A robust counterpart model and matheuristic-oriented evolutionary algorithm for evaluating energy consumption of project scheduling with uncertainty

Makespan is a key metric for evaluating project progress, while energy consumption directly impacts green performance metrics. These are the key metrics that managers focus on. Based on this, an energy-aware multi-mode resource-constrained project scheduling problem is proposed. However, activity durations in real project scheduling are often uncertain. Energy consumption and makespan cannot be accurately evaluated due to uncertain activity durations. In response to this, a multi-objective mixed-integer linear programming (MILP) model is proposed to trade off makespan and total energy consumption with uncertainty. Then, the uncertainty level and reliability level are introduced to quantify uncertain activity durations. Finally, the MILP model is transformed into a robust counterpart model to obtain robust non-dominated solutions for small-scale instances. Additionally, a matheuristic-oriented multi-objective evolutionary algorithm is designed to address large-scale instances. Finally, extensive numerical experiments are conducted to validate the proposed model and algorithm. The experimental results demonstrate that the robust counterpart model can quickly obtain a set of robust non-dominated solutions for small-scale instances. The matheuristic local optimization approach can indeed rapidly improve the quality of robust non-dominated solutions. Furthermore, the matheuristic-oriented multi-objective evolutionary algorithm outperforms state-of-the-art algorithms in terms of several multi-objective evaluation indicators.