Comparative performance of the NSGA-II and MOPSO algorithms and simulations for evaluating time–cost–quality–risk trade-off in multi-modal PERT networks.

Nowadays, attention to the goals of cost, quality, time, and risk is essential in every project. In this regard, the beneficiaries of each project seek to reduce the cost, time, and risk and increase the quality of the project simultaneously. As cost, risk, time, and quality are critical factors in project management, this study primarily focused on examining the trade-offs among these criteria to determine how increased costs and decreased risks can lead to reduced project implementation time and improved quality. To this end, in this research, a mathematical programming approach and metaheuristic algorithms have been suggested for PERT networks. The model is developed through a simulation process, and then the values of decision and response variables are obtained in each implementation. Finally, an artificial neural network model is designed, and several sample problems are generated on small, medium, and large scales to solve the model. This study has several contributions, including the development of a mathematical programming model for PERT networks that considers the cost–risk–time–quality trade-off. Additionally, an artificial neural network model is proposed for solving problems of various sizes. At the same time, NSGA-II and MOPSO algorithms are utilized to handle NP-hard problems in the mathematical programming of PERT networks. Furthermore, the model considers multi-dimensional activities, with cost, quality, risk, and time as the four objective functions in the PERT network. Finally, AHP–TOPSIS methods are used to evaluate the effectiveness of NSGA-II and MOPSO algorithms. The findings illustrated that the NSGA-II algorithm performed better than the MOPSO algorithm in all three designed problems. The proposed model became practical and closer to reality than the previous models by eliminating unrealistic assumptions. [ABSTRACT FROM AUTHOR]