Optimization problems exist in science research and engineering application, it is attractive and challenging to research the solving method. The traditional optimization algorithms such as enumeration method, search algorithms based on grads, Newton method etc, have the characteristics of a perfect mathematical foundation, reliability, maturation. But the traditional optimization algorithms have the complex computation and have the strict demand to the continuity of objective function. At the same time, it is difficult to search the global optimum when the optimization problem is dispersed, no derivative, severe pathological. In recent years, Evolutionary computation, such as Genetic Algorithms, Particle Swarm Optimizer, provides new ideas and means for solving optimization problems. Genetic Algorithm has the merits of intelligence, not requiring differential coefficient or other assistant information. And Particle Swarm Optimizer is not need the problem's character information and not need to set many parameters. Genetic Algorithms and Particle Swarm Optimizer are effective methods to solve optimization problems. At the same time, algorithms exit some shortcomings, such as premature convergence, easily falling into local optimal solution. So optimization algorithms can not meet the needs of practical application. Then, designing effective algorithms for solving optimization problems is of practical significance.In this paper, it chooses Genetic Algorithm and Particle Swarm Optimizer as research objects, and research on solving kinds of optimization problems. The main contents of paper as follows:(1) The paper analysis optimization problems, Genetic Algorithm, Particle Swarm Algorithm, and elaborate the basic principles, basic processes, elements and the application of Genetic Algorithm, introduces the principles, basic steps and the basic characteristics of Particle Swarm Algorithm.(2) The paper proposes an improved Genetic Algorithm (Leading Crossover Genetic Algorithm, LCGA). It executes the same location crossover in order to generate new individual when two father individuals have the low similarity. Otherwise, when two father individuals have the high similarity, Genetic Algorithm executes different location crossover to get new individual. Then five different test functions are used to test the improved Genetic Algorithm. The simulation results show that the strategy is feasible and effective. (3) LCGA is applied to solving the knapsack problem which uses the method of greedy repair to handle constraints. The results show that Lead Crossover Genetic Algorithm finds optimal solution more effectively and more quickly than traditional Genetic Algorithm. It verifies the validity and superiority of LCGA.(4) The paper introduces an adaptive Particle Swarm Optimizer (New Adaptive Particle Swarm Optimizer, NAPSO). New Adaptive Particle Swarm Optimizer adaptively adjusts the inertia weight, and adopts different velocity and position formula according to judge whether there is stagnation of particle swarm in the run of algorithm. It will maintain the diversity of population, and improve the ability to out of local optimum and local search. Then, the proposed algorithm has been applied to a set of benchmark problems and compared with the traditional optimization algorithms. The results show the advantage of solving function optimization problems. The research will further enrich and improve the theory and application of Genetic Algorithm and Particle Swarm Optimizer. |