This paper considers the online scheduling problem on m(m≥3)parallel machines(the first k machines with grade 1 and the remaining m-k machines with grade 2)with two Go S levels and makespan as the objective function....This paper considers the online scheduling problem on m(m≥3)parallel machines(the first k machines with grade 1 and the remaining m-k machines with grade 2)with two Go S levels and makespan as the objective function.The jobs arrive over time with grade 1 or 2 and an arrival job can be assigned to a machine only when the grade of the job is no less than the grade of the machine.Three cases are considered:(i)For k=1,the authors present an online algorithm with competitive ratio of9/5.(ii)For 1<k<m-1,an online algorithm with competitive ratio of 2.280 is proposed.(iii)For k=m-1,an online algorithm is presented with competitive ratio of 2.All the three algorithms are based on greedy algorithm with a similar structure.At last,numerical instances are given and the average competitive ratios of the instances show good performance of the proposed algorithms.展开更多
We propose a new algorithm,named Asymmetric Genetic Algorithm(AGA),for solving optimization problems of steel frames.The AGA consists of a developed penalty function,which helps to find the best generation of the popu...We propose a new algorithm,named Asymmetric Genetic Algorithm(AGA),for solving optimization problems of steel frames.The AGA consists of a developed penalty function,which helps to find the best generation of the population.The objective function is to minimize the weight of the whole steel structure under the constraint of ultimate loads defined for structural steel buildings by the American Institute of Steel Construction(AISC).Design variables are the cross-sectional areas of elements(beams and columns)that are selected from the sets of side-flange shape steel sections provided by the AISC.The finite element method(FEM)is utilized for analyzing the behavior of steel frames.A 15-storey three-bay steel planar frame is optimized by AGA in this study,which was previously optimized by algorithms such as Particle Swarm Optimization(PSO),Particle Swarm Optimizer with Passive Congregation(PSOPC),Particle Swarm Ant Colony Optimization(HPSACO),Imperialist Competitive Algorithm(ICA),and Charged System Search(CSS).The results of AGA such as total weight of the structure and number of analyses are compared with the results of these algorithms.AGA performs better in comparison to these algorithms with respect to total weight and number of analyses.In addition,five numerical examples are optimized by AGA,Genetic Algorithm(GA),and optimization modules of SAP2000,and the results of them are compared.The results show that AGA can decrease the time of analyses,the number of analyses,and the total weight of the structure.AGA decreases the total weight of regular and irregular steel frame about 11.1%and 26.4%in comparing with the optimized results of SAP2000,respectively.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71390334 and 11271356
文摘This paper considers the online scheduling problem on m(m≥3)parallel machines(the first k machines with grade 1 and the remaining m-k machines with grade 2)with two Go S levels and makespan as the objective function.The jobs arrive over time with grade 1 or 2 and an arrival job can be assigned to a machine only when the grade of the job is no less than the grade of the machine.Three cases are considered:(i)For k=1,the authors present an online algorithm with competitive ratio of9/5.(ii)For 1<k<m-1,an online algorithm with competitive ratio of 2.280 is proposed.(iii)For k=m-1,an online algorithm is presented with competitive ratio of 2.All the three algorithms are based on greedy algorithm with a similar structure.At last,numerical instances are given and the average competitive ratios of the instances show good performance of the proposed algorithms.
文摘We propose a new algorithm,named Asymmetric Genetic Algorithm(AGA),for solving optimization problems of steel frames.The AGA consists of a developed penalty function,which helps to find the best generation of the population.The objective function is to minimize the weight of the whole steel structure under the constraint of ultimate loads defined for structural steel buildings by the American Institute of Steel Construction(AISC).Design variables are the cross-sectional areas of elements(beams and columns)that are selected from the sets of side-flange shape steel sections provided by the AISC.The finite element method(FEM)is utilized for analyzing the behavior of steel frames.A 15-storey three-bay steel planar frame is optimized by AGA in this study,which was previously optimized by algorithms such as Particle Swarm Optimization(PSO),Particle Swarm Optimizer with Passive Congregation(PSOPC),Particle Swarm Ant Colony Optimization(HPSACO),Imperialist Competitive Algorithm(ICA),and Charged System Search(CSS).The results of AGA such as total weight of the structure and number of analyses are compared with the results of these algorithms.AGA performs better in comparison to these algorithms with respect to total weight and number of analyses.In addition,five numerical examples are optimized by AGA,Genetic Algorithm(GA),and optimization modules of SAP2000,and the results of them are compared.The results show that AGA can decrease the time of analyses,the number of analyses,and the total weight of the structure.AGA decreases the total weight of regular and irregular steel frame about 11.1%and 26.4%in comparing with the optimized results of SAP2000,respectively.
