Optimization of Benchmark Functions using VTS-ABC Algorithm

optimisation of Benchmark Functions exploitation VTS-ABC AlgorithmPerformance Optimization of Benchmark Functions victimisation VTS-ABC Algorithm glister Guptaand Dharmender KumarAbstractA new varipismire based on tourney excerpt called VTS-ABC algorithmic rule is pop the questiond in this paper. Its performance is comp atomic subprogram 18d with bill ABC algorithm with diverse sizing of entropy on some(pre noinal) Benchmark take to the woodss and results evince that VTS-ABC provides break away quality of outcome than original ABC algorithm in all case.Keywords Artificial Bee liquidation Algorithms, Nature-Inspired Meta-heuristics,Optimizations, Swarm word Algorithms, Tournament selection. spoken intercourseABC Artificial Bee dependenceACO Ant Colony OptimizationBFS cylinder block Flow-Shop SchedulingDE disparateial EvolutionEA evolutionary AlgorithmGA catching AlgorithmMCN Maximum Cycle NumberPSO Particle Swarm OptimizationTS Tournament sizing of itTSP Travelling Salesman Problem1.INTRODUCTIONFor optimisation tasks, various algorithms throwbeendesigned which atomic yield 18 basedonnature-inspiredconcepts 1.Evolutionary algorithms(EA) and lotoptimizationalgorithms ar two diametric classes in which nature inspired algorithms are classified.Evolutionary algorithms wish well Geneticalgorithms (GA)andDifferentialevolution (DE) attempt to carry out the phenomenon ofnaturalevolution 2. However, a swarm similar ant village, a flock of birds preserve be described as prayer of interacting agents and their intelligence lieintheir way of interactions with other individuals andtheenvironment 3. Swarm optimization includes Particle swarm optimization (PSO) moldon socialbehaviorofbirdflocking 4, Ant dependency optimization (ACO) model on swarmofants and Artificial Bee Colony (ABC) model on the intelligent foraging behaviour of dulcorate bees 5. Some authorized characteristics of ABC algorithm which makesit moreattractivethan otheroptimizationalgorithms areEmploys only triple control statements ( cosmos size, supreme cycle progeny and limit) 6.Fast crossingspeed.Quite simple, flexible and robust 7 8.Easyintegrationwithotheroptimizationalgorithms.Therefore, ABC algorithm is a very popular nature inspired meta-heuristic algorithm employ to solve various kinds of optimization problems. In recent years, ABC has take in so much popularity and used widely in various diligence such as Constrained optimization, Image processing, Clustering, Engineering Design, Blocking go down shop scheduling (BFS), TSP, Bioinformatics, Scheduling and many others 9-18.Similar to other stochastic people-based approaches like GA, Ant Colony etc. ABC algorithm as well utilise Roulette Wheel selection utensil which chooses best solution everlastingly with high selection insistency and leads the algorithm into premature convergence. With ever-growing size of data prune, optimization of algorithm has become a big concern . This calls for a need of split algorithm.The aim of this paper is to create such an algorithm named VTS-ABC algorithm. This new tune is based on tourney selection mechanism and selects variant tourney size each time in order to select the employ bees sharing their cultivation with onlooker bees. Onlooker bees select solution from selected tourney size of solutions with less selection pressure so that high fittingness solutions cant dominate and give bettor quality of solutions with adult data raft as well. A lather solution is withal replaced by better solution generated haphazardly in each cycle. catch ones breath of the paper is divided in disparate sections as follows Introduction to standard ABC algorithm is described in section 2. Section 3 describes the proposed VTS-ABC algorithm. Experiments and its simulation results to show performance on several Benchmark fails are described in section 4 and in the last decisiveness of the paper is discussed.2.ARTIFICIAL BEE COLONY ALGORITHMIn 2005, Karaboga firstly proposed Artificial Bee Colony algorithm for optimizing numerical problems 19 which includes diligent bees, onlooker bees and scouts. The bee carrying out search hit-or-missly is known as a scout. The bee going to the aliment ascendent visited by it before and sharing its information with onlooker bees is known as employed bee and the bee hold on the dance area called onlooker bee. ABC algorithm as a collective intelligence searching model has three essential components sedulous bees, Unemployed bees (onlooker and scout bees) and Food starting times. In the setting of optimization problem, a feed ascendent represents a possible solution. The strength of a good food source indicates the solution providing better results to the prone optimization problem. The quality of nectar of a food source represents the seaworthiness lever of the associated solution.Initially, a willy-nilly distributed food source role of SNsize, the size of employed bees or onlooker bees is generated. Each solution xi is a D-dimensional vector that represents the number of optimized parameters and produced employthe equation 1where,xmaxandxminare the upper and lower take a hop of the parameterxi,respectively and j denotes the dimension. The fitness of food sources to find the worldwide optimal is calculate by the following formulawhere, fm(xm)is the object glass function value of xm. therefore the employed bee phase starts. In this phase, each employed bee xi finds a new food source viin its neighborhood using the equation 3where, t Cycle number Randomly chosen employed bee and k is not equal to i ( ) A series of random variable in the range -1, 1. The fitness of new solution produced is equivalenced with that of current solution and memorizes the better one by means of a greedy selection mechanism. employed bees share their information about food sources with onlooker bees waiting in the hive and onlooker bees probabi listically choose their food sources using fitness based selection technique such as roulette pluck selection shown in equation 4where, Pi fortune of selecting the ith employed bee, S size of it of employed bees, i Position of the ith employed bee and F Fitness value. Afterthatonlookerbeescarried outrandomly searchintheirneighborhood similar to employed bees and memorize the better one.Employed bees whose solutions cant be improved through a preset number of cycles, called limit, become scouts and their solutions are abandoned. Then, they find a new random food source position using the following equation 5Where, r A random number between 0 and 1 and these steps are repeated through a predetermined number