连接搜索空间结构、运行时间动态和问题难度：揭开禁忌搜索神秘面纱的一步
Linking Search Space Structure, Run-Time Dynamics, and Problem Difficulty: A Step Toward Demystifying Tabu Search
摘要：
禁忌搜索是一种有效的算法，它能为各种NP难组合优化问题找到高质量的解。尽管禁忌搜索取得了广泛的成功，研究人员对该算法的许多关键理论方面的理解很差，包括高级运行时间动态模型和影响问题难度的搜索空间特征的识别。我们认为这些问题的上下文中的作业车间调度问题（JSP），禁忌搜索算法已被证明是非常有效的领域。在此之前，我们证明了随机局部最优解和最近的最优解之间的平均距离与Taillard介绍的JSP的著名禁忌搜索算法的问题难度高度相关。在本文中，我们讨论了这种措施的各种缺点，并开发了一个新的模型的问题的难度，纠正这些不足之处。我们表明，Taillards算法可以高保真度地建模为直接随机游走的简单变体。随机游走模型解释了为随机JSP找到最优和次优解决方案所需的成本的几乎所有可变性，并解释了随机JSP与结构化JSP在难度上的差异。最后，我们讨论和实证两个新的预测禁忌搜索算法的行为。首先，构造初始解的方法不太可能影响禁忌搜索的性能。第二，禁忌任期应选择尽可能小，同时避免搜索停滞;值大于必要的导致性能显着下降。
英文摘要：
Tabu search is one of the most effective heuristics for locating high-quality solutions to a diverse array of NP-hard combinatorial optimization problems. Despite the widespread success of tabu search, researchers have a poor understanding of many key theoretical aspects of this algorithm, including models of the high-level run-time dynamics and identification of those search space features that influence problem difficulty. We consider these questions in the context of the job-shop scheduling problem (JSP), a domain where tabu search algorithms have been shown to be remarkably effective. Previously, we demonstrated that the mean distance between random local optima and the nearest optimal solution is highly correlated with problem difficulty for a well-known tabu search algorithm for the JSP introduced by Taillard. In this paper, we discuss various shortcomings of this measure and develop a new model of problem difficulty that corrects these deficiencies. We show that Taillards algorithm can be modeled with high fidelity as a simple variant of a straightforward random walk. The random walk model accounts for nearly all of the variability in the cost required to locate both optimal and sub-optimal solutions to random JSPs, and provides an explanation for differences in the difficulty of random versus structured JSPs. Finally, we discuss and empirically substantiate two novel predictions regarding tabu search algorithm behavior. First, the method for constructing the initial solution is highly unlikely to impact the performance of tabu search. Second, tabu tenure should be selected to be as small as possible while simultaneously avoiding search stagnation; values larger than necessary lead to significant degradations in performance.
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