^2/5, gravitational acceleration, g = �9.8, position ofball along the beam, d = 0.04, radius of the ball, R = 0.01.

The real nonlinear system is approximated to double differenti-ator as shown in Fig. 10. MATLAB simulations were carried firstusing CCA and CCA–GA algorithms to determine the optimal setof PID parameters. The set of PID parameters are then imple-mented real time on experimental setup discussed above. Perfor-mance index for fitness evaluation constitutes summation ofsettling time and steady state error for a period of 10 s.

The real time output of the ball–beam system with a step inputis shown in Fig. 11. Initially the ball is placed at one end (maximum

Fig. 12. Pulse input response with duty cycle 50%.

Fig. 13. Fitness profile of ball–beam system.

Fig. 14. Tuning of parameters system during 80 decades.

length 40 cm) of the beam. For the desired position of the ball at10 cm, the overshoot and settling time is shown in Fig. 11a. Forthe desired position as 20 cm and 30 cm, the overshoot and settlingtime is shown in Fig. 11b and c, respectively. It is evident fromabove figures that there is reduction in overshoot and settling timeas the desired position approaches near the initial point of the ball(40 cm) for the same set of PID parameters. The response for a de-sired position having pulse input with duty cycle of 50% and ampli-tude varying between 20 cm and 0 cm is also studied as shown inFig. 12. The response has a large overshoot in comparison to stepresponse with the same desired position.

The fitness profile of ball and beam system using CCA–GA isshown in Fig. 13. The comparison of performance using CCA andCCA–GA algorithms are shown in Table 2. For 80 numbers of dec-ades, the tuning of three parameters towards optimal solution isillustrated in Fig. 14

4. Conclusions

This paper proposes a novel hybrid approach consisting GA (ge-netic algorithm) and CCA (colonial competitive algorithm) and itsperformance is evaluated using various test functions. Theimprovement is shown in terms of convergence rate of the objec-tive function towards the optimality in comparison to CCA forhigher dimension. It was analyzed that as the dimension increases,the solution converges to suboptimal region in case of CCA algo-rithm and requires more number of decades. Also, the proposedCCA–GA algorithm is implemented on a real time ball–beam sys-tem supplied by Googol Technology for tuning the PID controller.As evident from the graphical and empirical results, the suggestedhybrid system performed well.

Our future research would include the analysis and perfor-mance of fuzzy controller in the presence of output noise or inputdisturbances as in case of pulse input the overshoot is large in com-parison to step input of same desired position.

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