Multi-objective optimization via evolutionary algorithm (MOVEA) for high-definition transcranial electrical stimulation of the human brain

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.