Considering Workload Uncertainty in Strategy Gradient-based Hyper-heuristic Scheduling for Software Projects

ObjectiveThe Software Project Scheduling Problem (SPSP) is essential for allocating resources and arranging tasks in software development, and it affects economic efficiency and competitiveness. Deterministic assumptions used in traditional models overlook common fluctuations in task effort caused by requirement changes or estimation deviation. These assumptions often reduce feasibility and weaken scheduling stability in dynamic development settings. This study develops a multi-objective model that integrates task effort uncertainty and represents it using asymmetric triangular interval type-2 fuzzy numbers to reflect real development conditions. The aim is to improve decision quality under uncertainty by designing an optimization method that shortens project duration and increases employee satisfaction, thereby strengthening robustness and adaptability in software project scheduling.MethodsA Policy Gradient-based Hyper-Heuristic Algorithm (PGHHA) is developed to solve the formulated model. The framework contains a High-Level Strategy (HLS) and a set of Low-Level Heuristics (LLHs). The High-Level Strategy applies an Actor-Critic reinforcement learning structure. The Actor network selects appropriate LLHs based on real-time evolutionary indicators, including population convergence and diversity, and the Critic network evaluates the actions selected by the Actor. Eight LLHs are constructed by combining two global search operators, the matrix crossover operator and the Jaya operator with random jitter, with two local mining strategies, duration-based search and satisfaction-based search. Each LLH is configured with two neighborhood depths (V1=5 and V2=20), determined through Taguchi orthogonal experiments. Each candidate solution is encoded as a real-valued task-employee effort matrix. Constraints including skill coverage, maximum dedication, and maximum participant limits are applied during optimization. A prioritized experience replay mechanism is introduced to reuse historical trajectories, which accelerates convergence and improves network updating efficiency.Results and DiscussionsExperimental evaluation is performed on twelve synthetic cases and three real software projects. The algorithm is assessed against six representative methods to validate the proposed strategies. HyperVolume Ratio (HVR) and Inverted Generational Distance (IGD) are used as performance indicators, and statistical significance is examined using Wilcoxon rank-sum tests with a 0.05 threshold. The findings show that the PGHHA achieves better convergence and diversity than all comparison methods in most cases. The quantitative improvements are reflected in the summarized values (Table 5, Table 6). The visual distribution of Pareto fronts (Fig. 4, Fig. 5) shows that the obtained solutions lie below those of alternative algorithms and display more uniform coverage, indicating higher convergence precision and improved spread. The computational cost increases because of neural network training and the experience replay mechanism, as shown in Fig. 6. However, the improvement in solution quality is acceptable considering the longer planning period of software development. Modeling effort uncertainty with asymmetric triangular interval type-2 fuzzy numbers enhances system stability. The adaptive heuristic selection driven by the Actor-Critic mechanism and the prioritized experience replay strengthens performance under dynamic and uncertain conditions. Collectively, the evidence indicates that the PGHHA provides more reliable support for software project scheduling, maintaining diversity while optimizing conflicting objectives under uncertain workload environments.ConclusionsA multi-objective software project scheduling model is developed in this study, where task effort uncertainty is represented using asymmetric triangular interval type-2 fuzzy numbers. A PGHHA is designed to solve the model. The algorithm applies an Actor-Critic reinforcement learning structure as the high-level strategy to adaptively select LLHs according to the evolutionary state. A prioritized experience replay mechanism is incorporated to enhance learning efficiency and accelerate convergence. Tests on synthetic and real cases show that: (1) The proposed algorithm delivers stronger convergence and diversity under uncertainty than six representative algorithms; (2) The combination of global search operators and local mining strategies maintains a suitable balance between exploration and exploitation. (3) The use of type-2 fuzzy representation offers a more stable characterization of effort uncertainty than type-1 fuzzy numbers. The current work focuses on a single-project context. Future work will extend the model to multi-project environments with shared resources and inter-project dependencies. Additional research will examine adaptive reward strategies and lightweight network designs to reduce computational demand while preserving solution quality.