Abstract:

In order to overcome the problem for the greatly-taken time,high space complexity and slow convergence of the traditional interval algorithm in solving the global optimization,an affine algorithm introducing the traditional affine algorithm and the local optimization algorithm is proposed. In this new algorithm,the upper bound of the global optimal solution is obtained by the local optimization algorithm and the affine arithmetic for the objective
function in each subinterval,and the carding or discarding of the corresponding interval is determined according to the comparison between the lower bound of the affine arithmetic in each subinterval and the upper bound of the global optimal solution. Moreover,the subinterval containing the optimal value is obtained by deleting the subinterval without the optimal value. Numerical simulation results show that,as compared with the traditional interval optimization algorithm,the proposed algorithm possesses higher convergence speed and occupies less system resource.

Key words: global optimization, affine algorithm, interval algorithm, deterministic algorithm