A Multi-Objective Imperialist Competitive Algorithm for solving discrete time, cost and quality trade-off problems with mode-identity and resource-constrained situations.

The Discrete Time–Cost–Quality Trade-off Problem (DTCQTP) is one of the most important problems in project scheduling applications. In DTCQTP an optimal combination of construction methods is decided with the objective of minimizing cost and time while maximizing quality. Due to real world resource-constrained situations in projects, this model is expanded to mode-identity resource-constrained DTCQTP model. In this model, each activity has multiple modes to be performed. In each mode, the required resources for performing the activity are different in at least one type. In addition, each activity can be done either in a normal way or in a crashing way in each performing mode. Based on the mode-identity situation, the activities belonging to the same subset should be executed in the same mode. In this paper, we present a Multi-Objective Imperialist Competitive Algorithm (MOICA) to solve our proposed model. We explain the elements of the algorithm and solve some problems generated for this model – including large size and small size instances – by this algorithm. The performance of our proposed algorithm is evaluated by comparison with four well-known algorithms: NSGAII; PESAII-clustering; PESAII-grid based; and SPEA2. The obtained results show the effectiveness of the proposed algorithm.