Particle Swarm Optimization Based Dynamic Optimization Research

Dynamic optimization, frequently encountered in areas such as chemical engineering, aeronautics and astronautics, biological engineering, is a significant tool to deal with bottolnecks in industries and achieve objectives of saving energy, reducing cost, exploiting potential and improving efficiency. For its huge practical value, dynamic optimization wins great popularity among numerous researchers across the world.Transforming a infinite dimensional dynamic optimization problem into a finite dimendional static optimization problem by discretizing time is one of the most important methods for dynamic optimization. In this sense, to solve a dynamic optimization problem is indeed to solve a static one. Traditional gradient based methods for static optimization suffer from several restrictions, such as requirement of good analytical properties of objective function or constraints, heavy dependence on an initial guess and difficulty in computing gradient information. On the other hand, intelligent optimization methods have shown their simplicity, flexibility and strong abiity to search globally, received wide population and gradually stood out to be a class of optimization methods which is as important as gradient based methods. This thesis proposes a general framework based on control variable parmeterization for solving dynamic optimization problems and then focuses on several improvements of particle swarm optimization and their application to dynamic optimization. The main work and contribution of this thesis is as follows:(1) A general framework based on control variable parameterization for solving dynamic optimization is proposed and the emphasis is laid on intelligent optimization methods for solving dynamic optimization problems.(2) The principles of diffenential evolution, ant colony optimization for continous function and particle swarm optimizaton are presented clearly and the three methods are combined with control variable parameterization to solve dynamic optimization problems. The performace of three methods are tested on several classical dynamic optimization problems. Numerical results show that PSO outperforms DE and ACO in that PSO requires smaller population size, has less parameters to determine and faster convergence rate.(3) To alleviate the drawback of slow convergece rate and "dimensionality disaster", a population distribution characteristics based adaptive particle swarm optimization (APSO) algorithm for dynamic optimization and a sub-swarm based modified cooperative particle swarm optimization (MCPSO) algorithm for dynamic optimization are proposed, respectively. APSO introduces the concept of evolutionary factor and evolutionary state according to population distributon characteristics and adaptively adjusts inertia weight and acceleration coefficients to imporve covergence rate. To lower the dimension for optimization, MCPSO splits the search space into multiple lower dimensional subspaces and each sub-swarm is assigned to optimize a component of the whole solution vector. The evaluation of objective function is conducted by sharing information among sub-swarms. Numerical results reveal that APSO and MCPSO are stable, more accurate and efficient than the traditional PSO algorithm.(4) A constrained particle swarm optimization algorithm for dynamic optimization is designed to solve Bang-Bang optimal control problem efficiently, in which the whole time interval is divided subintervals with varying length and the length of each subinterval is treated as a variable to be optimized. Numerical results indicate that the constrained particle swarm optimization algorithm is better in terms of computaional accuracy and efficiency than PSO dealing with subintervals of identical length. In addtion, inspired by region reduction strategy, an iteratively adaptive particle swarm optimization algorithm is proposed to further improve convergence rate for solving dynamic optimization problem.