Research On Improved Particle Swarm Optimization Algorithms For Optimization Problems

The optimization theory and algorithm is a subject developed frommathematic, of which the researching objects are how to find and determine theoptimal solution in many scenarios. In the history, for different optimizationproblems, many optimization methods have been proposed by scholars, for example,the Newton’s method, the conjugate gradient method, the Lagrange multipliermethod, and so on. These mature local optimization algorithms can find thelocal best solution properly. But with the expansion of human living space,the new problems emerge unceasingly, which possess higher complexity,restriction, nonlinearity, and modeling difficulty. These analyticoptimization algorithms used in solving local optimal solutions have beenshown unable to satisfy the requirements of people. So algorithms which areeasy to be parallelized and of some smart features, are needed. As the answer,the stochastic optimization algorithm appears.The stochastic optimization algorithms, such as the genetic algorithm,simulated annealing method, artificial neural network method, swarmintelligence algorithm, show the powerful potential for solving optimizationproblems. They can find the optimal solution within the reasonable time. Inthe recent years, as one of the swarm intelligence algorithms, the ParticleSwarm Optimization algorithm begin to obtain attentions gradually. It isinitially inspired by the simulation of birds flock’s looking for food, whichuses particles of no mass and no volume as units, and uses collaboration andparallel communication between swarms to search for the optimal solution.Because of its high speed convergence, using less parameters and the abilityof solving complex optimization problems which traditional optimizationalgorithms can t do properly, it is widely applied among function optimization,training of neural network, pattern recognition, and some engineering problems.Although the Particle Swarm Optimization algorithm has a20-yeardevelopment since proposed, it is still not mature enough in both theory andpractice. Like other stochastic optimization algorithms, it has the samedisadvantages such as tending to be trapped into local optimal solutions, slowconvergence speed in the later period of evolvement and low precision. Theimprovement of convergence speed and precision becomes the focus of attentionof most researchers.On the base of summarizing the Particle Swarm Optimization theory andalgorithm, aiming at its early maturing problem, this paper presents theimprovements of convergence stage to the PSO algorithm. First, inspired by the dreaming mechanism, a new optimization algorithm called Dream Particle SwarmOptimization, which includes two stages that represents day and night, isproposed. This algorithm slows the convergence stage down by distorting theposition of particles in the night stage and then using the information afterdistortion to move particles in the day stage, to achieving the goal ofescaping from the local optimal solutions.Then based on this, a PSO algorithm which is based on the epidemic modelis proposed. It applies the space information of particles to the ability ofdreaming by using the epidemic process.Finally, another PSO algorithm using the classical theory of fluidmechanics is presented, treating particles as fluid, in which particles havepressure to each other. This new idea assigns density, pressure and othercharacteristics to particles, evolves according to the Bernoulli’s principle.By comparing to the benchmark functions in the tests of finding the globaloptimal solutions, convergence time and other aspects, all of the threealgorithms show better results than some typical PSO improved algorithms.Comparing to the Dream Particle Swarm Optimization algorithm, although theEpidemic Particle Swarm Optimization algorithm needs more input parameters,it is more controllable in convergence time. The Fluid Mechanics ParticleSwarm Optimization algorithm is, but it could gains better results in solvingmultimodal problems.At last, with the research of Particle Swarm Optimization algorithm, somemore optimal proposals has been given; and by summarization, further researchdirection, such as proving the effectiveness of parameter choice of algorithmin theory, using other epidemic model and related improved algorithms, mappingthe Cartesian coordinate system in the Fluid Particle Swarm Optimization topotential flow coordinate system, and applying the algorithm into actualproblems in different fields and improving strategies according to differentproblems to design algorithm fitting their characters, has been proposed too.