Effects of Topological Structure of Project Network on Computational Cost

Abstract

Understanding how network complexity affects optimization algorithms is crucial for improving computational efficiency. This study investigates how variations in network complexity impact the performance of optimization algorithms. By examining networks with different serial/parallel indicator (I2) values, the research uncovers several key insights into how topology influences computational requirements. The experiments show that higher I2 values, which are closer to serial configurations, heighten the problem's complexity. This study reveals that networks with lower I2 values, which exhibit steeper time-cost curves with fewer solutions over their efficient frontiers, require significantly more CPU time, indicating that project complexity does not necessarily scale with the extend of the Pareto fronts. This contradicts the expectation that more Pareto front solutions would inherently demand greater computational resources. Lastly, the study highlights that while the number of time-cost realizations is often used to gauge project complexity, it may not be conclusive on its own and that one complexity measure can outperform another. Although it can be an effective indicator, it does not fully capture the computational challenges posed by different network topologies. This study further acknowledges the difficulty in establishing a clear link between project performance and complexity due to the multifaceted nature of the problem. The findings suggest that exploring similar problems in other contexts could provide valuable insights into understanding and managing computational complexity.