中文摘要：

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（岱）；在中、低噪声水平上的相关性态优于Tikhonov正则化方法．

英文摘要：

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 strat- egy 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.