Research On Improvement And Applications Of Swarm Intelligent Algorithms

Optimization problem is a common problem in human production and social practice.Starting from the practical complex optimization problems,this research discussed the ant colony algorithm and the particle swarm optimization algorithm,which belong to swarm intelligent algorithm,then improved the algorithms and tested them in practical problems.At the same time,aiming at the logistics distribution centerlocation problem,the traditional nonlinear programming method is improved.The algorithm is tested and its practical application are completed.This paper discussed and studied from four aspects:In the first part,the ant colony algorithm is introduced and improved.The effectiveness of the improved algorithm is verified by the practical shortest path problem.It is proved that the expected strength of the shortest path increases with the increasing of iteration time when the parameters are ??1 and ??0.The expected sequence of the shortest path selection {?1(t)}monotonically increases and meets the condition(?)?1(t)=1.The ant colony algorithm is proved to be convergent for the shortest path problem and the parameter range of convergence is computed theoretically.The convergence of ant colony algorithm and the improved algorithm is analyzed under different parameter values.The following conclusions are obtained:1)Changing the value of pheromone intensity has obvious influence on the convergence of the algorithm.When the parameters are ?=0.9.?=11,?=5,ant colony algorithm has better convergence effect in the condition of Q=1 or Q=1000 and improved ant colony algorithm has better convergence effect in the condition of Q=1 or Q=100000.2)The larger the number of ants,the better the convergence of the algorithms,but it will inevitably lead to the increase of iteration time.3)When the parameter value are ??1 and ??0,the ant colony algorithm and the improved algorithm are convergent.When the above conditions are not satisfied,the algorithms do not converge.4)Different values of pheromone volatilization factor have little effect on the optimal value when it is valued between 0 and 1.The second part describes the particle swarm optimization(PSO)algorithm and introduced the fastest search direction forthe PSO algorithm to complete the improvement of the PSO algorithm.The position and velocity formulas of the algorithm iteration are analyzed.By solving the second order linear nonhomogeneous difference equation with constant coefficients,the parameter range of convergence of PSO and improved PSO algorithm are computed as B-?>1/2,-1<?<1.The convergence of the algorithmsare analyzed under different parameters.When ?=1.c1=0,c2=0,neither algorithm converges.The test function is used to test the PSO algorithm and the improved algorithm.It is verified that the improved algorithm is better than the original algorithm in terms of stability,convergence accuracy and speed.We apply PSO to the calculation of hydrogeological parameters and analyze the convergence,accuracy and sensitivity of the algorithm.The precision and sensitivity are improved by PSO algorithm.It provides a reliable algorithm for the establishmentof hydrological model and the determination of the aquifer parameters.In the third part,the ant colony algorithm and the PSO algorithm are combined.The ant colony algorithm is updated iteratively with the idea of genetic algorithm.The hybrid algorithm is applied to solve the travel salesman problem.The best one of the hybrid algorithm is to combine random crossover strategy D and mutation strategy B.(The crossover strategy D is randomly selecting a substring in the parent string 1,inserting the substring into the determined position of the parent string 2,and deleting the existing and repeated nodes in the parent string 2 at the same time to get the substring strategy.Mutation strategy B is randomly selecting a node from the 1?n visited nodes,exchanging this node with the previous visited nodes in the original path,and keeping the access order of the other nodes unchanged,then getting the new path.)The result of the shortest path,computed in the worst hybrid algorithm,is far better than the result from the ant colony algorithm.It shows that the hybrid algorithm combining PSO and ant colony algorithm is an effective improved algorithm.We analyzed the parameters of the hybrid algorithm to get the optimal iterative scheme.In the fourth part,firstly,the principle of classic method of solving unconstrained nonlinear programming such as gradient method,Newton method and quasi Newton method are analyzed and two improved algorithms are proposed.Through numerical experiments,the improved algorithmsare compared with the original algorithms and it is verified the improved algorithmsis better in iterative speed and accuracy.Secondly,the algorithm is applied in solving the logistics distribution centerlocation problem.In the location area,the new distribution center is built according to huff gravity model,and the maximum profit of the new distribution center is solved by using the maximum profit principle of the distribution center.Finally,this paper focused on the trust region algorithm.We extended the trust region algorithm to nonsmooth optimization field,the quasi cut vector is introduced to replace the gradient vector and gives a new method to update the approximate matrix in solving the trust region subproblem.The global convergence and superlinear convergence speed of the improved algorithm are verified the oretically.