GPU-accelerated Evolutionary Many-objective Optimization Using Tensorized NSGA-III

TL;DR

TensorNSGA-III is proposed, a fully tensorized implementation of NSGA-III that leverages GPU parallelism for large-scale many-objective optimization and investigates the critical role of large population sizes in many-objective optimization and demonstrates the scalability of TensorNSGA-III in such scenarios.

Abstract

NSGA-III is one of the most widely adopted algorithms for tackling many-objective optimization problems. However, its CPU-based design severely limits scalability and computational efficiency. To address the limitations, we propose {TensorNSGA-III}, a fully tensorized implementation of NSGA-III that leverages GPU parallelism for large-scale many-objective optimization. Unlike conventional GPU-accelerated evolutionary algorithms that rely on heuristic approximations to improve efficiency, TensorNSGA-III maintains the exact selection and variation mechanisms of NSGA-III while achieving significant acceleration. By reformulating the selection process with tensorized data structures and an optimized caching strategy, our approach effectively eliminates computational bottlenecks inherent in traditional CPU-based and naïve GPU implementations. Experimental results on widely used numerical benchmarks show that TensorNSGA-III achieves speedups of up to $3629\times$ over the CPU version of NSGA-III. Additionally, we validate its effectiveness in multiobjective robotic control tasks, where it discovers diverse and high-quality behavioral solutions. Furthermore, we investigate the critical role of large population sizes in many-objective optimization and demonstrate the scalability of TensorNSGA-III in such scenarios. The source code is available at https://github.com/EMI-Group/evomo

Figures (6)

• Figure 1: Association of individuals with reference points in NSGA-III based on perpendicular distance.
• Figure 2: Random Selection in TensorNSGA-III: The indicator tensor (blue) and mark tensor (red) form a temporary indicator (orange), which combines with the cache tensor (yellow) to determine selected individuals (green).
• Figure 3: Mean IGD values and 95% confidence intervals for different population sizes and iterations on DTLZ2, DTLZ5, DTLZ7 using TensorNSGA-III.
• Figure 4: Mean HV values and 95% confidence intervals for different population sizes and iterations on MNKLandscape, MOKnapsack using TensorNSGA-III.
• Figure 5: Comparison of HV values and 95% confidence intervals on MoSwimmer, MoHalfcheetah and MoHopper between TensorNSGA-III and basic search.