非线性方程组的仿射尺度内点信赖域算法

Affine Scaling Interpoint Trust Region Algorithm for Nonlinear Equations

很多领域研究寻优问题时,所采用的寻优算法普遍存在全局搜索能力差、收敛速度慢的问题,导致求出的解无法达到最优。针对上述问题,研究了一种非线性方程组的仿射尺度内点信赖域算法。构建目标最小化或者目标最大化非线性方程组,并针对方程组设置等式或者不等式约束条件;在约束条件下,利用仿射尺度内点信赖域算法求取非线性方程组最优解;将所研究算法应用到有功优化当中,以线损最小化和电压偏差最小化构建非线性方程组,并为其设置四个约束条件,利用仿射尺度内点信赖域算法求取最优解。实验结果表明:与自适应粒子群算法、樽海鞘群算法以及改进差分灰狼算法相比,所研究算法应用下,线损以及电压偏差均要更小,说明仿射尺度内点信赖域算法的求解结果更优,算法的寻优能力更强。

When studying optimization problems in many fields,the problems of poor global search ability and slow convergence speed generally exist in the algorithm,which leads to the solution not reaching the optimum.An affine scale interior-point trust region algorithm for nonlinear equations is proposed.The objective minimization or objective maximization nonlinear equations are constructed,with the equality or inequality constraints set for the equations.Under the constraint conditions,the affine scale interior point trust region algorithm is used to obtain the optimal solution of the nonlinear equations.The proposed algorithm is applied to active power optimization,and the nonlinear equations are constructed with line loss minimization and voltage deviation minimization.Four constraint conditions are set for them,and the affine scale interpoint trust region algorithm is used to obtain the optimal solution.The experimental results show that compared with the adaptive particle swarm optimization algorithm,salps group algorithm and improved differential gray Wolf algorithm,the line loss and voltage deviation of the proposed algorithm are smaller under application,indicating that the affine scale interpoint trust region algorithm has better solution results and better search ability.