基于多目标优化的病态逆问题求解

针对科学和工程研究中的病态逆问题,提出了基于多目标优化的求解方法.该方法将各次观测所得问题方程组残差作为多目标,并进一步将该多目标转化为单一目标,通过遗传算法寻求问题最优解,从而利用多次观测的有效信息,达到稳定病态逆问题解的目的.数值算例表明,该方法在参数反演精度和抗噪方面,显著优于最小二乘法(LS);在中、低噪声水平上的相关性态优于Tikhonov正则化方法.

Resolution Strategy for Ill-posed Inverse Problems Based on Multi-objective Optimization

The resolution strategy for ill-posed inverse problems encountered in science and engineering researches is put forward,based on multi-objective optimization.In the strategy,the residues of the equations of inverse problem corresponding with each measure are regarded as multi-objectives to be optimized,then the multi-objective is incorporated to one objective which can be optimized using genetic algorithm.Using the efficient information of each measure,the strategy gives a robust solution for the ill-pose inverse problem.Numerical examples show that the strategy's performances in solution precision and noise immunity are significantly better than least square method(LS) and Tikhonov regularization method when measurement noise lies in medium and low levels.