Metaheuristic optimization work.

Software development effort estimation (SDEE) is recognized as vital activity for effective project management since under or over estimating can lead to unsuccessful utilization of project resources. Machine learning (ML) algorithms are largely contributing in SDEE domain, particularly ensemble effort estimation (EEE) works well in rectifying bias and subjectivity to solo ML learners. Performance of EEE significantly depends on hyperparameter composition as well as weight assignment mechanism of solo learners. However, in EEE domain, impact of optimization in terms of hyperparameter tunning as well as weight assignment is explored by few researchers. This study aims in improving SDEE performance by incorporating metaheuristic hyperparameter and weight optimization in EEE, which enables accuracy and diversity to the ensemble model. The study proposed Metaheuristic-optimized Multi-dimensional bagging scheme and Weighted Ensemble (MoMdbWE) approach. This is achieved by proposed search space division and hyperparameter optimization method named as Multi-dimensional bagging (Mdb). Metaheuristic algorithm considered for this work is Firefly algorithm (FFA), to get best hyperparameters of three base ML algorithms (Random Forest, Support vector machine and Deep Neural network) since FFA has shown promising results of fitness in terms of MAE. Further enhancement in performance is achieved by incorporating FFA-based weight optimization to construct Metaheuristic-optimized weighted ensemble (MoWE) of individual multi-dimensional bagging schemes. Proposed scheme is implemented on eight frequently utilized effort estimation datasets and results are evaluated by 5 error metrices (MAE, RMSE, MMRE, MdMRE, Pred), standard accuracy and effect size along with Wilcox statistical test. Findings confirmed that the use of FFA optimization for hyperparameter (with search space sub-division) and for ensemble weights, has significantly enhanced performance in comparison with individual base algorithms as well as other homogeneous and heterogenous EEE techniques.

软件开发工作量估算（Software Development Effort Estimation，SDEE）被公认为有效项目管理的关键环节，因为估算偏差（过高或过低）均会导致项目资源无法得到高效利用。机器学习（Machine Learning，ML）算法在SDEE领域已得到广泛应用且贡献突出，其中集成工作量估算（Ensemble Effort Estimation，EEE）在修正单一ML学习器的偏差与主观性方面表现尤为优异。集成工作量估算的性能极大程度依赖于超参数组合以及单一学习器的权重分配机制。然而，在EEE领域中，针对超参数调优与权重分配的优化效果，仅有少数研究者展开了相关探索。本研究旨在通过在EEE框架中融入元启发式超参数与权重优化手段，提升SDEE的性能，为集成模型赋予更高的精度与多样性。本研究提出了元启发式优化多维装袋方案与加权集成（Metaheuristic-optimized Multi-dimensional bagging scheme and Weighted Ensemble，MoMdbWE）方法，该方法通过提出的搜索空间划分策略与名为多维装袋（Multi-dimensional bagging，Mdb）的超参数优化方案得以实现。本研究选用的元启发式算法为萤火虫算法（Firefly Algorithm，FFA），用于优化三种基础ML算法（随机森林、支持向量机与深度神经网络）的最优超参数，这是因为FFA在平均绝对误差（Mean Absolute Error，MAE）维度展现出了优异的适应度表现。进一步的性能提升则通过引入基于FFA的权重优化手段，构建针对各多维装袋方案的元启发式优化加权集成（Metaheuristic-optimized weighted ensemble，MoWE）实现。所提方案在8个常用的工作量估算数据集上完成了实验实现，并通过5项误差指标（MAE、均方根误差RMSE、平均相对误差均值MMRE、中位数相对误差幅度MdMRE、预测率Pred）、标准精度指标与效应量，辅以威尔科克森统计检验（Wilcox Statistical Test）进行了性能评估。实验结果证实，针对超参数（结合搜索空间细分）与集成权重的FFA优化方案，相较单一基础算法以及其他同类、异类EEE技术，性能得到了显著提升。