<p>Problem with dimensions 6 × 6 with 2 processors.</p>

Efficient task scheduling remains a key challenge in High-Performance Computing and Internet of Things (IoT) systems, where the sequential execution of nested loops often limits parallelism. This paper proposes a hybrid approach that dynamically parallelizes nested loops in heterogeneous IoT environments. The suggested method (PSOALS) combines Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and wave-angle scheduling to model nested loops as two-dimensional iteration spaces and minimize communication overhead. By encoding loop iterations as particles and using a dependency-aware fitness function, PSOALS enhances makespan, resource utilization, and scalability. The key contributions of this work include: a dynamic scheduling framework for efficient loop parallelization and dependency management, a wave-angle scheduling mechanism to improve task execution order by balancing load and communication delays, and the integration of mutation and diversity techniques to enhance the quality of the solution. Experimental results across various IoT configurations show that PSOALS outperforms block-based, cyclic, and GA-based scheduling methods in convergence speed, stability, and execution time. The proposed approach offers a scalable and adaptive solution to future IoT challenges, including real-time processing, energy efficiency, and large-scale deployment.高效任务调度始终是高性能计算（High-Performance Computing）与物联网（Internet of Things, IoT）系统中的核心挑战，这类系统中嵌套循环的串行执行往往会限制并行性。本文提出一种混合方法，可在异构物联网环境中对嵌套循环进行动态并行化处理。所提方法（PSOALS）将粒子群优化（Particle Swarm Optimization）、遗传算法（Genetic Algorithm）与波角调度（wave-angle scheduling）相结合，将嵌套循环建模为二维迭代空间并尽可能降低通信开销。通过将循环迭代编码为粒子，并采用依赖感知的适应度函数，PSOALS能够优化总完工时间、资源利用率与可扩展性。本研究的核心贡献包括：一是构建面向高效循环并行化与依赖管理的动态调度框架；二是提出波角调度机制，通过平衡负载与通信延迟来优化任务执行顺序；三是集成变异与多样性增强技术，以提升求解质量。针对多种物联网配置开展的实验结果表明，PSOALS在收敛速度、稳定性与执行时长方面均优于基于块的、循环式以及基于遗传算法的调度方法。所提方法可为未来物联网面临的各类挑战提供可扩展且自适应的解决方案，这些挑战包括实时处理、能效优化与大规模部署。