Application Of Ant Colony Optimization For Searching All Function Extremum

Ant Colony Optimization (ACO) is another intelligent optimal algorithm after the simulated annealing,the genetic algorithms,and the tabu search etc, which is firstly proposed by Italian scholar M.Dorigo and his colleagues. Now it has been applied to solve a series of combination optimization problems widely,such as Traveling Salesman Problem,Quadratic Assignment Problem,Vehicle Routing Problem,Graph Coloring Problem and so on. These applications showed that ACO has great superiority in solving complicated discrete optimization problems. The application on continuous function optimization problems is another reserch topic for ACO, and the multi-modal function optimization is an important aspect of function optimization. However, the study of ACO on this topic is mainly focused on solving the maximum (minimum) value of a given function currently and all the multiple values is poor. So in this thesis, ACO is applied to search all the function extremum. The main research contents are as follow:(1) Development, biological mechanism and current research situation of ant colony optimization are introduced. Moreover, the modeling course and realizing steps are introduced in detail.(2) ACO for finding all the multiple values of function is introduced in detail. A new feature can be seen when ACO was applied to finding multiple optima of a multimodal function. The new feature is that, through ants'transference to neighbor intervals several times, there is no ant in some intervals, and a lot of or several ants in other intervals. Generally speaking, the intervals in which ants are distributed are just the intervals which contain extreme values. Firstly, the author studied the new feature. Then based the new feature, this paper presents a novel ant colony algorithm to find all the multiple values of function. The characteristic of the algorithm is that only the intervals in which ants are distributed are thinned again in order to search for extreme values. If the thinned intervals are small enough, the algorithm will stop. Experiments show that the algorithm presented in this paper can find out all the multiple optima of a given multimodal function. Especially, the new algorithm is not only of high precision, but also of fast convergence and of good stability.(3) In order to understand the algorithm present in this paper easily, the data structure and the procedure code of the algorithm are introduced in detail.