论文标题
关于离散仿真优化的随机标尺方法的注释
A Note on the Stochastic Ruler Method for Discrete Simulation Optimization
论文作者
论文摘要
在本文中，我们提出了Yan和Mukai在1992年最初描述的随机标尺方法的放松，以渐近地确定离散模拟优化问题的全局最佳。随机标尺的“原始”版本及其变体要求最佳解决方案的下一个估计值通过一定数量的测试，相对于随机标尺，将选择作为最佳解决方案的下一个估计值。这项要求 - 所有测试都需要通过 - 可以导致有希望的候选解决方案被拒绝，并可以减慢算法的收敛性。我们提出的对随机统治者算法的修改使这一要求放松了这一要求，并且我们从分析上表明，当当前解决方案附近的新解决方案是当前解决方案的下一个估算的“成功”候选者时，我们提出的随机标尺方法的变体会造成较少的计算开销。然后，我们以数字显示这可以通过多个数值示例产生加速收敛到最佳解决方案。我们还为在与原始随机标尺方法基础的假设集中相同的假设集中提供了渐近收敛的理论基础。
In this paper, we propose a relaxation to the stochastic ruler method originally described by Yan and Mukai in 1992 for asymptotically determining the global optima of discrete simulation optimization problems. The `original' version of the stochastic ruler and its variants require that a candidate for the next estimate of the optimal solution pass a certain number of tests with respect to the stochastic ruler to be selected as the next estimate of the optimal solution. This requirement - that all tests need to be passed - can lead to promising candidate solutions being rejected and can slow down the convergence of the algorithm. Our proposed modification to the stochastic ruler algorithm relaxes this requirement, and we show analytically that our proposed variant of the stochastic ruler method incurs lesser computational overhead when a new solution in the neighborhood of the current solution is a `successful' candidate for the next estimate of the current solution. We then show numerically that this can yield accelerated convergence to the optimal solution via multiple numerical examples. We also provide the theoretical grounding for the asymptotic convergence in probability of the variant to the global optimal solution under the same set of assumptions as those underlying the original stochastic ruler method.
