一种求解非线性多目标优化问题的隧道法
A Tunneling Method for Nonlinear Multi-objective Optimization Problems
AI总结：
针对含多局部帕累托前沿的非凸非线性多目标优化问题，提出无需先验参数与目标排序的隧道法，通过辅助函数迭代寻优构建全局帕累托前沿近似，设计算法并证明收敛，数值实验验证了方法有效性。
摘要：
本文借鉴单目标隧道法的部分思路，提出了一种用于求解非线性多目标优化问题的隧道法。该方法无需预先选取任何参数，也不需要目标函数的排序信息。在任意临界点处，通过构造辅助函数来寻找一个优于前一个临界点的新临界点。通过反复执行隧道过程，可针对可能包含多个局部帕累托前沿的非凸多目标优化问题，构建更全面的全局帕累托前沿近似。随后基于该辅助函数设计了算法，并在较弱假设下证明了算法的收敛性。最后通过多个数值算例验证了所提方法的有效性，同时佐证了理论结果的正确性。
英文摘要：
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering information of the objective functions. At any critical point, an auxiliary function is developed to find a different critical point that dominates the previous one. By repeatedly applying the tunneling procedure, it is possible to construct a broader approximation to the global Pareto front in nonconvex multi-objective optimization problems that may contain multiple local Pareto fronts. An algorithm is then designed based on this auxiliary function, and the convergence of this algorithm is justified under some mild assumptions. Finally, several numerical examples are presented to illustrate the effectiveness of the proposed method and to justify the theoretical results.
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