The optimization problem is an important branch of modern mathematics which involves many different disciplines. Its objective is to find a set of parameter values subject to certain constraints in order to achieve the best performance of the system. With the rapid progress of human society and the development of science and technology, more and more complex, non-linear, systemic problems are difficult or even impossible to be solved using traditional optimization. Swarm intelligence, by studying the self-organizing behaviors of socialized animals (such as ant colony, bees, birds, etc.), gets rid of the shackles of classical logic computing to offer a rapid and reliable means for the solution of problems hard to be solved using traditional methods, especially for systematic complexity problems (such as NP problems), as well as realistic problems presented in real applications.Particle Swarm Optimization (PSO) algorithm is proposed by James Kennedy and Russell Eberhart in 1995, which is a new breed of Swarm Intelligence (SI). In order to improve the convergence performance of PSO, Jun Sun proposed the Quantum-behaved Particle Swarm Optimization (QPSO) algorithm based on PSO by comparing human learning process and particles’behavior patterns in quantum space. QPSO’s desired features such as distribution, self-organization, collaboration, robustness and easy implementation have made it applicable both in scientific researches and engineering applications. The ever-growing attention from scholars of related research fields has made it an emerging and important research field.Although the PSO and QPSO algorithm gained fruitful research results in terms of optimization performance and application, as an emerging computational intelligence method, there are many issues to be further studied and refined:Firstly, PSO and QPSO exist premature convergence. The lack of population diversity is the primary reason for algorithms premature convergence. Global search and local search are able to be balanced for PSO and QPSO by the analysis of both algorithms’updating mechanism, population topology structure and population diversity maintenance mechanism.Secondly, the analysis of algorithms is far from systematic, lacking theoretic analysis of runtime behavior, convergence, convergence speed, parameter selection, robustness, computational complexity, etc.Thirdly, regardless of the algorithm adopted (PSO or QPSO), existing information is processed by a particle in an independent and random fashion, which merely adapts to historic data randomly, without the differentiation of various information types. One problem yet to be solved is the enhancement of algorithm optimization performance by making use of the existing information in a more reasonable manner.In addition, limited options are offered for potential well models in QPSO algorithms. In the state of art of QPSO,δ potential well model is the dominant choice for the modeling of particles’attraction potential in the quantum space whereas studies on other types of potential wells are quite rare. Nevertheless, particles exhibit different probability density functions in the classical forbidden zone of different potential well models, which presents various impacts on problem solutions. Therefore, it is necessary to design QPSO algorithms and analyze the performances through different potential well models.Aiming at tackling problems faced with PSO and QPSO algorithms, with premature avoidance and optimizing performance enhancement as the primary goal, control reinforcement of population diversity and inter-particle information sharing methods as the main research means, the author has done researches on problems such as the selection of information sharing methods in PSO algorithms, the determining of potential well center and the selection between various potential well prototypes in QPSO algorithms, etc. The contributions of this thesis include as follows:API-PSO (Adaptive Partly Informed Particle Swarm Optimization) algorithm is proposed, which can be used as the alternative for the traditional sharing method of population experience adopted in PSO algorithms, to adaptively select population-shared experience according to performances of neighboring particles. Compared with standard PSO algorithms, the new algorithm chooses the advantageous information over disadvantageous information to present more reasonable of population information. The results from mathematical analysis of API-PSO’s population diversity and convergence can be effectively used for configuration of algorithm parameters, which set the fundamentals to ease lack of population diversity, facilitate population development and enhance algorithm precision and efficiency. (Chapter 2)The optimization process of QPSO is essentially continuous movements of particles towards the potential well center. The study on the principles of QPSO shows that the selection of potential well model and determining of potential well center pi are critical to algorithm performance. To tackle the above problem, this thesis first analyzes the random factors in the formula used to determine the potential well center based on 8 potential well, harmonic oscillator and square potential well, then correlates the recognition of personal experience and that of population experience by the use of binary uniform Copula function, and eventually proposes the Binary Correlation QPSO (BC-QPSO) algorithm suitable for different potential well models. In addition, convergence conditions are given for different algorithms by theoretical analysis, and configuration strategies are offered for BC-QPSO parameters in the three different potential well models by experiments. Given constant acceleration coefficients and linearly declining controlling parameters, the experiment results show that population diversity decreases with the increment of correlation p between binary correlation factors r1 and r2. BC-QPSO exhibits best local optimization given p=l whereas best global optimization given p=-l. (Chapter 3)In QPSO models, in addition to personal experience and population experience, the distance between the current position and the average best position is also key to the determination of a particle’s position in the solution space at next iteration. Using the multivariate Copula function for the depiction of correlation between r1, r2 and u, this thesis proposes the Ternary correlation QPSO algorithm, i.e. TC-QPSO. Besides, the method for ternary correlative generation is implemented through Cholesky square root equation using a random variable in interval [0,1]. Experiment results show that when negative correlation exists between correlative factors, on the basis of balanced use of existing information, the "waiting effect" can be reinforced for particles, restricting particles’aggregation speed towards potential well center. Therefore the algorithm is prevented from falling into local best optimization, indicating remarkable optimization performance of TC-QPSO. (Chapter 4)The multi-subgroup interactive evolution mode provides an effective means for PSO performance enhancement. Two dual-subgroup interactive and quantum-behaved PSO algorithms are proposed in this thesis, namely Dual Group QPSO with Different Related Factors (DFR-QPSO) and Dual Group QPSO with Different Well Centers (DWC-QPSO). The entire population is divided into two equally-sized independent subgroups in the solution space. For each subgroup, DRF-QPSO adopts different information processing method during interactions, whereas DWC-QPSO set different potential well center during evolution. Experiment results show that the collaboration between the master and slave subgroups strengthens a more thorough inter-particle study, reinforces the global searching ability, prevents the population from falling into local optimization at early stages, thus improving the convergence performance of standard QPSO. (Chapter 5)To tackle traffic bottleneck problem, the DWC-QPSO algorithm and non-linear feedback theory are combined in this thesis to design the PI controller and the self-adaptive traffic control algorithm for on-ramps. After that, the application of DRF-QPSO model in the Power Economic Dispatch is conducted. The simulation results show these two algorithms are more effective than other swarm intelligence algorithms. (Chapter 6)... |