二次指派问题的局部最优网络
Local Optima Networks of the Quadratic Assignment Problem
摘要：
使用最近提出的组合景观模型，局部最优网络（LON），我们进行了彻底的分析的两种类型的实例的二次分配问题（QAP）。该网络模型是景观的简化，其中节点对应于局部最优值，边缘说明了它们的吸引域之间的相邻概念。该模型的灵感来自物理化学中提出的势能面的“固有网络”概念。从所谓的均匀QAP实例和类实数QAP实例中提取的局部最优网络，显示出明显区分这两种类型实例的特征。分析结果除了明确证实了搜索难度随问题维数的增加而增加外，还提供了新的证据，说明了为什么类实数实例更容易用启发式搜索精确求解，而均匀实例更容易近似求解。虽然局部最优网络模型仍在发展中，我们认为，它提供了一个新的组合景观，开辟了新的分析工具和理解问题的难度在组合优化的可能性。
英文摘要：
Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the landscape in which the nodes correspond to the local optima, and the edges account for the notion of adjacency between their basins of attraction. The model was inspired by the notion of 'inherent network' of potential energy surfaces proposed in physical-chemistry. The local optima networks extracted from the so called uniform and real-like QAP instances, show features clearly distinguishing these two types of instances. Apart from a clear confirmation that the search difficulty increases with the problem dimension, the analysis provides new confirming evidence explaining why the real-like instances are easier to solve exactly using heuristic search, while the uniform instances are easier to solve approximately. Although the local optima network model is still under development, we argue that it provides a novel view of combinatorial landscapes, opening up the possibilities for new analytical tools and understanding of problem difficulty in combinatorial optimization.
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