一种新的并行协同地形平滑算法及其在 TSP 和 UBQP 中的应用
A New Parallel Cooperative Landscape Smoothing Algorithm and Its Applications on TSP and UBQP
AI总结：
本文将同伦凸变换扩展至无约束二元二次规划（UBQP），提出单峰UBQP构建方法与地形平滑迭代局部搜索（LSILS）框架，并开发并行协同变体PC-LSILS，有效提升了UBQP和TSP的求解性能。
摘要：
组合优化问题（COP）因其解空间中存在大量局部最优解而难以求解。人们提出了各种方法来平滑 COP 的解空间，包括针对旅行商问题（TSP）的同伦凸（HC）变换。本文通过提出一种构建任意规模单峰玩具 UBQP 的方法，将 HC 变换方法扩展到无约束二元二次规划（UBQP）。我们在理论上证明了所构造的玩具 UBQP 的单峰性。随后，我们利用 HC 变换框架应用该单峰玩具 UBQP 来平滑原始 UBQP，并实证验证了平滑效果。接着，我们引入一个结合 HC 变换的迭代算法框架，称为地形平滑迭代局部搜索（LSILS）。我们在各种 UBQP 实例上进行的实验分析表明了 LSILS 的有效性。此外，本文提出了 LSILS 的并行协同变体，记为 PC-LSILS，并将其应用于 UBQP 和 TSP。实验结果表明，PC-LSILS 改善了 HC 变换的平滑性能，并进一步提升了算法的整体性能。
英文摘要：
Combinatorial optimization problem (COP) is difficult to solve because of the massive number of local optimal solutions in his solution space. Various methods have been put forward to smooth the solution space of COPs, including homotopic convex (HC) transformation for the traveling salesman problem (TSP). This paper extends the HC transformation approach to unconstrained binary quadratic programming (UBQP) by proposing a method to construct a unimodal toy UBQP of any size. We theoretically prove the unimodality of the constructed toy UBQP. After that, we apply this unimodal toy UBQP to smooth the original UBQP by using the HC transformation framework and empirically verify the smoothing effects. Subsequently, we introduce an iterative algorithmic framework incorporating HC transformation, referred as landscape smoothing iterated local search (LSILS). Our experimental analyses, conducted on various UBQP instances show the effectiveness of LSILS. Furthermore, this paper proposes a parallel cooperative variant of LSILS, denoted as PC-LSILS and apply it to both the UBQP and the TSP. Our experimental findings highlight that PC-LSILS improves the smoothing performance of the HC transformation, and further improves the overall performance of the algorithm.
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。
