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
A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Coue...A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.展开更多
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.
基金supported by the National Natural Science Foundation of China (No. 10772110)
文摘A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.
