Hanqing Liu

An Chen, Zhigang Ren, Muyi Wang et al.

Problem decomposition plays a vital role when applying cooperative coevolution (CC) to large scale global optimization problems. However, most learning-based decomposition algorithms either only apply to additively separable problems or face the issue of false separability detections. Directing against these limitations, this study proposes a novel decomposition algorithm called surrogate-assisted variable grouping (SVG). SVG first designs a general-separability-oriented detection criterion according to whether the optimum of a variable changes with other variables. This criterion is consistent with the separability definition and thus endows SVG with broad applicability and high accuracy. To reduce the fitness evaluation requirement, SVG seeks the optimum of a variable with the help of a surrogate model rather than the original expensive high-dimensional model. Moreover, it converts the variable grouping process into a dynamic-binary-tree search one, which facilitates reutilizing historical separability detection information and thus reducing detection times. To evaluate the performance of SVG, a suite of benchmark functions with up to 2000 dimensions, including additively and non-additively separable ones, were designed. Experimental results on these functions indicate that, compared with six state-of-the-art decomposition algorithms, SVG possesses broader applicability and competitive efficiency. Furthermore, it can significantly enhance the optimization performance of CC.

Hanqing Liu, Na Ruan, Joseph K. Liu

The consensus protocol named proof of work (PoW) is widely applied by cryptocurrencies like Bitcoin. Although security of a PoW cryptocurrency is always the top priority, it is threatened by mining attacks like selfish mining. Researchers have proposed many mining attack models with one attacker, and optimized the attacker's strategy. During these mining attacks, an attacker pursues a higher relative revenue (RR) by wasting a large amount of computational power of the honest miners at the cost of a small amount of computational power of himself. In this paper, we propose a mining attack model with two phases: the original system and the multi-attacker system. It is the first model to provide both theoretical and quantitative analysis of mining attacks with two attackers. We explain how the original system turns into the multi-attacker system by introducing two attackers: the internal attacker and the external attacker. If both attackers take the attacking strategy selfish mining, the RR of the internal attacker in multi-attacker system will drop by up to 31.9% compared with his RR in original system. The external attacker will overestimate his RR by up to 44.6% in multiattacker system. Unexpected competitions, auctions between attackers and overestimation of attackers' influence factor are three main causes of both attackers' dropping RR. We propose a mining strategy named Partial Initiative Release (PIR) which is a semi-honest mining strategy in multi-attacker system. In some specific situations, PIR allows the attacker to get more block reward by launching an attack in multi-attacker system.