of cycles called Maximum Cycle Number (MCN).3.PROPOSED WORK VTS-ABC ALGORITHMIn every meta-heuristic algorithm mainly two factors need to be ratiod for global optimization outcome i.e. Exploration and Exploitation but ABC is a poor balance of these two factors. Various varian ts of ABC have been modelled for its proceeds in different phases by number of researchers like Sharma and Pant have proposed a variant of ABC called RABC for solving the numerical optimization problem 20 and Tsai et al. have presented an interactive ABC optimization algorithm to solve combinational optimization problem 21 in which the concept of universal gravitational military for the movement of onlooker bees is introduced to resurrect the exploration ability of the ABC algorithm. D. Kumar and B. Kumar also follow-uped various papers on ABC and give a modified RABC algorithm based on topology for optimization of benchmark functions 22 23.Intelligence of ABC algorithm mainly depends upon the communication between individual agents. Employed beesshare their information with onlooker bees waiting in the hive and flow of this information from one individual to another depends on the selection mechanism used. Different selection schemes select different individuals to share the i nformation which affect the communication ability of individuals and primarily the outcome of the algorithm. ABC algorithm uses Roulette wheel selection mechanism in which each onlooker bee selects the food source based on certain probability. Each onlooker bee selects the best food source with high selection pressure and lead to premature convergence. To cover this problem, its new variant is proposed in which Tournament Selection method is utilise based on Cycle number and number of employed bees.In Tournament selection, a tournament size (TS) is chosen to select the number of employed bees sharing the information with onlooker bees. For better exploration, TS=2 i.e. binary star Tournament is applied in early stages and for better exploitation, variable tournament size is applied based on the current cycle number (CYL) and size of employed bee in middle stages. As the stages grow, this method kit and boodle similar to Roulette wheel method in the end. Hence, the selection pres sure is less in early stages and more in final stages which provide us better quality of solution. As variable size of tournament is used at different stages of the algorithm, hence the algorithm named VTS-ABC (Variable Tournament Size Artificial Bee Colony) algorithm. Method used for calculating TS is shown in equation 6 and equation 7If SN = 20If SNWhere Here, two equations are shown for calculating tournament size of tournament selection method. The purpose of using these two equations is to increase the speed of algorithm. When the size of employed bee i.e. given population of food source positions is small like 10, a solution can be easily found by changing the tournament size by 1 but as the size grows i.e. when best food source position is to be found in large set of population for example when SN=40 or more than 40, change magnitude size of tournament by 1 and 2 only is a very tedious task as it will take more time to run the algorithm. Hence, in order to increase speed of algorithm, the tournament size based on current cycle and size of population is increased.One more concept is applied to increase its convergence speed. At each iteration or cycle, a new solution is generated randomly similar to scout and its fitness value is calculated. Greedy selection mechanism is applied between new solution and worst one and the better solution is memorized. Hence, it helps in finding good quality of solution as well as improving the convergence speed and provides better balance between exploration and exploitation.4.experiments and simulation results4.1 Benchmark FunctionsThe Benchmark Functions used to compare the performance of VTS-ABC algorithm with original ABC algorithm are illustrated belowSphere FunctionSchwefel FunctionGriewank FunctionWhere Ackley FunctionHere, ObjVal is the function value calculated for each food source position. A food source is represented by X and population size is taken of n*p matrix where n is the no. of possible food source positions and p represents the dimension of each position.4.2 Performance Measures show ResultThe experimental results of VTS-ABC and ABC algorithm in MATLAB are taken under the parameter of size of food source positions (n*p) i.e. different size of population with different dimensions are taken to run and compare both algorithms. MCN is set as 2000 and each algorithm is run for 3 iteration i.e. Runtime=3. Limit for scouts is set equals to 300. In order to provide the quantitative assessment of the performance of an optimization algorithm, Mean of Global Minimum i.e. mean of minimal objective function value at each cycle of all iterations are taken as performance measure whose determine are shown in table1and physical body 1-4.Table1 Mean of Global minimum on different size of dataFig. 1 Mean of Sphere function values on different size of dataFig. 2 Mean of Schwefel function values on different size of dataFig. 3 Mean of Griewank function values on different size of dataFig. 4 Mean of Ackley function values on different size of dataFigure 1 to 4 show simulation results of ABC and VTS-ABC algorithm with different size of data on Sphere, Schwefel, Griewank, Ackley respectively and reveal that VTS-ABC algorithm provides us better quality of solution than original ABC algorithm by minimizing objective function value or producing higher fitness solutions.5. DISCUSSION AND conclusionIn this paper, a new algorithm VTS-ABC is presented. In this algorithm, firstly variable tournament size (TS) is applied to select the food source position for onlooker bees which helps to achieve diversity in solution. Then to increase convergence speed, a new solution is generated in each cycle which replaced the worst one. In order to demonstrate the performance of proposed algorithm, it is applied on several Benchmark functions with different size of data set as input. Simulation results show that it provides better quality of solution than original ABC algorithm in every case . Therefore, it can be applied in different fields of optimization with large and higher dimensions data set efficiently.ReferencesYugal Kumar and Dharmender Kumar, parametric Analysis of Nature Inspired Optimization TechniquesInternational diary of computing device Applications, vol. 32, no. 3, pp. 42-49, Oct. 2011.P. J. Angeline, J. B. Pollack and G.M. 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