The uniform and extension distribution of the optimal solution are very important criterion for the quality evaluation of the multi-objective programming problem. A genetic algorithm based on agent and individual dens...The uniform and extension distribution of the optimal solution are very important criterion for the quality evaluation of the multi-objective programming problem. A genetic algorithm based on agent and individual density is used to solve the multi-objective optimization problem. In the selection process, each agent is selected according to the individual density distance in its neighborhood, and the crossover operator adopts the simulated binary crossover method. The self-learning behavior only applies to the individuals with the highest energy in current population. A few classical multi-objective function optimization examples were used tested and two evaluation indexes U-measure and S-measure are used to test the performance of the algorithm. The experimental results show that the algorithm can obtain uniformity and widespread distribution Pareto solutions.展开更多
A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the con...A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the conjugate space of a Banach space B, be a given probability space. Then every B*-valued w*-u-measurable function defined on is w*-equivalent to a B*-valued u-measurable function defined on if and only if B* has the Radon-Nikodym property with respect to展开更多
文摘The uniform and extension distribution of the optimal solution are very important criterion for the quality evaluation of the multi-objective programming problem. A genetic algorithm based on agent and individual density is used to solve the multi-objective optimization problem. In the selection process, each agent is selected according to the individual density distance in its neighborhood, and the crossover operator adopts the simulated binary crossover method. The self-learning behavior only applies to the individuals with the highest energy in current population. A few classical multi-objective function optimization examples were used tested and two evaluation indexes U-measure and S-measure are used to test the performance of the algorithm. The experimental results show that the algorithm can obtain uniformity and widespread distribution Pareto solutions.
基金Project supported by the National Natural Science Foundation of China the Natural Science Foundation of Fujian Province of China.
文摘A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the conjugate space of a Banach space B, be a given probability space. Then every B*-valued w*-u-measurable function defined on is w*-equivalent to a B*-valued u-measurable function defined on if and only if B* has the Radon-Nikodym property with respect to
