真正困难的二次分配问题所在：QAP-SAT实例
Where the Really Hard Quadratic Assignment Problems Are: the QAP-SAT instances
AI总结：
针对二次分配问题（QAP）的相变现象，提出基于子模性的QAP-SAT设计以刻画问题难度，经分支定界与禁忌搜索实验验证，两类临界参数高度相关，可预测困难实例。
摘要：
二次分配问题（Quadratic Assignment Problem, QAP）是进化计算领域，乃至更广泛的组合优化领域的核心研究方向之一。本文研究QAP的相变现象，即在问题参数的狭窄区间内，问题的计算复杂度与可满足性会发生剧烈变化。为探究这一现象，我们基于子模性提出了一种新的初始问题设计方案QAP-SAT，通过新特征刻画问题难度。我们使用分支定界求解器和禁忌搜索求解器对该分解方法开展了实验研究，随后提出了一个相变参数。实验表明，对于禁忌搜索而言，相变可满足性的临界参数与求解代价的临界参数高度相关，从而可用于预测困难实例。
英文摘要：
The Quadratic Assignment Problem (QAP) is one of the major domains in the field of evolutionary computation, and more widely in combinatorial optimization. This paper studies the phase transition of the QAP, which can be described as a dramatic change in the problem's computational complexity and satisfiability, within a narrow range of the problem parameters. To approach this phenomenon, we introduce a new QAP-SAT design of the initial problem based on submodularity to capture its difficulty with new features. This decomposition is studied experimentally using branch-and-bound and tabu search solvers. A phase transition parameter is then proposed. The critical parameter of phase transition satisfaction and that of the solving effort are shown to be highly correlated for tabu search, thus allowing the prediction of difficult instances.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
