Project managers always try to do their best to conduct their projects as fast as they can. Additionally, not only do they try to reduce the required financial resources, but also they aim to reach the highest possible quality. As a result, time, costs, and quality are three important parameters which need to be considered not only in the process of decision-making but also in the process of conducting a project. For a general contractor, who conducts a significant part of a project by subcontracting, a proper selection of sub-contractors which simultaneously optimizes time, cost, and quality is a great challenge. In this paper, a new model is presented for solving sub-contractor selection problem considering time, cost, and quality aspects. Also, two metaheuristic approaches, namely non-dominated sorting genetic algorithm version III (NSGA-III), and a multi-objective imperialist competitive algorithm (MOICA) are presented for solving the proposed model. Since the effect of different parameters on the performance of the algorithm is significant, the Taguchi method with a novel response value is used to adjust the parameters of the proposed algorithms. Four performance metrics are used to evaluate the outcomes of these algorithms. A comparative study is done to compare the performance of the proposed methods with NSGA-II. The findings demonstrate that the proposed MOICA provides a wide range of options for project manager, while proposed NSGA III improves the quality of solutions in construction projects. When the project is facing many constraints, having more options helps to make more appropriate decisions. The quality of the solutions becomes more important if the project constraints are less. The current study provides an applicable tool for project manager for selection of sub-contractors considering time, cost, and quality aspects. This research also assists general contractor to propose a suitable price in tender stage. As a lack of efficient tool selecting the sub-contractors considering project constraints, this study is one of the first research studies that proposed a tool in order to select sub-contractors so that the project constraints are met.