该文研究带时间窗约束的车辆路径问题(Vehicle Routing Problem with Time Windows,VRPTW),这是一个典型的NP-Hard问题。针对传统粒子群算法求解带时间窗约束的车辆路径问题容易陷入局部最优的缺陷,提出了一种基于多策略方法改进的粒子...该文研究带时间窗约束的车辆路径问题(Vehicle Routing Problem with Time Windows,VRPTW),这是一个典型的NP-Hard问题。针对传统粒子群算法求解带时间窗约束的车辆路径问题容易陷入局部最优的缺陷,提出了一种基于多策略方法改进的粒子群算法(Multi-Strategy improved particle Swarm Optimization Algorithm,MSPSO)来解决该问题。该算法采用惯性权重递减策略,使得算法在前期的全局搜索和后期的局部搜索都能够有良好的表现,通过引入随机选择策略更新粒子最优位置,可以增加解空间的多样性,有效避免算法陷入局部最优。最后通过测试Solomon Benchmark算例的结果,在25个客户的C103数据集上MSPSO算法对比RWPSO算法的行驶距离降低了38.29,对比S-PSO算法在C103、R103这两个数据集与最优解误差分别降低了1.76%和3.99%。在50个客户C1系列数据集上MSPSO算法对比PSO算法行驶距离分别减少了14.26、45.66、67.7,与数据集的最优解误差基本能保持在1%以内。从实验结果可以证明MSPSO算法在求解VRPTW问题方面具有优越性和有效性。展开更多
The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.展开更多
One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, ...One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.展开更多
Slater选举是最优化问题,也是NP-hard问题,此类问题一般被认为不存在多项式时间的算法。考虑到其求解的复杂度与回答集求解的复杂度是一致的,为此,提出一种利用回答集程序(Answer Set Programming,ASP)求解Slater选举的新方法。首先,使...Slater选举是最优化问题,也是NP-hard问题,此类问题一般被认为不存在多项式时间的算法。考虑到其求解的复杂度与回答集求解的复杂度是一致的,为此,提出一种利用回答集程序(Answer Set Programming,ASP)求解Slater选举的新方法。首先,使用饱和技术为Slater选举建立逻辑上等价的ASP模型;其次,对模型进行正确性证明;最后,调用回答集求解器DLV求解Slater选举的具体实例,并在实验结果中说明其可行性。该方法不仅可求解Slater选举问题,而且在ASP中所使用的饱和技术还为其他同类的最优化问题提供了一种新的逻辑表示途径。展开更多
研究了基于下行无线信息和能量协同传输(simultaneous wireless-information and power-transfer,SWIPT)大规模多输入单输出(multiple-input and single-output,MISO)系统的吞吐率优化问题.该系统为时分双工(time division duplex,TDD)...研究了基于下行无线信息和能量协同传输(simultaneous wireless-information and power-transfer,SWIPT)大规模多输入单输出(multiple-input and single-output,MISO)系统的吞吐率优化问题.该系统为时分双工(time division duplex,TDD)模式,同时移动站采用先收集后传输的协议.在下行信噪比(signal-to-noise ratio,SNR)和移动站的传输功率约束下,为实现上行吞吐率的最大化,对功率分配系数和下行传输时间进行了联合优化,由于该问题为非凸优化问题,采用基于拉格朗日乘子的梯度算法进行优化.最后,通过与单独优化下行传输时间算法的比较,验证了该联合优化算法的优越性.展开更多
文摘该文研究带时间窗约束的车辆路径问题(Vehicle Routing Problem with Time Windows,VRPTW),这是一个典型的NP-Hard问题。针对传统粒子群算法求解带时间窗约束的车辆路径问题容易陷入局部最优的缺陷,提出了一种基于多策略方法改进的粒子群算法(Multi-Strategy improved particle Swarm Optimization Algorithm,MSPSO)来解决该问题。该算法采用惯性权重递减策略,使得算法在前期的全局搜索和后期的局部搜索都能够有良好的表现,通过引入随机选择策略更新粒子最优位置,可以增加解空间的多样性,有效避免算法陷入局部最优。最后通过测试Solomon Benchmark算例的结果,在25个客户的C103数据集上MSPSO算法对比RWPSO算法的行驶距离降低了38.29,对比S-PSO算法在C103、R103这两个数据集与最优解误差分别降低了1.76%和3.99%。在50个客户C1系列数据集上MSPSO算法对比PSO算法行驶距离分别减少了14.26、45.66、67.7,与数据集的最优解误差基本能保持在1%以内。从实验结果可以证明MSPSO算法在求解VRPTW问题方面具有优越性和有效性。
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
基金Supported by the National 863 Project (2003AA002030)
文摘One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.
文摘Slater选举是最优化问题,也是NP-hard问题,此类问题一般被认为不存在多项式时间的算法。考虑到其求解的复杂度与回答集求解的复杂度是一致的,为此,提出一种利用回答集程序(Answer Set Programming,ASP)求解Slater选举的新方法。首先,使用饱和技术为Slater选举建立逻辑上等价的ASP模型;其次,对模型进行正确性证明;最后,调用回答集求解器DLV求解Slater选举的具体实例,并在实验结果中说明其可行性。该方法不仅可求解Slater选举问题,而且在ASP中所使用的饱和技术还为其他同类的最优化问题提供了一种新的逻辑表示途径。
文摘研究了基于下行无线信息和能量协同传输(simultaneous wireless-information and power-transfer,SWIPT)大规模多输入单输出(multiple-input and single-output,MISO)系统的吞吐率优化问题.该系统为时分双工(time division duplex,TDD)模式,同时移动站采用先收集后传输的协议.在下行信噪比(signal-to-noise ratio,SNR)和移动站的传输功率约束下,为实现上行吞吐率的最大化,对功率分配系数和下行传输时间进行了联合优化,由于该问题为非凸优化问题,采用基于拉格朗日乘子的梯度算法进行优化.最后,通过与单独优化下行传输时间算法的比较,验证了该联合优化算法的优越性.
