Improved genetic algorithm for multimode resource-constrained project scheduling considering carbon emission allowances

Under increasingly stringent climate policies, it is essential to account for carbon emissions in project scheduling. In this study, we examine a multimode resource-constrained project scheduling problem in which alternative activity modes differ in resource consumption and carbon intensity under renewable-resource constraints, a project-level carbon quota, and a carbon trading price. The objective is to minimize the total cost, which is defined as the sum of the activity execution cost and the net cost of buying and selling emission allowances. We formulate a cost-minimization model that incorporates a cap-and-trade mechanism and derive several analytical properties to identify infeasible activity-mode selections and reveal how changes in activity modes affect the total project cost. Guided by these properties, we develop a hybrid genetic algorithm with feasibility filtering and cost-oriented mode adjustments during population initialization and evolution. Tests on benchmark instances show that, compared with the best competing method, the proposed algorithm reduces the average relative deviation by 89% with only a moderate increase in computation time. Sensitivity analysis further indicates that relaxing the project-deadline coefficient and renewable-resource strength can jointly reduce the total cost by approximately 4%; within the tested range of carbon-quota factors, increasing the quota can reduce the total cost by up to approximately 5%, and increasing the carbon-price factor from 1.0 to 1.4 increases the total cost by approximately 24%, highlighting the strong impact of carbon pricing on project economics.