论文标题
确保通过Bezier曲线参数化在进化双目标优化中通过Bezier曲线参数化设置 - 应用于前列腺癌的近距离透透治疗计划
Ensuring smoothly navigable approximation sets by Bezier curve parameterizations in evolutionary bi-objective optimization -- applied to brachytherapy treatment planning for prostate cancer
论文作者
论文摘要
双目标优化的目的是获得一组(近)帕累托最佳溶液的近似集。然后,决策者通常使用近似前端的可视化来选择最终所需的解决方案。正面提供了解决方案的导航订购,但这种排序不一定映射到通过决策空间的平滑轨迹。这迫使决策者分别检查每个解决方案的决策变量,并有可能使近似集的导航不直觉。在这项工作中,我们旨在通过根据决策变量在解决方案之间实施平稳性或连续性形式来提高近似设置可通道。将平滑度作为对常见的基于基于统治的多目标进化算法的限制并不直接。因此,我们使用最近引入的未拥挤的Hypervolume(UHV)将多目标优化问题重新制定为单目标问题,其中参数化近似集被直接优化。我们在这里研究参数化近似集在决策空间中的平滑曲线。我们与基因池最佳混合进化算法(GOMEA)一起解决了所得的单目标问题,我们称之为所得算法bezea。我们分析了蓝齐的行为,并将其与GOMEA的优化以及基于统治的多目标GOMEA进行了比较。我们表明,可以使用蓝色获得高质量的近似集,有时甚至优于基于统治和UHV的算法,而通过决策空间保证导航轨迹的平滑度。
The aim of bi-objective optimization is to obtain an approximation set of (near) Pareto optimal solutions. A decision maker then navigates this set to select a final desired solution, often using a visualization of the approximation front. The front provides a navigational ordering of solutions to traverse, but this ordering does not necessarily map to a smooth trajectory through decision space. This forces the decision maker to inspect the decision variables of each solution individually, potentially making navigation of the approximation set unintuitive. In this work, we aim to improve approximation set navigability by enforcing a form of smoothness or continuity between solutions in terms of their decision variables. Imposing smoothness as a restriction upon common domination-based multi-objective evolutionary algorithms is not straightforward. Therefore, we use the recently introduced uncrowded hypervolume (UHV) to reformulate the multi-objective optimization problem as a single-objective problem in which parameterized approximation sets are directly optimized. We study here the case of parameterizing approximation sets as smooth Bezier curves in decision space. We approach the resulting single-objective problem with the gene-pool optimal mixing evolutionary algorithm (GOMEA), and we call the resulting algorithm BezEA. We analyze the behavior of BezEA and compare it to optimization of the UHV with GOMEA as well as the domination-based multi-objective GOMEA. We show that high-quality approximation sets can be obtained with BezEA, sometimes even outperforming the domination- and UHV-based algorithms, while smoothness of the navigation trajectory through decision space is guaranteed.