Research On Optimization Algorithms Based On Particle Swarm Optimization And Differential Evolution

Optimization is an important branch of mathematics, which is a subject with strong application and abundant content. The objective of optimization is to find the best or better solutions for the given practical problems from feasible solutions. The various methods which are proposed to solve the optimization problems in order to achieve the objective of optimization are called optimization methods. People attach importance to optimization methods all the time, along with the development of systems science and the requirement of various areas, optimization methods have been constantly applied to various areas of the economy, nature, military affairs and society research. Optimization methods based on mathematics methods are centuries-old, which are also in the developing process, and they can be classified into analytic methods, direct methods, and numerical calculation methods and so on. These traditional methods mostly aim at certain given problems, and the request for search space is relatively strict, and some methods also need the differential coefficients information of the function to be optimized. On the other hand, along with the development of science and technology, actual optimization problems become more and more complex, and optimization problems represent the characteristics of complexity, constraint, nonlinearity, multi-minimum, and difficult to model. So, traditional methods are no longer fit for solving optimization problems seeking some new optimization methods has become an important research objective and hot research direction.As a kind of optimization technology which solves problems through simulating the process and mechanism of biologic evolutionary, evolutionary computation provides new ideas and means for solving optimization problems, and it has attracted people's numerous attention in recent years. Evolutionary computation adopts simple coding technology to denote various complex structures, and guides study and determins searching direction through simple evolution operation and natural selection of survival of the fittest on a group of code. Evolutionary computation organizes search using the population mode, which makes it search multi-areas in the solution space at the same time, and this mode also make it fit for large-scale parallel searching specially. The natural selection of survival of the fittest and simple evolution operation make evolutionary computation possesses the characteristics of not confined by its constrained conditions of searching space (such as differentiable, continuous) and not requiring other assistant information (such as differential coefficient). Comparing to traditional mathematical methods, the ones based on evolutionary computation for solving optimization problems have the advantages of stronger adaptability, higher agility, wonderful global character, wider application areas, effectiveness and controlling searching direction according to the rules of probability varying, so the methods based on evolutionary computation can achieve effective solutions in more cases. Particle Swarm Optimization (PSO) algorithm and Differential Evolution (DE) algorithm are two effective and simple evolution algorithms proposed recently, because they are easy to comprehend and realize, they develop very rapidly, and have been successfully applied in many fields. Therefore, this thesis researched fuzzy clustering problems, constrained optimization problems, and multi-objective optimization problems based on the PSO algorithm and DE algorithm, proposed several new algorithms to solve these optimization problems. The main contents of this thesis include:⑴For the PSO algorithm and DE algorithm, this thesis introduced their principles in detail and analyzed the effect of parameter selection on their performance, and provided the process of the algorithm, and also compared them with other ones.⑵Aiming at the constrained optimization problems , this thesis introduced the concept of semi-feasible region, proposed a novel rule of tournament selection , and improved the fitness function of PSO algorithm based on tournament selection and penalty function. Making use of the characteristics of PSO algorithm, this thesis designed a selection operator for the semi-feasible region and proposed a novel evolutionary algorithm for solving constrained optimization problems using PSO algorithm.⑶For the problems of FCM algorithm including local minimum and sensitive of to the initialization values, this thesis combined PSO algorithm with FCM algorithm and proposed a new fuzzy clustering algorithm. It mainly replaced the iteration process based on the gradient descent of FCM, which makes the new algorithm have a strong global searching capacity. At the same time, FCM is no longer dependent on the initialization values, and its efficiency and effectiveness are improved.