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矩阵最小剩余问题及其最优近似问题的对称解
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作者 尹凤 黄光鑫 《成都理工大学学报(自然科学版)》 CAS CSCD 北大核心 2008年第2期212-215,共4页
主要给出了矩阵的最小剩余问题及其最优近似问题的对称解。首先,分别给出了与矩阵最小剩余问题及其最优近似问题等价的线性方程;其次,用广义奇异值分解得到了与最小剩余问题等价的线性方程的对称解,即最小剩余问题的对称解;最后,通过寻... 主要给出了矩阵的最小剩余问题及其最优近似问题的对称解。首先,分别给出了与矩阵最小剩余问题及其最优近似问题等价的线性方程;其次,用广义奇异值分解得到了与最小剩余问题等价的线性方程的对称解,即最小剩余问题的对称解;最后,通过寻求与最优近似问题等价的线性方程的对称解,从而得到了矩阵的最优近似问题的最优近似解。 展开更多
关键词 广义奇异值分解 最小剩余问题 最优近似问题 对称解 最小二乘解
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Improvement of Lagrangian relaxation performance for open pit mines constrained long-term production scheduling problem 被引量:2
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作者 E.Moosavi J.Gholamnejad +1 位作者 M.Ataee-pour E.Khorram 《Journal of Central South University》 SCIE EI CAS 2014年第7期2848-2856,共9页
Constrained long-term production scheduling problem(CLTPSP) of open pit mines has been extensively studied in the past few decades due to its wide application in mining projects and the computational challenges it pos... Constrained long-term production scheduling problem(CLTPSP) of open pit mines has been extensively studied in the past few decades due to its wide application in mining projects and the computational challenges it poses become an NP-hard problem.This problem has major practical significance because the effectiveness of the schedules obtained has strong economical impact for any mining project.Despite of the rapid theoretical and technical advances in this field,heuristics is still the only viable approach for large scale industrial applications.This work presents an approach combining genetic algorithms(GAs) and Lagrangian relaxation(LR) to optimally determine the CLTPSP of open pit mines.GAs are stochastic,parallel search algorithms based on the natural selection and the process of evolution.LR method is known for handling large-scale separable problems; however,the convergence to the optimal solution can be slow.The proposed Lagrangian relaxation and genetic algorithms(LR-GAs) combines genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers.This approach leads to improve the performance of Lagrangian relaxation method in solving CLTPSP.Numerical results demonstrate that the LR method using GAs to improve its performance speeding up the convergence.Subsequently,highly near-optimal solution to the CLTPSP can be achieved by the LR-GAs. 展开更多
关键词 constrained long-term production scheduling problem open pit mine Lagrangian relaxation genetic algorithm
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