Novel Hybrid Algorithms For Unconstrained Global Optimization Problems With Continuous Variables

Unconstrained global optimization problem with continuous variables is an important independent branch of modern optimization, it has been widely used in various areas, sunch as in science, engineering, business and management, etc. Genetic algorithm (GA) is a kind of global random search methods simulating biological evolution mechanisms. It has been found that lonely using GA to solve optimization problem may lead to premature convergence. Note that traditional optimization methods often have good convergence and local search capability. Hybridizing GA and local search algorithm will result in a novel algorithm called hybrid algorithm which synthesized high accuracy and convergence rate of traditional optimization and global convergence of GA.In the thesis, status and development of global optimization problems are introduced firstly, and then the major factor, evaluation criterion, convergence theory, current research status, and the existing difficulties of GA are summarized. The main contributions of this thesis can be summarized as follow:In chaper 3, In order to make the genetic algorithms escape from local minima in solving global optimization problems, a smooth function was introduced as the fitness function. This function can eliminate all such local optimal solutions which are worse than the optimal solutions found so far. Taking the properties of the smooth function into consideration, a sphere search was designed which can help smooth function escape from local minima and find the new descent region, and unconstrained search and golden search are applied in local search to improve the performance of local search. Finally, a novel hybrid algorithm called NHA for global optimization problems was proposed, and its global convergence is proved in detail. Finally, the effectiveness is demonstrated by numerical simulations for all test functions.In chaper 4, Consider influence of initial population and genetic operator to the algorithm, a improved hybrid algorithm named INHA is proposed, its initial population and crossover operator using uniform design method, an non-uniform mutation operator is designed by balancing the ability of global search and local exploitation. The simulation results indicate the effectiveness of the proposed algorithm.