In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log ...In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log h) of the running time for the general sequential B&B algorithm and the lower bound Ω(m/p+h log p) for the general parallel best-first B&B algorithm in PRAM-CREW are proposed, where p is the number of processors available. Moreover, the lower bound Ω(M/p+H+(H/p) log (H/p)) is presented for the parallel algorithms on distributed memory system, where M and H represent total number of the active nodes and that of the expanded nodes processed by p processors, respectively. In addition, a nearly fastest general parallel best-first B&B algorithm is put forward. The parallel algorithm is the fastest one as p = max{hε, r}, where ε = 1/ rootlogh, and r is the largest branch number of the nodes in the state-space tree.展开更多
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc...A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.展开更多
我国风电基地和负荷中心呈逆向分布,需要通过跨区输送实现异地消纳促进风电可持续发展,目前风电和输电网规划不协调的问题极为突出,提出了风电与输电网综合协调投资规划模型。首先提出了以用户费用、风电及输电网投资总成本最小为目标...我国风电基地和负荷中心呈逆向分布,需要通过跨区输送实现异地消纳促进风电可持续发展,目前风电和输电网规划不协调的问题极为突出,提出了风电与输电网综合协调投资规划模型。首先提出了以用户费用、风电及输电网投资总成本最小为目标函数的风电与输电网投资混合整数线性规划模型(Mixed-Integer Linear Programming,MILP),以确定最优的风电投资规模以及配套输电网建设,通过改进分支定界方法对模型进行求解,通过算例分析验证所构建模型的科学性和合理性。展开更多
基金This paper was supported by Ph. D. Foundation of State Education Commission of China.
文摘In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log h) of the running time for the general sequential B&B algorithm and the lower bound Ω(m/p+h log p) for the general parallel best-first B&B algorithm in PRAM-CREW are proposed, where p is the number of processors available. Moreover, the lower bound Ω(M/p+H+(H/p) log (H/p)) is presented for the parallel algorithms on distributed memory system, where M and H represent total number of the active nodes and that of the expanded nodes processed by p processors, respectively. In addition, a nearly fastest general parallel best-first B&B algorithm is put forward. The parallel algorithm is the fastest one as p = max{hε, r}, where ε = 1/ rootlogh, and r is the largest branch number of the nodes in the state-space tree.
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)the Fundamental Research Funds for the Central Universities(K50511700004)
文摘A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.
文摘由于超大规模MIMO(Extremely Large-scale MIMO,XL-MIMO)系统中空间非平稳性的存在,使得部分天线对系统性能贡献较小,从而增加了系统能耗。通过天线选择并结合波束成形从而优化系统性能。以最小化基站发射功率为目标建模,在满足信干噪比和基站激活天线数的约束下,优化基站处的波束成形矩阵。由于该优化问题是典型的混合整数非线性规划问题,传统方法使用连续近似来求解,然而获得的解都是次优解。鉴于此,首先提出采用分支定界算法(Branch and Bound,BAB)求解上述优化问题,从而保证解的最优性。然而,BAB算法在处理大规模问题,特别是基站天线数大于128时,计算复杂度往往过高。为了解决这一问题,提出了一种基于图神经网络和多层感知机(Graph Neural Network and Multilayer Perceptron,GNN+MLP)的方法,通过利用GNN在BAB树的根节点提取一次全局特征,并在每个子节点利用MLP提取局部特征,通过结合全局特征和局部特征来训练一个二进制的节点分类器,以判断当前节点是否需要进一步分支,从而加速计算的过程。仿真结果表明,在天线数等于512时,GNN+MLP比BAB减少了54.2%的计算时间。
文摘我国风电基地和负荷中心呈逆向分布,需要通过跨区输送实现异地消纳促进风电可持续发展,目前风电和输电网规划不协调的问题极为突出,提出了风电与输电网综合协调投资规划模型。首先提出了以用户费用、风电及输电网投资总成本最小为目标函数的风电与输电网投资混合整数线性规划模型(Mixed-Integer Linear Programming,MILP),以确定最优的风电投资规模以及配套输电网建设,通过改进分支定界方法对模型进行求解,通过算例分析验证所构建模型的科学性和合理性。
