ABSTRACT

We investigate the potential of applying a state-of-the-art, local derivative-free solver, Py-BOBYQA to global optimization problems. In particular, we demonstrate the potential of a restarts procedure – as distinct from multistart methods – to allow Py-BOBYQA to escape local minima (where ordinarily it would terminate at the first local minimum found). We also introduce an adaptive variant of restarts which yields improved performance on global optimization problems. As Py-BOBYQA is a model-based trust-region method, we compare largely with other global optimization methods for which (global) models are important, such as Bayesian optimization and response surface methods; we also consider state-of-the-art representative deterministic and stochastic codes, such as DIRECT and CMA-ES. We find numerically that the restarts procedures in Py-BOBYQA are effective at helping it to escape local minima, when compared to using no restarts in Py-BOBYQA. Additionally, we find that Py-BOBYQA with adaptive restarts has comparable performance with global optimization solvers for all accuracy/budget regimes, in both smooth and noisy settings. In particular, Py-BOBYQA variants are best performing for smooth and multiplicative noise problems in high-accuracy regimes. As a by-product, some preliminary conclusions can be drawn on the relative performance of the global solvers we have tested with default settings.

摘要

我们调查了应用最先进的本地技术的潜力无导数求解器，Py-BOBYQA 到全局优化问题。特别是，我们展示了重新启动过程的潜力——与多启动方法不同——以允许 Py-BOBYQA 逃避局部最小值（通常它会在找到的第一个局部最小值处终止）。我们还引入了一种自适应的重启变体，它可以提高全局优化问题的性能。由于 Py-BOBYQA 是一种基于模型的信任域方法，我们在很大程度上与其他（全局）模型很重要的全局优化方法进行了比较，例如贝叶斯优化和响应面方法；我们还考虑了最先进的代表性确定性和随机代码，例如 DIRECT 和 CMA-ES。我们从数值上发现 Py-BOBYQA 中的重启程序在帮助它摆脱局部最小值方面是有效的，与在 Py-BOBYQA 中不使用重新启动相比。此外，我们发现具有自适应重启的 Py-BOBYQA 在平滑和嘈杂的设置中，对于所有精度/预算方案，具有与全局优化求解器相当的性能。特别是，Py-BOBYQA 变体在高精度状态下的平滑和乘性噪声问题上表现最佳。作为副产品，可以对我们使用默认设置测试的全局求解器的相对性能得出一些初步结论。