毫秒级在线混合计数器Optimization
Online Mixed-Integer Optimization in Milliseconds
摘要：
我们提出了一种使用机器学习以非常高的速度解决在线混合整数优化（MIO）问题的方法。通过利用在线优化的重复性，我们能够大大加快解决方案的时间。我们的方法使用[BS 21]中提出的优化框架的声音将最优解编码为表示为策略的少量信息量。这样，优化算法的核心部分就变成了一个可以很快解决的多类分类问题。在这项工作中，我们将该框架扩展到实时和高速应用程序，重点是参数混合整数二次优化（MIQO）。我们提出了一个非常快速的在线优化算法，包括一个前馈神经网络（NN）的评价和一个线性系的解决方案，其中矩阵已经被分解。因此，这种在线方法不需要任何求解器或迭代算法。我们所提出的方法的速度都在所需的总计算和测量的执行时间。我们估计的浮点运算（触发器）的数量需要完全恢复的最优解的函数的问题尺寸。与最先进的MIO例程相比，我们的方法的在线运行时间是非常可预测的，并且可以低于单个矩阵分解时间。我们基准我们的方法对国家的最先进的求解器Guesthouse获得从两到三个数量级的加速从燃料电池能源管理，稀疏的投资组合优化和运动规划与避障的例子。
英文摘要：
We propose a method to solve online mixed-integer optimization (MIO) problems at very high speed using machine learning. By exploiting the repetitive nature of online optimization, we are able to greatly speedup the solution time. Our approach encodes the optimal solution into a small amount of information denoted as strategy using the Voice of Optimization framework proposed in [BS21]. In this way the core part of the optimization algorithm becomes a multiclass classification problem which can be solved very quickly. In this work, we extend that framework to real-time and high-speed applications focusing on parametric mixed-integer quadratic optimization (MIQO). We propose an extremely fast online optimization algorithm consisting of a feedforward neural network (NN) evaluation and a linear system solution where the matrix has already been factorized. Therefore, this online approach does not require any solver nor iterative algorithm. We show the speed of the proposed method both in terms of total computations required and measured execution time. We estimate the number of floating point operations (flops) required to completely recover the optimal solution as a function of the problem dimensions. Compared to state-of-the-art MIO routines, the online running time of our method is very predictable and can be lower than a single matrix factorization time. We benchmark our method against the state-of-the-art solver Gurobi obtaining from two to three orders of magnitude speedups on examples from fuel cell energy management, sparse portfolio optimization and motion planning with obstacle avoidance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
