Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most c...Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not. The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace. Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e.g., Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.展开更多
文摘Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not. The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace. Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e.g., Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.
