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Analysis of Convergence Effect Via Different Genetic Operations D.F.Fam & S.P. Koh & S.K. Tiong & K.H. Chong Department of Electronic & Communication Engineering, Universiti Tenaga Nasional, Km 7, Jalan Kajang-Puchong, 43009 Kajang, Selangor. se20597@uniten.edu.my,johnnykoh@uniten.edu.my,siehkiong@uniten.edu.my,chongkh@uniten.edu.my Abstract: Genetic Algorithms (GAs), Evolution Strategies (ES), Evolutionary Programming (EP) and Genetic Programming (GP) are some of the best known types of Evolutionary Algorithm (EA)where it is a class of global search algorithms inspired by natural evolution. In this research, genetic algorithm is one of the optimization techniques used to maximize the performance of solar tracking system .This paper presents analysis of convergence effect via different genetic operations used in Genetic Algorithm as explained in the introduction and methodologies. Simulation Results will demonstrate the ability of GA to produce different solutions via different genetic operations to maximize the performance of solar tracking system. Index Terms—genetic algorithm, solar tracking, genetic operations 1. Introduction The basic principles of GA was developed by John Holland [1] They have since been reviewed and the concepts have been applied on a wider range [2],[3],[4] in today’s world. The GA is derived from Darwin’s theory of Natural Selection. A GA mimics the reproduction behavior observed in biological populations and employs the principal of “survival of the fittest” in its search process. The idea is that an individual (design solution) is more likely to survive if it is adapted to its environment (design objectives and constraints). Therefore, over a number of generations, desirable traits will evolve and remain in genome composition of the population over traits with weaker characteristics. A GA differs from conventional optimization in many ways. It allows coding for a combination of both discrete and continuous design variables. A GA is population based search, which results in multiple solutions in one run, rather than only one solution. Apart from that, GA needs objective function values and not its derivatives (As required in gradient based methods) which may not exist in many real world applications.Literature review shows that only few researchers cited some finding regarding GA based solar tracking system as follow: Khlaichom et al. applied a closed loop control using genetic algorithm (GA) method for a two-axis (altitude over azimuth) solar tracking system. A sensor fabricated from poly crystalline solar cell converts solar radiation to voltage. In their algorithm the decoder and counter receive signals from an optical encoder and convert it to the current corresponding to degree-position of the axle turns. Data is then transferred to a PC via an interface card for maximum tracking. The system tracks the sun with +/-10 0 in both axes. The tests and analyses explained that the solar tracking system using GA increases the output voltage to 7.084% in comparison to that with no GA [5]. Syamsiah Mashohor et al. evaluated the best combination of GA parameters to optimize a solar tracking system for PV panels in terms of azimuth angle and tilt angle. Simulation results demonstrated the ability of the proposed GA system to search for optimal panel positions in term of consistency and convergence properties. It also has proved the ability of the GA-Solar to adapt to different environmental conditions and successfully track sun positions in finding the maximum power by precisely orienting the PV panels.[6] However, recent researches for GA based solar tracking system are based on the traditional GA algorithm structure which is shown as below: // populations // t=0 Step 1= Initialize P (t) Evaluate P(t) While (Solution NOT found OR Max Generation NOT Reached) Do t= t + 1 Select P(t) from P(t-1) Recombine P(t) { Do Crossover Do Normal Mutation } Evaluate P(t) If { P(t) = Solution; End If } End As shown in the Algorithm above, traditional genetic algorithms are composed of four key processing as shown below [7] : 1) initialize P(t) 2) evaluate P(t) 3) select P(t) 4) recombine P(t) Anyhow, most population-based, reproductive, optimization algorithms such as genetic algorithms had a critical problem called premature convergence problem [8, 9, 10]. This problem occurs when highly fit parents in a population pool breed many similar offspring in the early evolution time. If the highly fit individuals are local optima areas, then newly generated offspring from the parents are also near the local optima areas. In this coming methodology section, an explanation of different genetic operations will be studied and results section will show the best genetic operations in preventing premature convergence problem. 2. Methodology Methodology part is divided into few sub sections below: 1) Conventional crossover and mutation 2) Crossover only 3) Clone and selective mutation 2.1 Conventional Crossover and Mutation Using conventional method of having crossover and mutation in Genetic Algorithm will affect its performance. One of the typical problem is Premature Convergence Problem [11,12].Most individuals in a prematurely converged situation are located at some local optimum areas and they can’t get out of the local optimum areas because the exploration power of mutation is low. If we increase the exploration power by setting the mutation probability to high, then the speed of convergence to global optimum areas becomes slow. As a result, it is very difficult for genetic algorithms to escape this premature convergence problem. This considerably makes the performances of genetic algorithms degrade. 