In this paper, we model a multi-mode time–cost–quality trade-off project scheduling problem under generalized precedence relations using mixed-integer mathematical programming. Several solution procedures, including the classical epsilon-constraint, the efficient epsilon-constraint method, dynamic self-adaptive multi-objective particle swarm optimization (DSAMOPSO), and the multi-start partial bound enumeration algorithm, are provided to solve the proposed model. Several test problems are simulated and solved with the four methods and the performance of the methods are compared according to a set of accuracy and diversity comparison metrics. Additional analyses and tests are performed on the generated Pareto fronts of the solution procedures. Computational experiments are conducted to determine the validity and the efficiency of the DSAMOPSO method. The results show that this method outperforms the other three methods. We also carry out a sensitivity analysis of the DSAMOPSO algorithm to study the effects of parameter changes on the CPU time.