The set-union knapsack problem(SUKP)is proved to be a strongly NP-hard problem,and it is an extension of the classic NP-hard problem:the 0-1 knapsack problem(KP).Solving the SUKP through exact approaches is computatio...The set-union knapsack problem(SUKP)is proved to be a strongly NP-hard problem,and it is an extension of the classic NP-hard problem:the 0-1 knapsack problem(KP).Solving the SUKP through exact approaches is computationally expensive.Therefore,several swarm intelligent algorithms have been proposed in order to solve the SUKP.Hyper-heuristics have received notable attention by researchers in recent years,and they are successfully applied to solve the combinatorial optimization problems.In this article,we propose a binary particle swarm optimization(BPSO)based hyper-heuristic for solving the SUKP,in which the BPSO is employed as a search methodology.The proposed approach has been evaluated on three sets of SUKP instances.The results are compared with 6 approaches:BABC,EMS,gPSO,DHJaya,b WSA,and HBPSO/TS,and demonstrate that the proposed approach for the SUKP outperforms other approaches.展开更多
1引言
F. F.Codd于七十年代提出了著名的关系数据库模型,经过几十年发展,以它为基础的关系数据库系统得到了广泛的流行和认可,它有着层次模型和网状模型无可比拟的优点,如灵活性、逻辑和物理独立性、数据完整性等.然而,它也有自身的不足...1引言
F. F.Codd于七十年代提出了著名的关系数据库模型,经过几十年发展,以它为基础的关系数据库系统得到了广泛的流行和认可,它有着层次模型和网状模型无可比拟的优点,如灵活性、逻辑和物理独立性、数据完整性等.然而,它也有自身的不足,就是对于不确定性的数据处理能力较差.展开更多
A new expression of vague sets is given. Based on the reference [3,4],we discuss the definition of intersec-tion and union and some properties of vague set again ,then similarity measure and examples are presented.
基金Supported partly by the Natural Science Foundation of Fujian Province(2020J01843)the Science and Technology Project of the Education Bureau of Fujian(JAT200403)
文摘The set-union knapsack problem(SUKP)is proved to be a strongly NP-hard problem,and it is an extension of the classic NP-hard problem:the 0-1 knapsack problem(KP).Solving the SUKP through exact approaches is computationally expensive.Therefore,several swarm intelligent algorithms have been proposed in order to solve the SUKP.Hyper-heuristics have received notable attention by researchers in recent years,and they are successfully applied to solve the combinatorial optimization problems.In this article,we propose a binary particle swarm optimization(BPSO)based hyper-heuristic for solving the SUKP,in which the BPSO is employed as a search methodology.The proposed approach has been evaluated on three sets of SUKP instances.The results are compared with 6 approaches:BABC,EMS,gPSO,DHJaya,b WSA,and HBPSO/TS,and demonstrate that the proposed approach for the SUKP outperforms other approaches.
文摘A new expression of vague sets is given. Based on the reference [3,4],we discuss the definition of intersec-tion and union and some properties of vague set again ,then similarity measure and examples are presented.