2.2 Crossover Only Crossover is a genetic operator that combines two chromosomes (parents) to produce a new chromosome (offspring). The purpose of crossover is to produce the new offspring which is better than both of the parents if it takes the best characteristics from each of the parents. Crossover occurs during evolution according to a user-definable crossover probability. In this experiment, a single point crossover is used. Consider the following 2 parents which have been selected for crossover. The “|” symbol indicates the randomly chosen crossover point. Parent 1: 11001|010 Parent 2: 00100|111 After interchanging the parent chromosomes at the crossover point, the following offspring are produced: Offspring1: 11001|111 Offspring2: 00100|010 Crossover can not generate quite different offspring from their parents because it uses acquired information from their parents. 2.3 Clone and selective mutation In most function optimization problems, their input variables are encoded into the binary strings of individuals. Since the binary strings represent binary numbers for each variable, the higher the bit position of string is, the larger the bit weight has. From this, it is helpful to mutate some part of strings of individuals according to their fitness. That is, if an individual has low fitness, then we mutate the most significant part in order to largely change because we regard the individual to be far from the global optimum. Otherwise, we mutate the least significant part in order to do fine tuning because the individual has high probability to be near global optimum. This selective mutation can make genetic algorithms fast approach to the global optimum and quickly get out of premature convergence. As a result, it will increase the performances of genetic algorithms. 3. Simulation A solar tracking has been developed to evaluate the application of genetic algorithm as depicted in Figure 3. It would explore the intensity of sunlight at different angles and locate the highest intensity with the GA simulation. The solar tracking is placed at the origin point of (Xo=45 °, Yo=45 °). The default base point is at the centre of the workspace. In the simulation, the solar cell will keep on searching the highest intensity location with GA searching method. Both stepper motors controlling X and Y axis of solar tracking will receive the signals through motion controller to determine the angles of movement for both axis. Highest intensity that is absorbed by solar cell will convert the digital voltage to analogue signal to be transmitted to Visual basic program via Programmable logic controller Panasonic FPX-C14R. The simulation has been carried out using the Conventional GA given in 3 tables below, Table 1, Table 2 and Table 3 with the objectives to analyse the convergence effect. Table 1: Conventional GA simulation parameter Simulation Parameter Value Maximum Generation Population, p o Chromosome length Selection Method Crossover Rate, p c Mutation Rate, p m Mutation Point, m p No.BestChromosomes Kept, k b Crossover Type 50 10 8 Roulette Wheel 80% 0.025 2 1 Dynamic Table 2: Conventional GA simulation parameter with Crossover Only Simulation Parameter Value Maximum Generation Population, p o Chromosome length Selection Method Crossover Rate, p c No.BestChromosomes Kept, k b Crossover Type 50 10 8 Roulette Wheel 80% 1 Dynamic Table 3: Conventional GA simulation parameter with clone and selective mutation Simulation Parameter Value Maximum Generation Population, p o Chromosome length Selection Method Crossover Rate, p c Elitism Rate, E c Selective Mutation No.BestChromosomes Kept, k b Crossover Type 50 10 8 Roulette Wheel 80% 80% 0.025 1 Dynamic Results of this implementation will be shown in the section as below. 4. Preliminary Results This solar tracking has been performed under on a sunny day around 11am at school field. From the first simulation parameters requirement which publish conventional genetic algorithm characteristic, gathered results will be shown as graph below: 0 10 20 30 40 50 60 70 80 90 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Generation Fitness value Best: 0.018654 Mean: 0.018654 Best fitness Mean fitness Graph 1 : Best Fitness Value- 0.018654 using conventional GA 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Generation Avergae Distance Average Distance Between Individuals data1 Graph 2 : Average distance between individuals in each generation using conventional GA 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 Generation Individual crossover children mutation children Graph 3 : genealogy of each individual across the generations using conventional GA Graph 3 : Best, worst and mean score for each generation using conventional GA 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 Selection Function Individual Number of children state.Selection Graph 4 : Number of children that is produced by each individual using conventional GA 0 5 10 15 20 25 30 35 40 45 50 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Generation Fitness value Best: 0.018079 Mean: 0.018079 Best fitness Mean fitness Graph 5 : Best Fitness Value- 0.018019 using conventional GA with Crossover only 10 20 30 40 50 60 70 80 90 100 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Generation Best, Worst, and Mean Scores Best Score Median Score Worst Score 5 10 15 20 25 30 35 40 45 50 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Generation Avergae Distance Average Distance Between Individuals data1 Graph 6 : Average distance between individuals in each generation using conventional GA without crossover only 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 Generation Individual crossover children mutation children Graph 7 : genealogy of each individual across the generations using conventional GA with crossover only Graph 8 : Best, worst and mean score for each generation using conventional GA with crossover only 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Selection Function Individual Number of children state.Selection Graph 9 : Number of children that is produced by each individual using conventional GA with crossover only 5 10 15 20 25 30 35 40 45 50 