This paper deals with two resource-constrained project scheduling problems with due dates in the activities, the TardinessRCPSP and the DeadlineRCPSP. In the TardinessRCPSP the objective is total tardiness minimisation, whereas the DeadlineRCPSP tries to minimise the project length while fulfilling the due date for each activity. In the first part of the paper, an algorithm called hybrid genetic algorithm with transmitted justification (HGATJ) is developed for both problems. This algorithm is based on an algorithm for the classical Resource Constrained Project Scheduling Problem (RCPSP), but uses an extra gene in the codification to control the use of a key technique called justification. Computational results show that the new approach outperforms the heuristics proposed for these problems in a recent paper. The second part of this article adapts the HGATJ to (heuristically) solve the multi-objective problem combination of the TardinessRCPSP and the DeadlineRCPSP. A path-relinking phase is introduced in the algorithm to produce a better Pareto front.