Researches On Particle Swarm Optimizers And Their Applications

There are various optimization problems in the fields of science and engineering, and researches on how to solve these problems are still challenging and attractive. The traditional gradient based optimization methods as steepest descent method, Newton method and conjugate direction method build on rigorous mathematical foundation, high computational efficiency, reliable procedures and have been widely used in various fields for many years. However, these traditional methods can't deal with many problems in reality, which are generally discrete, uncontinuous, derivative-free and so on. And sometimes, only local optima are acquired because of the improper initial solution for the gradient based methods. Since John Holland proposed Genetic Algorithm (GA) in 1975, Evolutionary Algorithms (EAs) have become the promising methods for solving various optimization problems. EAs have many advantages over the traditional methods. On the one hand, the evolutionary algorithms are intelligent in searching, learning and adapting after designating the fitness function and EAs don't require differentiability of objective functions and constraints. On the other hand, the parallel mechanism makes the EAs be able to obtain multiple solutions in a single run.Particle Swarm Optimizer (PSO) is a relatively new population-based EA developed by James Kennedy and Russel Eberhart in 1995. PSO emulates the swarm behavior of insects, animals herding, birds flocking, and fish schooling, in which collaborative search for food exhibits a potential computational model. Each member in the swarm adapts its search patterns by learning from its own experiences and other members'experiences. These phenomena are studied and mathematical models are constructed. In PSO, a member in the swarm, called a particle, represents a potential solution which is a point in the search space. The global optimum is regarded as the location of food. Each particle has a fitness value and a velocity to adjust its flying direction according to the best experiences of the swarm to search for the global optimum in the n-dimensional solution space. PSO has many advantages, such as simplicity in concept, easiness to implement, global search, robustness and independence of problems.Therefore, PSO is chose as research subject of this thesis and studies on how PSO solves various problems are conducted, including solving single-objective problems, multi-objective problems and high dimension problems. PSO is also applied to the multidisciplinary design optimization of a gear reducer. The main research topics and contributions are as follows:(1) A hybrid vertical Mutation and fine granularity Learning strategy based PSO (MLPSO) is proposed in order to optimize single-objective problems, which overcomes some disadvantages of PSOs as convergence in local optima, slow convergence rate and low precision.Some novel strategies are proposed in MLPSO. Firstly, a hybrid vertical mutation operator combining uniform distribution mutation and Gaussian distribution mutation is developed to improve its abilities to escape from local optima and conduct local search. Then, a fine granularity learning strategy is adopted to prompt the convergence rate by reusing the local information generated from mutation operator. Also, the velocity update equation proposed by Maurice Clerc is modified to reduce its randomness. MLPSO is also employed to solve constrained optimization problems by incorporating a constraint handling mechanisms based on making distinction between feasible and infeasible solutions. At last, MLPSO is verified by experiments on many benchmark functions and comparison with other algorithms in literature.(2) After studying such key mechanisms of Multi-Ojective PSOs (MOPSOs) as how to keep population diversity, retain non-dominated solutions in external archive and select a leader for each particle, a Diversity-guided Two Stages MOPSO (DTSPSO) is proposed to improve the performance of existing MOPSOs.Most MOPSOs try to keep population diversity by adopting mutation operators but mutation operators generally slow the population convergence rate. Therefore, DTSPSO dynamically select different mutation operators according to current population diversity so as to reduce side effect of mutation operators and improve its efficiency. On the other hand, DTSPSO is divided into two stages according its ways to select leaders. At the first stage, a modified sigma approach is adopted to prompt population to converge rapidly. At the second stage, a tournament selection is used to prompt well distribution of solutions in external archive. Also, Pareto dominance ranking and crowding distance are used to fix the size of external archive. Experiments are carried out on several classical multi-objective optimization problem benchmark functions and the results show that DTSPSO can escape from local optima, cost less function evaluations and keep solution well distributed.(3) A Fast Cooperative Coevolutionary PSO (FCPSO) is proposed to cope with the large scale complex problems and its scalability is especially emphasized and verified. FCPSO is designed by employing the mechanisms of cooperative coevolution as its framework and PSO with mutation operator as its search engine.PSOs are generally effective for optimization problems with decision variables between 10 and 30. When they are used to optimize problems with more decision variables, function evaluations needed increase exponentially and therefore they become unavailable. So, a cooperative coevolutionary PSO is developed to optimize large scale complex problems, especially problems with 1000 decision variables. FCPSO is detailed from several aspects including problem decomposition, collaborator selection and assignment of fitness value and so on. Experiments on several benchmark functions with decision variables from one hundred to one thousand are conducted. FCPSO can solve these unimodal and multimodal benchmark functions while the function evaluations needed only linearly or approximately linearly increase with decision variables. Also, the experiments for blended FCPSO with common population are conducted to raise its precision. However, this measure is only effective for some problems. By now, no literature related to PSO is found to optimize problem with 1000 decision variables.(4) Based on the studies on the scalability of FCPSO, a Cooperative Coevolutionary andε-dominance based MOPSO (CEPSO) is proposed for multi-objective problems.MOPSOs suffer from the curse of dimensionality, cost more function evaluations and are often trapped in local optima. Therefore, CEPSO is proposed to attack these disadvantages. In CEPSO, the multi-objective problems are decomposed according to their decision variables and are optimized by corresponding subswarms respectively. Uniform distribution mutation operator is adopted to avoid premature convergence. All subswarms share one archive based onε-dominance, which is also used as leader set. Collaborators are selected from external archive based on tournament and used to construct context vectors in order to evaluate particles in subswarm. CEPSO is tested on several classical MOP benchmark functions with more than 30 decision variables and the results show that CEPSO can optimize high dimension problems, escape from local optima and generate more Pareto solutions. The function evaluations needed only linearly or approximately linearly increase with decision variables. No cooperative coevolution andε-dominance archive based MOPSOs are found in literature.(5) A Collaborative Optimization (CO) method based on MLPSO is proposed to verify the performance of PSO in practical applications, in which MLPSO is served as optimizers both system level and discipline level.Collaborative optimization is one of the multidisciplinary design optimization methods and is often employed to provide optimal solutions. However, CO has the disadvantages as increased computational time, slow convergence and unexpected nonlinearity of the compatibility constraints. Therefore, a CO method based on MLPSO is proposed to handle the mentioned difficulties and MLPSO is served as optimizers both system level and discipline level, which can deal with various objective functions and constraints, some of which can not be solved by traditional gradient-based optimization algorithms. The proposed method is demonstrated on the multidisciplinary design optimization of a Gear Reducer and the results show its feasibility and effectiveness.The researches show that PSO can not only solve various optimization problems which traditional optimization methods can not deal with, but also is better than other EAs in escaping from local optima, costing less function evaluations and its scalability. This study further enriches PSO in theoretical researches and practical applications.