A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with resp...A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.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
We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the mul...We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.展开更多
伴随水电规模的扩大,水电站群优化调度的计算量不断增加,需要探求新的方法。在分析离散微分动态规划(discrete differentiation and dynamic programming,DDDP)算法的基础上,提出了基于分治模式的梯级水电站长期优化调度的细粒度并行离...伴随水电规模的扩大,水电站群优化调度的计算量不断增加,需要探求新的方法。在分析离散微分动态规划(discrete differentiation and dynamic programming,DDDP)算法的基础上,提出了基于分治模式的梯级水电站长期优化调度的细粒度并行离散微分动态规划(parallel discrete differentiation and dynamic programming,PDDDP)方法,并以澜沧江梯级的6个电站系统长期优化调度问题为应用实例,在多核计算环境下进行验证。结果表明,多核环境下的PDDDP方法简便易行,能充分利用闲置计算资源、大幅度提高优化调度的计算效率,是解决大规模复杂水电系统调度的高效和实用方法。展开更多
文摘A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.
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We introduce and analyze a family of linear least-squares Monte Carlo schemesfor backward SDEs, which interpolate between the one-step dynamic programmingscheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamicprogramming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Ouralgorithm approximates conditional expectations over segments of the time grid. Wediscuss the optimal choice of the segment length depending on the 'smoothness' of theproblem and show that, in typical situations, the complexity can be reduced compared tothe state-of-the-art multi-step dynamic programming scheme.
文摘伴随水电规模的扩大,水电站群优化调度的计算量不断增加,需要探求新的方法。在分析离散微分动态规划(discrete differentiation and dynamic programming,DDDP)算法的基础上,提出了基于分治模式的梯级水电站长期优化调度的细粒度并行离散微分动态规划(parallel discrete differentiation and dynamic programming,PDDDP)方法,并以澜沧江梯级的6个电站系统长期优化调度问题为应用实例,在多核计算环境下进行验证。结果表明,多核环境下的PDDDP方法简便易行,能充分利用闲置计算资源、大幅度提高优化调度的计算效率,是解决大规模复杂水电系统调度的高效和实用方法。
