The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application,...The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.展开更多
针对昂贵约束多目标离散优化问题,提出一种基于随机森林和自适应随机排序的昂贵多目标进化算法(a random forest and adaptive stochastic ranking based multi-objective evolutionary algorithm,RFASRMOEA).为了提高代理模型对离散问...针对昂贵约束多目标离散优化问题,提出一种基于随机森林和自适应随机排序的昂贵多目标进化算法(a random forest and adaptive stochastic ranking based multi-objective evolutionary algorithm,RFASRMOEA).为了提高代理模型对离散问题的近似精度,RFASRMOEA采用随机森林作为代理模型辅助进化算法进行搜索.同时,为提升综合性能,提出一种基于平衡适应度评估策略和自适应概率操作的自适应随机排序机制.具体地,平衡适应度评估策略利用种群迭代信息结合所设计的基于目标转移的多样性评估和基于余弦的收敛性评估,充分发掘种群个体潜力.而自适应概率操作通过动态调整随机排序机制的关注点,使得算法在前期探索更多可行域而后期迅速收敛于可行域,进而平衡约束条件的满足与目标函数优化之间的冲突.在测试问题上的实验结果表明,所提出算法在处理昂贵约束多目标离散优化问题时具有较高的竞争力.展开更多
基金Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)
文摘The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.
文摘针对昂贵约束多目标离散优化问题,提出一种基于随机森林和自适应随机排序的昂贵多目标进化算法(a random forest and adaptive stochastic ranking based multi-objective evolutionary algorithm,RFASRMOEA).为了提高代理模型对离散问题的近似精度,RFASRMOEA采用随机森林作为代理模型辅助进化算法进行搜索.同时,为提升综合性能,提出一种基于平衡适应度评估策略和自适应概率操作的自适应随机排序机制.具体地,平衡适应度评估策略利用种群迭代信息结合所设计的基于目标转移的多样性评估和基于余弦的收敛性评估,充分发掘种群个体潜力.而自适应概率操作通过动态调整随机排序机制的关注点,使得算法在前期探索更多可行域而后期迅速收敛于可行域,进而平衡约束条件的满足与目标函数优化之间的冲突.在测试问题上的实验结果表明,所提出算法在处理昂贵约束多目标离散优化问题时具有较高的竞争力.
