Study And Application Of Particle Swarm Optimization And Differential Evolution Algorithms

Both particle swarm optimization (PSO) and differential evolution (DE) are population-based stochastic optimization algorithms with good performance. In this thesis, PSO and DE are studied and several improved algorithms have been presented. Then, PSO and DE are applied to adaptive filter and antenna arrays synthesis.On PSO study, the formal sufficient and necessary condition for the deterministic standard PSO to converge, diverge or oscillate within a range, is first derived by using discrete time linear dynamic system theory. Based on the theory analysis, a general guideline for parameters selection is provided and the effects of randomness and interaction between particles are discussed. Then the information sharing mechanism of PSO is studied. Four kinds of PSO algorithms with different information sharing strategies are designed and compared. Some conditions for a good information sharing strategy are summarized.Based on the study of PSO theory and information sharing mechanism, also inspired by some effective sociological ideas, several improved PSO algorithms are proposed. These include:(1) Inspired by the idea of specialization and cooperation, a new adaptive particle swarm optimization (APSO) algorithm is proposed. In APSO, particles with different performance are assigned with different tasks and accordingly different inertial weights. And the acceleration coefficients are adaptively adjusted according to the inertial weight.(2) Based on the metaphor of "specialization and cooperation" and "the elites lead the majority" in hierarchical social organization, hierarchical subpopulation particle swarm optimization (HSPSO) algorithm is presented. In HSPSO, the entire population is divided into several subpopulations arranged in a hierarchy. The particles at higher level of the hierarchy are composed of the elite particles from different subpopulations of the lower level. Particles at different levels are assigned different tasks thus a good balance of exploration and exploitation can be obtained.(3) Two kinds of effectively informed particle swarm optimization (EIPSO) algorithms are presented. In EIPSO, the particle selectively shares the information of all its neighbors better than itself. Thus it can not only make the best of the information from its outstanding neighbors but also avoid the negative influence of its inferior neighbors.(4) A chaotic particle swarm optimization (CPSO) algorithm based on the essence of particle swarm is proposed. CPSO uses chaotic search rather than Kennedy's random number generator to search a promising region. The radius of the chaotic searching region is adaptively adjusted according to the distances between the personal best positions of particles.Then several improved adaptive filtering algorithms are studied and the idea of PSO is applied to the optimization of adaptive filter. Those improved adaptive filtering algorithms include:(1) A fuzzy step size least mean square (FSS-LMS) algorithm is proposed, in which the step size of LMS is adaptively adjusted by a zero-order Sugeno fuzzy inference system. The complexity and convergence performance of FSS-LMS algorithm are also analyzed.(2) The tap-length and tap-weight adjusting problems of variable order adaptive filter are converted into a single tap-weight adjusting problem. Then a general tap-length updating formula and a new variable tap-length LMS algorithm are presented. The rationality and convergence property of the new algorithm are analyzed.(3) A new tap-length algorithm is presented, which can converge to optimal order or tap-length under noises of different magnitudes. It is then applied to variable order adaptive lattice recursive least square (RLS) filter. The adjustment of correlative parameters when updating the lattice filter order is also discussed.(4) Based on the social psychology idea behind PSO and the feature of adaptive FIR filter, the proper expressions for the "inertial", "cognitive" and "social" parts are designed to update the combined adaptive filter. Thus a combined adaptive filtering algorithm based on the idea of PSO is presented. The theory analysis and simulation results show that the new algorithm can well balance the steady state misadjustment and tracking ability under different environments.On DE study, a new differential mutation strategy for DE, namely DE/BoR/*/*, is first presented by regarding differential mutation as a local search. DE/BoR/*/* uses the best one of several randomly chosen individuals as differential mutation base while the rest ones as donors for vector differences. Hence, both good diversity and quality of mutation bases are obtained, leading to better balance of exploration and exploitation.Then a comparative study of crossover in DE is carried out. In order to fairly compare two most often implemented crossover methods in DE, namely, binomial crossover and exponential crossover, and study the effect of prcbability distribution of crossover length and crossover continuity, two new crossover methods, namely consecutive binomial crossover and non-consecutive exponential crossover, are designed. The probability distribution and expectation of crossover length for binomial and exponential crossover used in this paper are derived. Various DE algorithms with different crossover methods including mutation-only DE are comprehensively compared. Based on the theoretical analysis and simulation results, the effect of crossover on the reliability and efficiency of DE is discussed. Some insights are revealed.Finally, DDE/BoR/1/bin and another new PSO algorithm, namely, effectively informed Gaussian particle swarm (EIGPS), are applied to unequally spaced antenna array synthesis to minimize the peak sidelobe level (PSLL). Effect of angle resolution on the PSLL has also been investigated. The simulation results show that both DDE/BoR/1/bin and EIGPS have good synthesis capacity and are able to obtain better results than those reported in some existing literatures.