Reduction of carbon emissions and project makespan by a Pareto-based estimation of distribution algorithm

Due to the increasing concerns about global warming, low-carbon production has been a hot topic around the world. In this paper, carbon emissions reduction and project makespan minimization are considered simultaneously. To formulate the problem, a multi-objective multi-mode resource-constrained project scheduling model with makespan and carbon emissions criteria is given. To solve the problem, a Pareto-based estimation of distribution algorithm (PBEDA) is proposed. Specifically, an activity-mode list is used to encode the individual of the population; a hybrid probability model is built to describe the probability distribution of the solution space; and two Pareto archives are adopted to store the explored non-dominated solutions and the solutions for updating the probability model, respectively. New individuals are generated in the promising search areas by sampling and updating the hybrid probability model. Besides, Taguchi method of design of experiments is adopted to study the effect of parameter setting. Finally, numerical results and the comparisons to other algorithms are provided to show the effectiveness of the PBEDA in terms of quantity and quality of the obtained solutions. The Pareto set derived by the PBEDA can be helpful for project manager to recognize the relationship between carbon emissions and makespan so as to properly trade-off the two criteria according to certain preference.