Agile Software Cost Estimation Model Based on Constricted Particle Swarm Optimization

Abstract

Cost estimation is a critical task in software engineering and is particularly challenging in Agile projects. Although various optimization methods have been proposed to improve estimation accuracy, estimates often still deviate from actual costs. This study proposes the use of Constricted Particle Swarm Optimization (CPSO) to tune an Agile cost estimation model. Based on data from 21 industrial Agile software development projects, the model uses historical story points, team velocity, team wages, and workdays as input features. The performance of the CPSO algorithm is then systematically evaluated on this small dataset. The model is reparameterized with four tunable parameters—$\alpha ,C,D$, and $E$—and CPSO is applied to minimize MMRE on the training folds to obtain optimal parameter sets. Evaluation is carried out using outer fivefold cross-validation, with hyperparameter tuning performed on the training data, and performance is compared with a standard PSO baseline and the results reported by Zia et al. The CPSO-optimized model achieves an MMRE of (4.74% $\pm$ 1.89%) on test folds and a PRED (10%) of (96.00% $\pm$ 8.94%). The MMRE represents a 9.71% relative reduction compared with the employed baseline and a 17.71% relative reduction compared with the result reported by Zia et al. The contribution of this study lies in systematically embedding CPSO into an identifiable agile cost estimation model and evaluating it within a rigorous outer-layer cross-validation and ensemble prediction framework. The results indicate that CPSO can effectively tune the Agile cost estimation model within the specific dataset and experimental setting considered in this study. The findings should be interpreted as an incremental contribution based on a small industrial dataset, and they provide parameter-level insights that may support future calibration of agile cost estimation models on larger and more heterogeneous datasets.