Optimization of Benchmark Functions using VTS-ABC Algorithm

Optimization of Benchmark Functions using VTS- alphabet algorithmPerformance Optimization of Benchmark Functions using VTS- alphabet Algorithm ostentate Guptaand Dharmender KumarAbstractA new variant based on tourney selection called VTS-ABC algorithm is provided in this paper. Its effect is comp bed with standard ABC algorithm with disparate size of info on several Benchmark functions and results show that VTS-ABC provides better quality of resultant role than original ABC algorithm in every case.Keywords slushy Bee colonisation Algorithms, Nature-Inspired Meta-heuristics,Optimizations, Swarm Intelligence Algorithms, Tournament selection.NOMENCLATUREABC factitious Bee ColonyACO Ant Colony OptimizationBFS Blocking Flow-Shop computer programingDE Differential organic evolutionEA Evolutionary AlgorithmGA Genetic AlgorithmMCN Maximum Cycle NumberPSO molecule Swarm OptimizationTS Tournament sizeTSP Travelling Salesman riddle1.INTRODUCTIONFor optimisation problems , various algorithms arrive atbeendesigned which are basedonnature-inspiredconcepts 1.Evolutionary algorithms(EA) and bourgeonoptimizationalgorithmsare two divers(prenominal) classes in which nature inspired algorithms are classified.Evolutionary algorithms like Geneticalgorithms (GA)andDifferentialevolution (DE) attempt to carry out the phenomenon ofnaturalevolution 2. However, a swarm like ant dependence, a flock of birds tolerate be described as collection of interacting agents and their intelligence lieintheir way of interactions with other individuals andtheenvironment 3. Swarm optimization includes Particle swarm optimization (PSO) modelon socialbehaviorofbirdflocking 4, Ant closure optimization (ACO) model on swarmofants and Artificial Bee Colony (ABC) model on the intelligent foraging behaviour of honey bees 5. Some outstanding characteristics of ABC algorithm which makesitmoreattractivethanotheroptimizationalgorithms areEmploys only three control parameters (populati on size, maximum motorcycle deem and limit) 6.Fastconvergencespeed.Quite simple, flexible and robust 7 8.Easyintegrationwithotheroptimizationalgorithms.Therefore, ABC algorithm is a very popular nature inspired meta-heuristic algorithm used to solve various kinds of optimization problems. In recent years, ABC has earned so ofttimes popularity and used widely in various application such as Constrained optimization, Image processing, crew, Engineering Design, Blocking flow shop scheduling (BFS), TSP, Bioinformatics, Scheduling and many others 9-18.Similar to other stochastic population-based approaches like GA, Ant Colony etc. ABC algorithm also utilize Roulette Wheel selection implement which chooses best(p) solution always with high selection pressure and leads the algorithm into premature convergence. With ever-growing size of dataset, optimization of algorithm has become a big concern. This calls for a need of better algorithm.The aim of this paper is to create such an alg orithm named VTS-ABC algorithm. This new variant is based on tournament selection mechanism and selects inconsistent tournament size individually time in order to select the utilize bees sharing their information with onlooker bees. Onlooker bees select solution from selected tournament size of solutions with less selection pressure so that high fitness solutions cant dominate and give better quality of solutions with large data set as well. A worst solution is also replaced by better solution generated randomly in each cycle.Rest of the paper is shared in different 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 functions are described in section 4 and in the last Conclusion of the paper is discussed.2.ARTIFICIAL BEE COLONY algorithmic programIn 2005, Karaboga firstly proposed Artificial Bee Colony algorithm fo r optimizing numerical problems 19 which includes employed bees, onlooker bees and scouts. The bee carrying out search randomly is known as a scout. The bee going to the nutrient writer visited by it before and sharing its information with onlooker bees is known as employed bee and the bee waiting on the dance area called onlooker bee. ABC algorithm as a collective intelligence searching model has three essential components Employed bees, Unemployed bees (onlooker and scout bees) and Food sources. In the consume of optimization problem, a aliment source represents a possible solution. The position of a good aliment source indicates the solution providing better results to the given optimization problem. The quality of nectar of a food source represents the fitness value of the associated solution.Initially, a randomly distributed food source position of SNsize, the size of employed bees or onlooker bees is generated. Each solution xi is a D-dimensional vector that represents th e number of optimized parameters and produced usingthe equation 1where,xmaxandxminare the upper and lower bound of the parameterxi, respectively and j denotes the dimension. The fitness of food sources to find the global optimal is metrical by the following formulawhere, fm(xm)is the objective function value of xm. Then 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 elect 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 equald with that of up-to-the-minute 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 probabilistically choose their food sources using fitness based selection technique such as roulette rotate selection shown in equation 4whe re, Pi Probability of selecting the ith employed bee, S Size of employed bees, i Position of the ith employed bee and F seaworthiness value. Afterthatonlookerbeescarried outrandomly searchintheirneighborhood similar to employed bees and memorize the better one.Employed bees whose solutions cant be improved through a predetermined 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 in the main two factors need to be balanced for global optimization outcome i.e. Exploration and Exploitation but ABC is a poor balance of these two factors. Various variants of ABC have been modelled for its improvement in different phases by number of researchers like Sharma and Pant hav e 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 force for the movement of onlooker bees is introduced to enhance the exploration ability of the ABC algorithm. D. Kumar and B. Kumar also reviewed 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 information which affect the communication ability of individuals and primarily the outcome of the algorithm. ABC algorithm uses Roulette cycle per second 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 overcome this problem, its new variant is proposed in which Tournament Selection method is utilize 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 Tournament is apply 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 works similar to Roulette wheel method in the end. Hence, the selection pressure 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 drive 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, increasing 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 conv ergence speed. At each iteration or cycle, a new solution is generated randomly similar to scout and its fitness value is calculated. prehensile 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 equal 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 hyaloplasm where n is the no. of possible food source positions and p represents the dimension of each position.4.2 Performance Measures trick ResultThe experimental results of VTS-AB C 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 sagacity of the performance of an optimization algorithm, Mean of Global Minimum i.e. mean of minimum objective function value at each cycle of all iterations are taken as performance measure whose values are shown in table1and figure 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 o f 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(prenominal) 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 palm of optimization with large and higher dimensions data set efficiently.ReferencesYuga l Kumar and Dharmender Kumar, Parametric Analysis of Nature Inspired Optimization TechniquesInternational Journal of Computer Applications, vol. 32, no. 3, pp. 42-49, Oct. 2011.P. J. Angeline, J. B. pollack and G.M. 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