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Generation Best, Worst, and Mean Scores best scores mean scores worst scores 0 5 10 15 20 25 30 35 40 45 50 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 Generation Fitness value Best: 0.017131 Mean: 0.017131 Best fitness Mean fitness Graph 10 : Best Fitness Value- 0.017131 with clone and selective mutation 5 10 15 20 25 30 35 40 45 50 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Generation Avergae Distance Average Distance Between Individuals data1 Graph 11 :Average distance between individuals in each generation using conventional GA with clone and selective mutation 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 11 Generation Individual elite parent crossover children Graph 12 : genealogy of each individual across the generations using conventional GA with clone and selective mutation Graph 13 : Best, worst and mean score for each generation using conventional GA with clone and selective mutation 5 10 15 20 25 30 35 40 45 50 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Generation Best, Worst, and Mean Scores best score mean score worst score 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 Selection Function Individual Number of children state.Selection Graph 14: Number of children that is produced by each individual using conventional GA with clone and selective mutation 5. Discussion From the result, graph 1, 5 and 10 shows 3 different fitness value which are 0.018654, 0.018019 and 0.017131 that could be achieved via 3 different genetic operation as below: Genetic operations Fitness Value Voltage Conventional GA 0.01863 10.024 Conventional GA with crossover only 0.018019 10.035 Conventional GA with clone and selective mutation 0.017131 10.050 Obviously, it shows genetic operation- Conventional GA with cloning of best chromosome and selective mutation could achieve the best fitness value with its ultimate voltage value at 50 th generation Graph 2,6 and 11 display the average distance between individuals for each generation is large and gets narrowed down for 10 th generation onwards. Conventional GA with normal process indicates that convergence starts much faster than other 2 genetic operations where the starting point is at 8 th generation as compared to 9 th generation for conventional GA with clone and mutation and 10 th generation for conventional GA with crossover only. Graph 7,8 and 13 shows the best, mean and worst score for 3 different genetic operations where it correlates to the distance between individuals across 50 generation where global minimum value is approached at an earlier stage for conventional genetic algorithm. With the earliest convergence and achieving the best fitness value at its ultimate voltage, it means that physical solar tracking could track the best intensity location controlled by output of genetic algorithm through controlling both motors X and Y movement. Graph 3,7 and 12 indicates genealogy for each individual across 50 generation for 3 different genetic operations. Generally, mutation and crossover children are produced indicated by both red and blue colours lines respectively. Mapping for each individual to the consecutive individual is linked to show the relationship between parent and children. Graph 4,9 and 14 shows number of children that is produced by each individual in a set of population for 3 different genetic operations. Each set of individual produces different number of children which is the sum of all 50 generation. 6. Conclusion This research paper has significantly analyzes convergence effects of 3 different genetic operations that will affect the speed and efficiency of solar tracking system to reach the highest intensity location under the sunlight coverage. The fitness value has identified the global minimum value for conventional GA with cloning and selective mutation method which is the most performing method as compared to other 2 methods. The proposed method improves search speed, good accuracy and approximate solution with the fitness value 0.017131 and 10.05V. 6. Reference [1] Holland, J. Adaptation in natural and artificial systems, Michigan: The University of Michigan Press, 1975 [2] Mitchell, M. An Introduction to Genetic Algorithms. Cambridge: The MIT Press,1996 [3] Koza, J.Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge: The MIT Press, 1992 [4] Whitley. An Overview of Evolutionary Algorithms. Journal of Information and Software Technology. 2001;43 : 817-831 [5] Khlaichom P, Sonthipermpoon K. Optimization of solar tracking system basedon genetic algorithms; 2006. http://www.thaiscience.info/. [6] Syamsiah Mashohor , Evaluation of Genetic Algorithm based Solar Tracking System for Photovoltaic Panels; ICSET,2008 [7] S.H.Jung, Selective Mutation for Genetic Algorithms, World Academy of Science, Engineering and Technology, vol 56, pp 478- 481,2009 [8] J. Andre, P. Siarry, and T. Dognon, An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization, Advances in engineering software, vol. 32, no. 1, pp. 49–60, 2001. [9] J. E. Smith and T. C. Fogarty, Operator and parameter adaptation in genetic algorithms, Soft computing ; a fusion of foundations, methodologies and applications, vol. 92, no. 2, pp. 81–87, 1997. [10] S. H. Jung, Queen-bee evolution for genetic algorithms, Electronics Letters, vol. 39, pp. 575–576, Mar. 2003. [11] D. B. Fogel, An Introduction to Simulated Evolutionary Optimization,IEEE Transactions on Neural Networks, vol. 5, pp. 3–14, Jan. 1994. [12] J. Andre, P. Siarry, and T. Dognon, An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization, Advances in engineering software, vol. 32, no. 1, pp. 49–60, 2001. . 0.7 0.8 Generation Avergae Distance Average Distance Between Individuals data1 Graph 2 : Average distance between individuals in each generation. 0.4 0.45 Generation Avergae Distance Average Distance Between Individuals data1 Graph 11 :Average distance between individuals in each generation