摘要目的:将进化算法用于辅助帕累托面导航，探索放疗计划多目标优化中的帕累托解集，基于单次偏好表达生成一系列具有多样性的计划供选择。方法:开发一种新的基于后验的多目标进化优化算法，与经由梯度算法得到的帕累托面上与约束条件一一对应的锚点计划结合，探索各锚点计划的线性组合。在对生成的种群进行单次偏好表达后，通过该优化算法输出一系列近似位于帕累托面上，剂量学参数较优且选择范围较广的计划组。纳入15例前列腺癌病例对开发的优化算法进行性能测试，靶区包含前列腺(PTV1)和淋巴结引流区(PTV2)，采用7野调强放疗计划，优化完成后调用matRad工具包计算计划剂量，并通过剂量学指标来综合评估算法性能。结果:通过开发的优化算法生成的计划组具有较好的多样性，其中膀胱、直肠和小肠的平均剂量的最大值与最小值之间的平均差值分别为10.8、10.4和2.9 Gy， V50最大值和最小值的平均差值分别为33.7%、31.4%和8.4%， V30的平均差值则为25.7%、21.6%和7.4%。相对于危及器官，靶区的帕累托解集检索范围相对较小。其中，PTV1的 D95%平均差值为4.0 Gy，PTV2的 D95%平均差值则为3.4 Gy。 结论:本研究基于后验的思想，首次将进化算法用于探索多目标优化得到的放疗计划帕累托解集，通过探索锚点计划的线性组合输出一系列具有多样性与可行性的调强放疗计划，有效地辅助物理师检索并选择最优治疗计划。

abstractsObjective:To explore the Pareto set in multi-criteria optimization for radiotherapy by facilitating Pareto surface navigation using an evolutionary algorithm and to generate a series of diverse plans based on a single preferential expression.Methods:A novel posterior-based multi-criteria evolutionary algorithm was developed. This algorithm, combined with anchor plans-each obtained from the Pareto surface using a gradient-based algorithm and corresponding to a specific constraint, was employed to explore the linear combinations of these anchor plans. Following the generation of a single preferential expression of the generated population, the proposed algorithm yielded a set of plans near the Pareto surface, offering more optimal dosimetric parameters. The performance of the algorithm was tested using 15 prostate cancer cases, with planning target volumes (PTVs) including the prostate (PTV1) and lymph node basins (PTV2). For each case, a 7-field intensity-modulated radiotherapy (IMRT) plan was generated and optimized. Subsequently, planned doses were calculated using the matRad toolkit, and the algorithm performance was assessed based on dosimetric indicators.Results:The multi-criteria evolutionary algorithm generated diverse plan sets. For organs at risk (OARs) bladder, rectum and small intestine, the average dose differences between the maximum and minimum of mean doses were determined at 10.8, 10.4, and 2.9 Gy, those of V50 ( ΔV50) were 33.7%, 31.4%, and 8.4%, and those of V30 ( ΔV30)were 25.7%, 21.6%, and 7.4%, respectively. In contrast, for the PTVs, the Pareto set yielded by the algorithm showed narrow search ranges. Specifically, the average differences in D95% ( ΔD95%) for PTV1 and PTV2 were 4.0 and 3.4 Gy, respectively. Conclusions:This study, grounded in a posterior-based approach, employs an evolutionary algorithm to explore the MCO-derived Pareto set of radiotherapy plans for the first time. A series of diverse and feasible IMRT plans are generated by searching the linear combination of anchor plans, thereby effectively assisting physicists in retrieving and selecting the optimal treatment plans.