Modeling and solving method for multi-task engineering project scheduling considering nonlinear time-varying constraints

To address the common challenges of dynamic resource fluctuations, uncertain task durations, and time-varying costs in practical engineering projects, this paper proposes a multi-task engineering project scheduling model considering nonlinear time-varying constraints and develops a hybrid intelligent optimization algorithm (IMHA) that integrates genetic algorithm, simulated annealing, particle swarm optimization, adaptive local search, and reinforcement-learning-assisted parameter adjustment. The proposed model incorporates multi-objective function formulation, resource/time/risk constraint modeling, nonlinear time-varying functions, and fuzzy uncertainty handling. To provide a more rigorous evaluation, the experimental comparison is extended from classical metaheuristics, including GA, PSO, and SA, to more advanced optimization methods, including NSGA-II, MOEA/D, adaptive large neighborhood search, and a dynamic RCPSP-oriented rolling-horizon heuristic. Using 35 test cases of varying scales and industry backgrounds, the experimental results show that IMHA is significantly better than GA, PSO, and SA in terms of project completion time, resource utilization, and algorithm stability, with an average reduction of about 11.5% in project duration and a 9.6% improvement in resource utilization. In addition, in the large-scale scheduling problem of 200 tasks, the running time is controlled within 15.6 min, demonstrating strong scheduling efficiency and robustness.