Global optimization heuristics are popular to optimize hard non-convex problems. Despite their irrefutably large cost-to-solution, in the lack of other working greedy or convex approaches, global optimization algorithms remain the no-brainer choice. Nevertheless, successful use often requires tedious adjustments to initial parameters to avoid premature convergence. The Coupled Simulated Annealing approach proposed a method based on the coupling of multiple optimizers to escape premature convergence, having achieved success in optimizing hyperparameters of many applications of machine learning; however, a careful choice of the generation temperature is still required. In this paper we propose the Perpetual Orbit technique as a solution to control the generation temperature and avoid search stagnation. In principle, this technique can also be applied to other ensemble- and population-based algorithms that have a dispersion variable. The results of our experiments show superior performance when using the proposed technique because it makes the Couple Simulated Annealing totally parameter-free and capable of reaching equal or better solutions in more than 85\% cases across all functions and competitor methods analyzed.
Simulated annealing with hit-and-run for convex optimization: rigorous complexity analysis and practical perspectives for copositive programming
我们使用Abernethy和Hazan [arXiv 1507.02528v2，2015]建议的温度更新类型对Kalai和Vempala [Math of OR 31.2（2006）：253-266]的模拟退火算法进行了严格的复杂性分析。该算法只需要假设可行集的成员预言，我们证明了它返回一个解决方案在多项式时间内，这是近最优的高概率。此外，我们提出了一些修改，以提高该方法的实际性能，并提出了一些数值结果的测试问题，从共正规划。
Simulated annealing: in mathematical global optimization computation, hybrid with local or global search, and practical applications in crystallography and molecular modelling
