论文标题
非Convex多目标优化程序的分段凸化方法，带有框约束
A Piecewise Convexification Method for Non-Convex Multi-Objective Optimization Programs with Box Constraints
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $α$-based Branch and Bound (${\rm αBB}$) method of global optimization and the interval subdivision, a series of convex relaxation sub-multiobjective problems for this non-convex multi-objective optimization problem are firstly obtained, and these sub-problems constitute a piecewise convexification problem of the original problem on the whole box. We then construct the (approximate, weakly) efficient solution set of this piecewise convexification problem, and use these sets to approximate the globally (weakly) efficient solution set of the original problem. Furthermore, we propose a piecewise convexification algorithm and show that this algorithm can also obtain approximate globally efficient solutions by calculating a finite subset of the efficient solution set of the multi-objective convex sub-problems only. Finally, its performance is demonstrated with various test instances.
