Several New Algorithms For Global Optimization Problems

Optimization methods are a kind of methods to search optimal solutions or acceptable ones for a given optimization problem. In this thesis, filled function methods, central force optimization methods and gravitation search method have been studied. We construct an improved filled function method, clustering-simplex central force optimization method and central force optimization method with self-adaptive adjusting population size, and sub-swarm gravitation search method. Moreover, a measure called G-measure which can describe the distribution of local minima in search space is constructed.The main contributions of this thesis are summarized as follows:(1).For global optimization problems with inequality constraints, a new filled function with only one parameter is constructed. Its properties are no weaker than the objective function and constraint functions. It has no minimizer in the region no lower than that of the current minimizer of the objective function, and must exists a minimizer in the region lower that of the current minimizer. Furthermore, a novel optimization algorithm based on the new filled function is proposed and the experiments are conducted. The results indicate the proposed algorithm is efficient.(2).Considering that the existing central force optimization(CFO) methods are hard to achieve a good balance between the evolution speed and the quality of solutions, an improved central force optimization method based on the simplex method(SM) is proposed and is called SM-CFO. By periodical insertion of the best individual obtained by the SM operator into the detector population of the CFO, the proposed algorithm can get a proper balance between SM and CFO and achieve cooperative search of the CFO and SM With the help of CFO, SM can get away from local minima, and with SM, CFO can improve its local exploiting capability. Furthermore, in order to enhance the ability of CFO and SM, an improved Nelder-Mead SM is proposed. Through a thorough sensitivity analysis on the parameters of the proposed algorithm, some suggestions for the paramete setting are put forward.(3).In Central Force Optimization(CFO) methods, the population size is an important parameter which directly influences the ability to search an optimal solution in the search space. A large number of population can enhance the convergent speed, but will cause a lot of computation cost in each generation. It is also not a good idea in case where the search space is small. So, it is reasonable to dynamically adjust the population size through the entire CFO evolution process. Based on this idea, an adaptive population based CFO, termed as APCFO, is proposed, in which the population size either grows or shrinks at every iteration based on the performance of the population. Moreover, to keep both the effectiveness of the proposed algorithm and the population diversity, a clustering algorithm and the good point set algorithm are used to design increasing/decreasing operator. A set of standard test functions is chosen to test our algorithm. The results of the experiments lead to the conclusion that the proposed algorithm is more effective and efficient than the compared algorithms.(4).A new measure called G-measure is constructed which can describe approximately the distribution of local minima in search space. G-measure combines several information of objective function: gradient, convexity and concavity, and rate of decline. Guided by this measure, more initial points can be scattered in the region where contains more local minima. On the contrary, fewer initial points can be put in the region where contains the fewer local minima or no local minima.(5).The dynamic multi-swarm gravitational search algorithm(DMS-GSA) based on integrating a clustering technique and a new information interactive strategy is proposed. Dynamic multi-swarm is a recently developed strategy and has strong exploration ability by using regrouping operation. However, the frequently regrouping operation results in the deficiency of the exploitation ability. In order to achieve a good balance between the exploration and exploitation, the clustering technique and information interactive by cooperative learning strategy is hybridized to DMS-GSA, which makes information be used more effectively to generate better quality solutions. In the proposed regroup strategy, swarm is divided into several sub-swarm by clustering technique, which make sub-swarms’ distributions are more balanced. In the information interactive strategy, for each sub-swarm, each dimension of the two worst particles learns from the better particle of two randomly selected sub-swarms using tournament selection strategy, so that particles can have more excellent exemplars to learn and can find the global optimum more easily.