使用马尔可夫决策过程对局部搜索元启发式算法进行建模
Modeling Local Search Metaheuristics Using Markov Decision Processes
AI总结：
本文提出了基于 Markov Decision Processes 的理论框架，用于分析局部搜索元启发式算法，提供收敛性结果与探索-利用权衡的明确刻画，指导算法选择，并展示了在 hill climbing 和 simulated annealing 中的应用。
摘要：
诸如 tabu search 或 simulated annealing 等局部搜索元启发式算法，是用于寻找组合优化问题近似最优解的流行启发式优化算法。然而，研究人员和从业者仍面临挑战：难以分析其行为，并难以在针对当前特定问题的海量可选元启发式算法中系统地进行选择。本文引入了一个基于 Markov Decision Processes (MDP) 的理论框架，用于分析局部搜索元启发式算法。该框架不仅有助于为单个算法提供收敛性结果，还对 exploration-exploitation 权衡提供了明确的刻画，并为从业者针对当前问题选择合适的元启发式算法提供了理论指导。我们详细介绍了该框架，并展示了如何将其应用于 hill climbing 和 simulated annealing 算法。
英文摘要：
Local search metaheuristics like tabu search or simulated annealing are popular heuristic optimization algorithms for finding near-optimal solutions for combinatorial optimization problems. However, it is still challenging for researchers and practitioners to analyze their behaviour and systematically choose one over a vast set of possible metaheuristics for the particular problem at hand. In this paper, we introduce a theoretical framework based on Markov Decision Processes (MDP) for analyzing local search metaheuristics. This framework not only helps in providing convergence results for individual algorithms, but also provides an explicit characterization of the exploration-exploitation tradeoff and a theory-grounded guidance for practitioners for choosing an appropriate metaheuristic for the problem at hand. We present this framework in detail and show how to apply it in the case of hill climbing and the simulated annealing algorithm.
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