GSet Dataset

The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging combinatorial optimization-based problems with tons of application areas that make this problem highly admissible. Due to its admissibility, the problem is solved using the Harris Hawk Optimization algorithm (HHO). Though HHO effectively solved some engineering optimization problems; in the field of combinatorial optimization-based problems, the number is very few with better outcomes than any other available metaheuristic algorithms in contemporary times. Thus HHO along with some additional operators is used to solve the max-cut problem. Synthesis and decomposition operators are used to modify the fitness of the hawk in such a way that they can provide precise results. A mutation mechanism along with an adjustment operator has improvised the outcome obtained from the updated hawk. To accept the potential result, the acceptance criterion has been used, and then the repair operator is applied in the proposed approach. The proposed system provided comparatively better outcomes on the G-set dataset than other state-of-the-art algorithms. It obtained 533 cuts more than the discrete cuckoo search algorithm in 9 instances, 1036 cuts more than PSO-EDA in 14 instances, and 1021 cuts more than TSHEA in 9 instances. But for four instances, the cuts are lower than PSO-EDA and TSHEA. Besides, the statistical significance has also been tested using the Wilcoxon signed rank test to provide proof of the superior performance of the proposed method. In terms of solution quality, MC-HHO can produce outcomes that are quite competitive when compared to other related state-of-the-art algorithms.

最大割问题（max-cut problem）的目标是对任意给定图进行割划分，使得因割边而拆分得到的两个顶点子集之间的割边总权重达到最大。尽管它属于基础的图划分问题，但却是最具挑战性的基于组合优化的问题之一，其应用场景极为广泛，因此该问题具有极高的研究价值。鉴于其研究价值，本文采用哈里斯鹰优化算法（Harris Hawk Optimization, HHO）对该问题进行求解。尽管哈里斯鹰优化算法已有效解决了部分工程优化问题，但在组合优化领域，能够优于当前主流元启发式算法的应用案例仍寥寥无几。因此，本文将哈里斯鹰优化算法与若干附加算子相结合，用于求解最大割问题。通过合成与分解算子对鹰群的适应度进行调整，以获得更为精准的求解结果。结合变异机制与调整算子，对更新后的鹰群求解结果进行优化。本文所提方法采用接纳准则筛选潜在最优解，并随后应用修复算子对解进行修正。在G集数据集（G-set dataset）上，本文所提方法的求解结果相较于其他主流先进算法更为优异。在9个测试实例中，其相较于离散布谷鸟搜索算法（discrete cuckoo search algorithm）多获得533个割边；在14个测试实例中，相较于PSO-EDA多获得1036个割边；在9个测试实例中，相较于TSHEA多获得1021个割边。但在4个测试实例中，其割边数量略低于PSO-EDA与TSHEA算法。此外，本文通过威尔科克森符号秩检验（Wilcoxon signed rank test）对结果进行统计显著性验证，以证明所提方法的性能优势。在求解质量方面，MC-HHO相较于其他同类主流先进算法，仍具备较强的竞争力。

搜集汇总

背景与挑战

背景概述

GSet Dataset是一个用于最大割问题研究的图论数据集，最大割问题是图划分中的组合优化难题，具有广泛的应用价值。该数据集通过Harris Hawk优化算法及其增强操作符（如合成、分解和修复机制）进行求解，在G-set数据集上相比其他先进算法（如离散布谷鸟搜索、PSO-EDA和TSHEA）表现出更优的切割性能，并通过统计检验验证了其有效性。