A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline performance. However, this analysis may be too pessimistic to give valuable insight on a problem. Several workarounds exist, such as randomized algorithms. This paper aims to propose computational methods to construct randomized algorithms and to bound their performance on the classical online bin stretching problem. A game theory method is adapted to construct lower bounds on the performance of randomized online algorithms via linear programming. Another computational method is then proposed to construct randomized algorithms which perform better than the best deterministic algorithms known. Finally, another lower bound method for a restricted class of randomized algorithm for this problem is proposed.

翻译：在线优化中一个被广泛研究的性能度量是竞争分析。它对应于算法在所有可能输入下的最坏情况性能与最优离线性能之比。然而，这种分析可能过于悲观，无法为问题提供有价值的见解。现有多种改进方法，例如随机算法。本文旨在提出计算方法来构建随机算法，并确定其在经典在线装箱拉伸问题上的性能界限。我们采用博弈论方法，通过线性规划构建随机在线算法性能的下界。随后提出另一种计算方法来构建性能优于已知最佳确定性算法的随机算法。最后，针对该问题的一类受限随机算法，提出了另一种下界构建方法。