<![CDATA[Permutation optimization is a fundamental problem in large-scale computing that arises in various applications such as scheduling, resource allocation, and combinatorial decision-making. As the size of the solution space grows exponentially, conventional optimization methods often struggle to achieve acceptable performance within reasonable computational time. Heuristic and metaheuristic algorithms have therefore become widely adopted due to their flexibility and ability to provide near-optimal solutions for NP-hard problems. However, increasing data scale significantly impacts their computational complexity, making efficiency and scalability critical concerns.This study aims to analyze the computational complexity and performance characteristics of several heuristic algorithms applied to permutation optimization in large-scale computing environments. The research employs a quantitative experimental approach combined with theoretical complexity analysis. Greedy heuristic, simulated annealing, genetic algorithm, and adaptive heuristic methods are evaluated using synthetic permutation datasets with varying sizes. Performance is assessed based on execution time, memory usage, scalability, and solution quality. The results indicate that greedy heuristics offer the fastest execution and lowest memory consumption but tend to produce suboptimal solutions due to their local search strategy. Simulated annealing improves solution quality through probabilistic exploration, while genetic algorithms achieve the highest-quality solutions at the cost of substantial computational and memory overhead. Adaptive heuristic algorithms demonstrate a balanced performance by dynamically adjusting parameters during execution, achieving near-optimal solutions with reduced computational complexity. Overall, this research highlights the trade-offs between efficiency and solution quality among heuristic algorithms and emphasizes the potential of adaptive heuristic approaches for large-scale permutation optimization. The findings provide valuable insights for designing efficient and scalable optimization algorithms suitable for real-world large-scale computing applications.]]>
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