For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate th...For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate the improvement of the solution quality. Firstly, the objective function is improved to solve the double and bias counting of violations broadly discussed. Then, a new method combining heuristic with constraint propagation is proposed which constructs initial solutions under a parallel framework. Based on constraint propagation, three filtering rules are designed to intersecting with three greedy functions, so the variable domain is narrowed in the process of the construction. The parallel framework is served to show its robustness in terms of the quality of the solution since it greatly increases the performance of obtaining the best solution. In the computational experiments, 109 instances of 3 sets from the CSPLib＇ s benchmarks are used to test the performance of the proposed method. Experiment results show that the proposed method outperforms others in acquiring the best-known results for 85 best-known results of 109 are obtained with only one construction. The proposed research provides an avenue to remedy the deficiencies of ＂sliding windows＂ technique and construct high quality initial solutions.展开更多
In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationsh...In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.展开更多
Let R be a Noetherian ring, M an Artinian R-module, and p ∈ CosRM. Thencograden. Homn（Rp, M） =-inf{i ｜πi（p, M） 〉 0} and πi（p, M） 〉 0 =〉 cogradeRpHomR（Rp, M） ≤ i ≤ fdRpHomR（Rp, M）,where πi （p,M） i...Let R be a Noetherian ring, M an Artinian R-module, and p ∈ CosRM. Thencograden. Homn（Rp, M） =-inf{i ｜πi（p, M） 〉 0} and πi（p, M） 〉 0 =〉 cogradeRpHomR（Rp, M） ≤ i ≤ fdRpHomR（Rp, M）,where πi （p,M） is the i-th dual Bass number of M with respect to p, cogradeRpHomR （Rp ,M） is the common length of any maxima[ HomR（Rp, M）-quasi co-regular sequence contained in pRp, and fdRp HomR（Rp, M） is the flat dimension of the Rp-module HomR（Rp, M）. We also study the relations among cograde, co-dimension and flat dimension of co-localization modules.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51435009,71302085)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ14E080002)K.C.Wong Magna Fund in Ningbo University
文摘For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate the improvement of the solution quality. Firstly, the objective function is improved to solve the double and bias counting of violations broadly discussed. Then, a new method combining heuristic with constraint propagation is proposed which constructs initial solutions under a parallel framework. Based on constraint propagation, three filtering rules are designed to intersecting with three greedy functions, so the variable domain is narrowed in the process of the construction. The parallel framework is served to show its robustness in terms of the quality of the solution since it greatly increases the performance of obtaining the best solution. In the computational experiments, 109 instances of 3 sets from the CSPLib＇ s benchmarks are used to test the performance of the proposed method. Experiment results show that the proposed method outperforms others in acquiring the best-known results for 85 best-known results of 109 are obtained with only one construction. The proposed research provides an avenue to remedy the deficiencies of ＂sliding windows＂ technique and construct high quality initial solutions.
文摘In this paper, let （R, m） be a Noetherian local ring, I lohtain in R an ideal, M and N be two finitely generated modules. Firstly, we study the properties of HI^t（M）, t = f-depth（I, M） and discuss the relationship between the Artinianness of HI^i（M, N） and the Artinianness of HI^i（N）. Then, we get that HI^d（M, N） is I-cofinite, if （R, m） is a d-dimensional Gorenstein local ring.
基金Partially supported by the National Natural Science Foundation of China （No. 11271275）.
文摘Let R be a Noetherian ring, M an Artinian R-module, and p ∈ CosRM. Thencograden. Homn（Rp, M） =-inf{i ｜πi（p, M） 〉 0} and πi（p, M） 〉 0 =〉 cogradeRpHomR（Rp, M） ≤ i ≤ fdRpHomR（Rp, M）,where πi （p,M） is the i-th dual Bass number of M with respect to p, cogradeRpHomR （Rp ,M） is the common length of any maxima[ HomR（Rp, M）-quasi co-regular sequence contained in pRp, and fdRp HomR（Rp, M） is the flat dimension of the Rp-module HomR（Rp, M）. We also study the relations among cograde, co-dimension and flat dimension of co-localization modules.
