The Research Of Particle Swarm Optimization Algorithm For Function Optimization Problems

PSO algorithm is a parallel evolutionary computation algorithm proposed byKennedy and Eberhart . It is inspired bythe swarming behavior of birds. It is simple, easyto be implemented and quick convergence. Nowadays PSO has wide applications indifferent fields and a lot of algorithms based on PSO have been proposed.Optimization problems that based on mathematics mainly inlcude constrainedoptimization and unconstrained optimization, this paper focuses on unconstrainedoptimization.Along with the developing of the research on different optimizationproblems,its application is becoming wider and wider. Most problems we meet arecontinuous optimization problems in engineering optimization. The target of this kind ofproblems is to find the best solution among a large number of solutions. The technic usedto solve optimization problems is usually asked to have the following characteristics:quick convergence, little controls parameters and less sensitive parameters. Differentfrom traditional methods used to solve optimization problems, inspired by the process ofbiology evolution people have proposed a lot of new methods for solving complexoptimization problems,such as Genetic Algorithm,Evolutionary Computation,EvolutionStrategies, Swarm IntelligenceAlgorithm and so on.PSO is an important algorithm in the domain of swarm intelligence. The study ofPSO algorithm has great meaning for solving function optimization problems. PSO is anoptimization algorithm based on iteration and a particle in the algorithm is seen as a'bird'of the solution space. Aparticle contain three important values, position,speed and fitnessvalues. Then a particle updates its speed,position and fitness value following personalbest and global best got by the swarm bynow until the global best is reached.Differential Evolution is originally proposed by Rainer Storn and Kenneth Price. DEalgorithm is an evolutionary algorithm based on numerical coding. There are threeoperations: mutation,cross and selection. It is similar with genetic algorithm exceptingthe mutation operation that based on the chromosome's differential vector. DE algorithmis quick convergence and the controls parameters are less sensitive. The way used in DE algorithm to update the individuals can keep the diversity of the swarm which can stopthe algorithm from trapping in local optimum.In despite of most theoretics research and application of swarm intelligence arefocus on optimization algorithm with certain, optimization problems under noisyenviroment is getting more and more important these days. The algorithms proposed inthis paper are used to slove the optimization problems under noisy enviroment and resultswe got is very good. Generally the noisy enviroment is simulated by random numberssubjected to Gaussian distribution.In this paper a lot of modified PSO algorithms based on the basic PSO algorithm arestudied. Three algorithms were proposed to solve function optimization problems undernoisy enviroment. Lots of experiments were taken to sovle the problems under certainand uncertain enviroment and the results showed the validity and correctness of theproposed algorithms.A self-adaptive particle swarm optimization algorithm is proposed in this paper anddetailed analyse is done about the selection of parameters. A lot of experiments weredone to prove the validity of the algorithm. In the explorative state, it is attracted by thecurrent global best position and its own personal best position. In the exploitation state, itis repelled away from its current personal best position and its personal worst position tosearch the other promising area. So a particle can decide which strategy to selectaccording to the degree of its evolution. At the same time a self-adjusted inertia weightwhich varies dynamically with each particle's evolution degree and the current swarmevolution degree is introduced into SAPSO algorithm. The experimental results show thatthe algorithm is better than the traditional particle swarm optimization algorithm nomatter for function optimization problems under certain or uncertain. The algorithm isvery sensitive to the threshold value, so the value should be tried and tuned graduallythrough experiments.A new optimization algorithm UPSOOHT(UPSO-OCBA-HT) is proposed based ona modified particle swarm optimization algorithm UPSO(Unified Particle SwarmOptimization). The algorithm is mainly focuses on uncertain optimization problems.Resampling is used to control noisy and how the magnitude of noisy will influence theoptimization algorithm is studied. The UPSO algorithm, HT and OCBA are combined inthe UPSOOHT. HT is used to improve the diversity of the swarm and keep the goodparticles. The use of resampling make the algorithm is useful especially for theoptimization problems with uncertainty. An algorithm HDPSO(HT-DE-PSO)based on particle swarm optimization algorithmand differencial evolution is proposed. In the algorithm each particle is updated usingPSO and then hypothesis test is used to generate the new swarm. In this process twoindividuals close to each other are compared, if the two solutions have no significantdifference in statistical sense then the better one will be kept and the worse one will beupdated using DE operators; otherwise both of them will be kept to form the newgeneration. The algorithm will go to the next iteration when we get N particles as the newgeneration. By this way a particle may be updated by two operators and the speed ofvelocity and the precision of convergencyis improved.In conclusion, the paper studied the PSO algorithm used to solve optimizationproblems deeply, summarized the reseach actuality of the algorithm,modified thetraditional PSO algorithm and proposed three new particle swarm optimizationalgorithms for solving function optimization problems. At the same time reseach andanalysis were taken for solving function optimization problems with uncertainty. Thealgorithms proposed in this paper were applied on both of the two kinds of problems andthe experimental results proved the validityof the algorithms.