Table 2 Comparison of optimization algorithms for non-planar path planning based on four criteria: surface quality, mechanical performance, production time, and support-free capabilities

Algorithm	Improving surface quality	Improving mechanical properties	Reducing production time	Support-free building
AERO³⁹	0	+	+	+
Neural and S3 slicing⁹	+	+	−	+
Stress-distribution reinforcement¹⁷	0	+	0	0
Heat distribution⁴⁰	0	+	0	+
NURBS¹⁰	+	0	0	+
Enneper-Weisenstrass⁴¹	0	−	0	+
Dynamic extrusion rate³⁸	+	−	0	0
Adaptive slicing^10,37	+	0	+	0

Ratings are assigned as + (positive effect), 0 (neutral or not mentioned), and − (negative effect).

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