Swarm Intelligence And Its Application In The Optimal Design Of Digital Filters

Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of agents interacting locally with their environment. SI provides a basis with which it is possible to explore collective problem solving without centralized control or the provision of a global model. SI algorithm is a kind of heuristic search method that can solve the specified problems by simulating the collective behaviors. The characteristic of SI algorithm is stochastic, parallel and distributed. Particle Swarm Optimization (PSO) algorithm, which inspired by social behavior of bird flocking or fish schooling, is one of the typical SI algorithms and it is developed by Eberhart and Kennedy in 1995. Since PSO algorithm was developed, it has attracted many researchers in the fields concerned as its characteristics of simple computation, easy realization, and few parameters. Based on the deep study of PSO algorithm and inspired by quantum physics, Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is proposed by us. QPSO algorithm has much fewer parameters and much stronger global search ability than the PSO algorithm.Theoretical analyses and algorithm improving on PSO algorithm and QPSO algorithm are mainly discussed in our work and the application of QPSO algorithm and its improvements in the optimal design of digital filters are also studied in the work. The main contents of this dissertation are as follows:(1) Research background of SI algorithms and optimal design of digital filters are expatiated. The current research situations of two typical SI algorithms are detailed introduced, which are Ant Colony Optimization (ACO) algorithm and PSO algorithm. An introduction of optimal design of different types of digital filters is presented. Research methods and ideas in the work are proposed.(2) Convergence of PSO algorithm is analyzed by algebraic method and then the conditions of convergence and repulse for PSO algorithm are reached. The conditions are shown to be true by the simulation experiments. According to the conditions a diversity-controlled PSO algorithm which is called DCPSO is proposed in order to solve the problem of premature convergence in PSO algorithm. In DCPSO algorithm, guided by the controlled swarm's diversity, the particles search in the attractive phase sufficiently and adjust them by moving away from the center of the swarm quickly in the repulsive phase once the diversity measure reach to a low bound. The attractive-repulsive procedure can guarantee the swarm search in a wide space and help to avoid trapping into the local minima. Experimental results on several well-known benchmark functions show that DCPSO has strong global optimization ability in solving the multimodal problems.(3) The thought of QPSO algorithm is discussed. Convergence criteria of random search algorithms are studied, including global convergence criteria and local convergence criteria. Based on these two convergence criteria, QPSO algorithm is proven to be a global search stochastic algorithm, which can provide the foundation for further studying the theoretical problems in QPSO algorithm.(4) The parameter of an algorithm is the key issue that affects the algorithm's performance and efficiency. The methods for taking values of Contraction-Expansion coefficient which is the only parameter in QPSO algorithm excluding the population size and iteration is analyzed systemically. Four strategies are proposed, including: setting the parameter as a fixed value, making the parameter take value linearly or nonlinearly according to the iteration, and letting the parameter take value adaptively according to the evolution results. Some guiding conclusions are summarized which can provide advantages for those algorithm users.(5) Premature convergence is also appeared in QPSO algorithm when solving multimodal problems. The reason for premature convergence lies in the collections of swarm which makes the swarm diversity decline and the particles lose the ability of searching in a wide space. Based on two types of diversity measure, an improvement on QPSO algorithm is proposed to avoid the swarm diversity getting into a low level. The improvement is realized by mutating the swarm's global best particle. The improved QPSO algorithm shows preferable ability in solving the multimodal problems.(6) By hybridizing QPSO algorithm and other evolutionary algorithms to improve the search efficiency and performance of QPSO algorithm. Firstly, mutation mechanism is introduced into QPSO algorithm. Mutation operator can increase the swarm's diversity and can put the particles into new search area. A set of mutation operators is used to compare the effects on QPSO algorithm. Secondly, crossover operator is used in QPSO algorithm and it could generate new positions for the particles instead of the origin method in the algorithm and then increase the swarm's diversity which can enhance the ability of jump out of the collective area. The hybrid QPSO algorithms show good performances by tested them on the benchmark functions.(7) The mathematic model of different types of digital filters and optimal design methods are discussed. FIR digital filter, IER digital filter, adaptive IIR digital filter and two-dimensional digital filter are analyzed. The essential of optimal design digital filters can be attributed to the global optimization problem. QPSO algorithm and its corresponding improvements are proposed to solve the digital filters' optimal design model. Several different design examples are used to examine the design effect of QPSO algorithm and its improvements. The results show that QPSO algorithm and its improvements can design better filters than those designed by other optimization algorithms.The main contributions in this work are summarized at last and further research considerations are put forward.