PurposeFor successful management of construction projects, a precise analysis of the balance between time and cost is imperative to attain the most effective results. The aim of this study is to present an innovative approach tailored to tackle the challenges posed by time-cost trade-off (TCTO) problems. This objective is achieved through the integration of the multi-verse optimizer (MVO) with opposition-based learning (OBL), thereby introducing a groundbreaking methodology in the field.Design/methodology/approachThe paper aims to develop a new hybrid meta-heuristic algorithm. This is achieved by integrating the MVO with OBL, thereby forming the iMVO algorithm. The integration enhances the optimization capabilities of the algorithm, notably in terms of exploration and exploitation. Consequently, this results in expedited convergence and yields more accurate solutions. The efficacy of the iMVO algorithm will be evaluated through its application to four different TCTO problems. These problems vary in scale – small, medium and large – and include real-life case studies that possess complex relationships.FindingsThe efficacy of the proposed methodology is evaluated by examining TCTO problems, encompassing 18, 29, 69 and 290 activities, respectively. Results indicate that the iMVO provides competitive solutions for TCTO problems in construction projects. It is observed that the algorithm surpasses previous algorithms in terms of both mean deviation percentage (MD) and average running time (ART).Originality/valueThis research represents a significant advancement in the field of meta-heuristic algorithms, particularly in their application to managing TCTO in construction projects. It is noteworthy for being among the few studies that integrate the MVO with OBL for the management of TCTO in construction projects characterized by complex relationships.