一种改进的基于群论的0-1背包折扣优化算法

Ran Wang, Zichao Zhang, Wing W. Y. Ng, Wenhui Wu
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引用次数: 4

摘要

折扣0-1背包问题(D0-1KP)已被证明是NP难问题,因此许多研究都集中在设计非确定性算法来解决它。基于群论的优化算法(GTOA)作为最近提出的进化算法(EA),可以为D0-1KP提供令人满意的结果。GTOA引入了代数的重要理论,即群论,来描述组合优化问题,并将群论中的经典运算应用于EA的算子设计。为了在每次进化迭代中根据一组现有的解生成更好的解,设计了一个重要的算子,称为随机线性组合算子(RLCO)。然而,应用群论中的运算的实际意义很难解释,并且所提出的RLCO缺乏可解释性,这给分析和改进算法带来了困难。在本文中,为了提高可解释性并进一步提高性能,我们提出了一种新的算子,称为随机xor算子(RXO),并从逐位运算的角度对其进行了解释。通过用RXO代替RLCO,实现了D0-1KP的一种新的GTOA算法。实验结果表明,它可以提供非常有竞争力的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An improved group theory-based optimization algorithm for discounted 0-1 knapsack problem

Discounted 0-1 knapsack problem (D0-1KP) has been proved to be NP-hard, thus a lot of researches focus on designing non-deterministic algorithms to solve it. Group theory-based optimization algorithm (GTOA), as a recently proposed evolutionary algorithm (EA), can provide satisfactory results to D0-1KP. GTOA introduces important theories of algebra, i.e., group theory, to describe combinatorial optimization problems, and applies the classic operations in group theory to design operators for EA. In order to generate a better solution according to a set of existing solutions during each evolutionary iteration, an important operator called random linear combination operator (RLCO) is designed. However, the practical meaning of applying the operations in group theory is hard to explain, and the proposed RLCO is lack of interpretability, causing difficulties in analyzing and improving the algorithm. In this paper, to improve the interpretability and further enhance the performance, we propose a new operator named random xor operator (RXO), and interpret it from the view point of bitwise operation. By replacing RLCO with RXO, a new GTOA algorithm is realized for D0-1KP. Experimental results demonstrate that it can provide very competitive performance.

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