使用提升的mp-MIQP解决方案的有效评估
Efficient evaluation of mp-MIQP solutions using lifting
摘要：
本文提出了一种有效的方法来评估多参数混合整数二次规划（mp-MIQP）的解决方案，例如在控制问题中涉及离散时间混合系统的二次成本。传统上，在线评估需要逐段二次值函数的顺序比较。作为主要贡献，我们引入了一个提升的参数空间，其中的分段二次值函数成为分段仿射，可以合并到一个单一的值函数定义在一个单一的多面体分区没有任何重叠。这使得使用单个二叉搜索树的高效点定位方法成为可能。数值实验包括一个电力电子应用程序，并展示了一个在线加速高达数量级。我们还展示了如何实现在线评估时间可以权衡对离线计算时间。
英文摘要：
This paper presents an efficient approach for the evaluation of multi-parametric mixed integer quadratic programming (mp-MIQP) solutions, occurring for instance in control problems involving discrete time hybrid systems with quadratic cost. Traditionally, the online evaluation requires a sequential comparison of piecewise quadratic value functions. As the main contribution, we introduce a lifted parameter space in which the piecewise quadratic value functions become piecewise affine and can be merged to a single value function defined over a single polyhedral partition without any overlaps. This enables efficient point location approaches using a single binary search tree. Numerical experiments include a power electronics application and demonstrate an online speedup up to an order of magnitude. We also show how the achievable online evaluation time can be traded off against the offline computational time.
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