A common approach to global optimization is to combine local optimization methods with random restarts. Restarts have been used as a performance boosting approach. They can be a means to avoid “slow progress” by exploiting a potentially good solution, and restarts can enable the potential discovery of multiple local solutions, thus improving the overall quality of the returned solution. A multi-start method is a way to integrate local and global approaches; where the global search itself can be used to restart a local search. Bayesian optimization methods aim to find global optima of functions that can only be point-wise evaluated by means of a possibly expensive oracle. We propose the stochastic optimization with adaptive restart (SOAR) framework, that uses the predictive capability of Gaussian process models as a means to adaptively restart local search and intelligently select restart locations with current information. This approach attempts to balance exploitation with exploration of the solution space. We study the asymptotic convergence of SOAR to a global optimum, and empirically evaluate SOAR performance through a specific implementation that uses the Trust Region method as the local search component. Numerical experiments show that the proposed algorithm outperforms existing methodologies over a suite of test problems of varying problem dimension with a finite budget of function evaluations.

全局优化的常用方法是将局部优化方法与随机重启结合在一起。重新启动已被用作提高性能的方法。通过开发潜在的好的解决方案，它们可以避免“进度缓慢”，重新启动可以潜在地发现多个本地解决方案，从而提高返回解决方案的整体质量。多起点方法是一种整合本地方法和全局方法的方法。全局搜索本身可用于重新启动本地搜索。贝叶斯优化方法的目的是找到只能通过可能昂贵的预言器进行逐点评估的函数的全局优化。我们提出了带有自适应重启（SOAR）的随机优化框架，使用高斯过程模型的预测能力作为自适应重启本地搜索并利用当前信息智能地选择重启位置的方法。这种方法试图平衡开发与解决方案空间的探索。我们研究了SOAR渐近收敛到全局最优值的情况，并通过使用Trust Region方法作为本地搜索组件的特定实现从经验上评估了SOAR性能。数值实验表明，在功能评估预算有限的情况下，该算法在不同问题维度的一系列测试问题上优于现有方法。我们研究了SOAR渐近收敛到全局最优值的情况，并通过使用Trust Region方法作为本地搜索组件的特定实现从经验上评估了SOAR性能。数值实验表明，在功能评估预算有限的情况下，该算法在不同问题维度的一系列测试问题上优于现有方法。我们研究了SOAR渐近收敛到全局最优值的情况，并通过使用Trust Region方法作为本地搜索组件的特定实现从经验上评估了SOAR性能。数值实验表明，在功能评估预算有限的情况下，该算法在一系列问题尺寸各异的测试问题上优于现有方法。