⑷The FCM algorithm is one of the most widely applied fuzzy clustering algorithms. However, the fuzzy clustering algorithms, which are represented by FCM, don't optimize the features of samples. It is immediate clustering using features of the samples. Thus it results in the fact that the effectiveness of the algorithms depends on the distribution of samples to a great extent. Only if the scale and the distributing shape of classes are similar among data sets, could the clustering effect be good. And it is sensitive to the noises and the isolated point in data sets. As we know, a complicated pattern classification problem in high-dimensional feature spaces has more clearly linear separability than it is in low-dimensional ones. It is ideal to distinguish, extract and amplify useful features through the nonlinear mapping. Thus a much more accurate clustering can be realized. This thesis, by using kernel functions first, maps the data in the input space to a high-dimensional feature space, andconstructs fuzzy dissimilarity matrix in it. Thus it can more accurately reflect the difference of attributes among classes. Then, it globally optimizes the initialization coordinates of the samples distributed randomly using PSO, which leads the Euclidean distance between samples approches to their fuzzy dissimilarity gradually. So as to realize the dynamic fuzzy clustering of arbitrarily distributed samples.⑸Many optimization problems are multi-objective optimization problems in production practice, engineering design, social production and economic development, such as production process control, design of complex software and hardware systems, analysis of social and economic benefits and so on. Therefore, it is of great importance to study the multi-objective optimization problem. This thesis detailed introducedly the basic concept of multi-objective optimization problems and the traditional multi-objective optimization methods and their limitations. It emphasized on the concept of multi-objective evolutionary algorithms, and enumerated some existed ones not based on and based on Pareto optimization concept, and analyzed their advantages and limitations. And it also introduced the maintenance methods of the diversity of the population and the evaluation metric of algorithm performance of the multi-objective evolutionary algorithm commonly used.⑹Traditional multi-objective optimization methods can not solve real multi-objective problems. Evolutionary computation is a computation technique based on population operations, which is very suitable for solving multi-objective optimization problems. This thesis improved the methods of selecting global extremum and individual ones, and presented a PSO based multi-objective optimization algorithm, which could be used to evaluate and select the optimal solution in solving multi-objective optimization problems. Numerical simulations show the effectiveness of it.⑺A new PSO multi-objective evolutionary algorithm is proposed. The algorithm divided an evolutionary swarm into several sub-swarms with different evolutionary directions according to the trait of multi-objective optimization problems and found the optimal non-dominance individuals in each sub-swarm to construct the global optimal region. The region guides evolution of the whole particle swarm. After every iteration, the evolutionary swarm should is re-classified, and this garantees the information exchange among the particles, make the whole particle swarm distributed uniformly and avoids local optimum and ensurs the diversity of the solution. The algorithm used the guiding function of global and individual extremum and fast convergence characteristics of PSO, and it can obtain the uniformly distributed Pareto optimal set by a few iterations.⑻This thesis defined the max-min distance density and proposed a multi-objective differential evolutionary algorithm based on it. The algorithm presented Pareto candidate solution set maintenance methods based on max-min distance density. Using Pareto dominance relationship among individuals and max-min distance density, the algorithm improved the selection operation of differential evolution, ensured the diversity of the Pareto solution set and the convergence of the algorithm, and realized solving multi-objective optimization problems by differential evolution.⑼In the research process, the author found that there are deteriorations in maintaining slolution set and selection in the process of solving multi-objective optimization problems based on DE. To this problem, this thesis firstly presented general multi-objective evolutionary algorithm based on DE, and analyzed two deteriorations in this algorithm, and this thesis proposed resolving methods correspond to these two deteriorations. Finally this thesis proposed a new multi-objective evolutionary algorithm based on DE. The deteriorations in the old algorithms are overcome by the proposed algorithm. The new algorithm guaranteed the convergence and diversity, and effectively improved its efficiency.In conclusion, this thesis detailedly introduced PSO algorithm and DE algorithm, in-depth researched clustering problems, constrained optimization problems, and multi-objective optimization problems, and indicated the limitations of the algorithm using evolutionary computation to solve optimization problems. This thesis proposed several improved new algorithms to solve these problems. Theoretical analysis and experimental results show the algorithm are feasible and efficient.