Designing a transcranial electrical stimulation (TES) strategy requires considering multiple objectives, such as intensity in the target area, focality, stimulation depth, and avoidance zone, which are often mutually exclusive. A computational framework for optimizing different strategies and comparing trade-offs between these objectives is currently lacking. In this paper, we propose a general framework called multi-objective optimization via evolutionary algorithms (MOVEA) to address the non-convex optimization problem in designing TES strategies without predefined direction. MOVEA enables simultaneous optimization of multiple targets through Pareto optimization, generating a Pareto front after a single run without manual weight adjustment and allowing easy expansion to more targets. This Pareto front consists of optimal solutions that meet various requirements while respecting trade-off relationships between conflicting objectives such as intensity and focality. MOVEA is versatile and suitable for both transcranial alternating current stimulation (tACS) and transcranial temporal interference stimulation (tTIS) based on high definition (HD) and two-pair systems. We performed a comprehensive comparison between tACS and tTIS in terms of intensity, focality, and steerability for targets at different depths.MOVEA facilitates the optimization of TES based on specific objectives and constraints, advancing tTIS and tACS-based neuromodulation in understanding the causal relationship between brain regions and cognitive functions and in treating diseases. The code for MOVEA is available at https://github.com/ncclabsustech/MOVEA.

翻译：设计经颅电刺激（TES）策略需综合考虑多个相互排斥的目标，如靶区强度、聚焦性、刺激深度及回避区域。目前缺乏一个能够优化不同策略并权衡这些目标的计算框架。本文提出名为"基于进化算法的多目标优化"（MOVEA）的通用框架，以解决无预设方向条件下设计TES策略的非凸优化问题。MOVEA通过帕累托优化实现多目标同步优化，单次运行即可生成帕累托前沿，无需手动调整权重且易于扩展至更多目标。该帕累托前沿由满足不同需求的最优解构成，同时兼顾强度与聚焦性等冲突目标间的权衡关系。MOVEA具有通用性，适用于基于高清及双电极系统的经颅交流电刺激（tACS）与经颅时间干扰刺激（tTIS）。我们对不同深度靶点的tACS与tTIS在强度、聚焦性及可操控性方面进行了全面比较。MOVEA能够根据特定目标与约束条件优化TES，推动基于tTIS和tACS的神经调控技术发展，为理解脑区与认知功能间的因果关系及疾病治疗提供支持。MOVEA代码已开源：https://github.com/ncclabsustech/MOVEA。